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<?xml version="1.0" encoding="utf-8"?>
<search>
<entry>
<title>实习纪要-2023/4/2</title>
<link href="/2023/04/02/work/work001/"/>
<url>/2023/04/02/work/work001/</url>
<content type="html"><![CDATA[<h1 id="实习工作内容记录"><a href="#实习工作内容记录" class="headerlink" title="实习工作内容记录"></a>实习工作内容记录</h1><h2 id="工作事件"><a href="#工作事件" class="headerlink" title="工作事件"></a>工作事件</h2><ol><li>重构设备拆装-考试插件数据库</li><li>IDFS-可视化巡检对接RTDS实时数据</li><li>重构设备拆装(APMS)->脚本工具服务(STS)-文件模块&步骤模块</li><li>独山子-大检修：文件预览&检修进度报表&首页驾驶舱接口开发</li><li>物料统计App迁移至后端成立单独服务，管网寻阀等待定</li></ol><h2 id="技术文档"><a href="#技术文档" class="headerlink" title="技术文档"></a>技术文档</h2><p>待补充</p><h2 id="下一步工作重点"><a href="#下一步工作重点" class="headerlink" title="下一步工作重点"></a>下一步工作重点</h2><ol><li>前端学习，掌握CSS调样式，JS、Vue框架、elementUI框架等公司前端基本框架</li><li>多构思提升系统服务性能方面的猜想，细节到代码</li><li>继续研究Spring框架源码，利用主流框架特点构建更完善的程序</li><li>写代码时多点细心，对基础Stream语法，Java设计模式代码对研究一点</li></ol><p>– 通用研发部-Java开发工程师 张文卓</p>]]></content>
</entry>
<entry>
<title>LeetCode刷题篇(21)-下一个排列</title>
<link href="/2022/10/03/leetcode/LeetCode(21)/"/>
<url>/2022/10/03/leetcode/LeetCode(21)/</url>
<content type="html"><![CDATA[<h1 id="下一个排列"><a href="#下一个排列" class="headerlink" title="下一个排列"></a>下一个排列</h1><p><a href="https://leetcode.cn/problems/next-permutation/">题目链接</a></p><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><blockquote><p>找出给定排列的下一个排列，也就下一个比当前字典序大的序列</p></blockquote><p>示例：</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">输入：nums = [1,2,3]</span><br><span class="line">输出：[1,3,2]</span><br></pre></td></tr></table></figure><h2 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h2><p>这个题目非常经典，也是面试经常考察的一道题<br>主要思想如下：</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line">例如当前序列为 1，4，2，5，3</span><br><span class="line"></span><br><span class="line">第一步：</span><br><span class="line">从右往左找出第一个非递增的数，当前序列中第一个是2</span><br><span class="line">因为从右往左依次是3->5->2，到了2就变小了；</span><br><span class="line"></span><br><span class="line">第二步：</span><br><span class="line">还是从右往左寻找第一个大于上面的2的第一个数；</span><br><span class="line">找到后首先是将两个数的下标对应的数进行交换，然后反转第一个下标的后面所有的数，这样就可以保证后面的数的最小的可能。</span><br></pre></td></tr></table></figure><h2 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h2><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">nextPermutation</span><span class="params">(<span class="keyword">int</span>[] nums)</span> </span>{</span><br><span class="line"> <span class="keyword">int</span> left = nums.length - <span class="number">2</span>;</span><br><span class="line"> <span class="comment">//以14253为例</span></span><br><span class="line"> <span class="comment">//找到第一个非递增的下标，即2所在的下标即是我们要找的下标，2则是较小数</span></span><br><span class="line"> <span class="keyword">while</span>(left >= <span class="number">0</span> && nums[left] >= nums[left + <span class="number">1</span>]){</span><br><span class="line"> left--;</span><br><span class="line"> }</span><br><span class="line"> <span class="comment">//找到left右边从最后一个数往前数第一个大于nums[left]的数就是第一个较大数</span></span><br><span class="line"> <span class="keyword">if</span>(left >= <span class="number">0</span>){</span><br><span class="line"> <span class="keyword">int</span> right = nums.length - <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">while</span>(right >= <span class="number">0</span> && nums[right] <= nums[left]){</span><br><span class="line"> right--;</span><br><span class="line"> }</span><br><span class="line"> <span class="comment">//找完两个数后可以交换两个数</span></span><br><span class="line"> swap(left,right,nums);</span><br><span class="line"> }</span><br><span class="line"> <span class="comment">//最后就是交换完后，第一次找的下标往后所有数需要反转，保证后半序列最小</span></span><br><span class="line"> reverse(left+<span class="number">1</span>,nums.length - <span class="number">1</span>,nums);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">swap</span><span class="params">(<span class="keyword">int</span> left,<span class="keyword">int</span> right,<span class="keyword">int</span>[] nums)</span></span>{</span><br><span class="line"> nums[left] = nums[left] ^ nums[right];</span><br><span class="line"> nums[right] = nums[left] ^ nums[right];</span><br><span class="line"> nums[left] = nums[left] ^ nums[right];</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">reverse</span><span class="params">(<span class="keyword">int</span> left,<span class="keyword">int</span> right,<span class="keyword">int</span>[] nums)</span></span>{</span><br><span class="line"> <span class="keyword">while</span>(left < right){</span><br><span class="line"> swap(left,right,nums);</span><br><span class="line"> left++;</span><br><span class="line"> right--;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 双指针 </tag>
</tags>
</entry>
<entry>
<title>2022秋招面试-张文卓</title>
<link href="/2022/08/30/%E9%9D%A2%E8%AF%95/"/>
<url>/2022/08/30/%E9%9D%A2%E8%AF%95/</url>
<content type="html"><![CDATA[<h1 id="面试"><a href="#面试" class="headerlink" title="面试"></a>面试</h1><h2 id="MetaApp一面"><a href="#MetaApp一面" class="headerlink" title="MetaApp一面"></a>MetaApp一面</h2><ul><li>Java数据类型</li></ul><p><img src="/%E9%9D%A2%E8%AF%95.assets/image-20220805083629864.png" alt="image-20220805083629864"></p><hr><p><img src="https://uploadfiles.nowcoder.com/images/20180713/3807435_1531450430478_A1E3D6CDC367DED01B519240FF9FA63F" alt="Java八大数据类型初始化值"></p><ul><li>final和finally的区别</li></ul><ul><li>阻断finally运行的方式</li></ul><ol><li>程序所在线程死亡</li><li>关闭CPU</li><li>System.exit(0)（手动关闭）</li></ol><ul><li>静态方法能不能被覆盖</li></ul><p>Java中静态方法<strong>可以被继承</strong>，但是不能被覆盖，即<strong>不能重写</strong>。</p><ul><li>构造器能不能被重写</li></ul><p>构造器不能被继承，因此不能被重写，但可以被重载。</p><ul><li>创建对象的方法？</li></ul><ul><li>序列化和反序列化的区别以及应用场景</li><li>tcp/ip属于哪一层</li><li>值传递和引用传递的区别？java是哪一种？</li><li>Java中有哪些锁？</li></ul><p><a href="https://blog.csdn.net/mazadazhangjia/article/details/124454234">Java中的锁有哪些？</a></p><p><a href="https://blog.csdn.net/weixin_60272582/article/details/123265596">java中的各种锁总结(简单全面版)</a></p><ul><li><p>线程池？</p></li><li><p>Spring源码？</p></li><li><p>Spring的IOC、AOP实现。AOP底层代理（jdk、cglib）</p></li><li><p>SpringMVC的组件了解吗？</p></li><li><p>Springbean作用域？注入一个bean的注解有哪些？</p></li><li><p>Spring中用到设计模式了吗？你了解的设计模式有哪些？</p></li><li><p>AOP多切面场景</p></li><li><p>Spring事务</p></li><li><p>Redis在项目中怎么使用？项目上线没？</p></li><li><p>Redis除了做缓存还能做什么？</p></li><li><p>Redis数据类型</p></li><li><p>Redis中String类型在项目中主要怎么用？能具体点吗？</p></li><li><p>场景：Redis怎么做一个排行榜？</p></li><li><p>Redis的bitmap</p></li><li><p>Redis做缓存和做过期时间两种都用过吗？怎么用的？</p></li><li><p>MySQL索引底层</p></li><li><p>聚簇索引和非聚簇索引</p></li><li><p>#{}和${}区别</p></li><li><p>Mybatis中xml配置文件中通常有哪些标签？</p></li></ul><p><a href="https://mybatis.net.cn/dynamic-sql.html">Mybatis动态SQL</a></p><ul><li>Mybatis中可以用枚举类型吗？</li><li>ArrayList底层？扩容机制？线程安全？</li><li>ArrayList和LinkedList区别？增删有何区别？ArrayList初始容量</li><li>HashMap底层？线程安全？</li><li>HashMap的put过程？1.7和1.8区别？</li></ul><blockquote><ol><li><p>通过key计算哈希算法与运算得出数组下标</p></li><li><p>如果数组下标元素为空，则将key和value封装为Entry对象（JDK1.7是Entry对象，JDK1.8是Node对象）并放入该位置。</p></li><li><p>下标位置不为空时：</p></li></ol><ul><li><p>jdk1.7：</p><ul><li>扩容：先扩容再将Entry对象插到链表</li><li>不需要扩容：头插法添加到链表中去</li></ul></li><li><p>jdk1.8：</p><p>首先判断当前node类型：</p><ul><li>红黑树node</li></ul><p>遍历红黑树，寻找相同的key，并覆盖，没有则</p><ul><li>链表node</li></ul><p>尾插法插入到链表的最后位置去，因为是尾插法，所以需要遍历链表，在遍历链表的过程中会判断是否存在当前的key，如果存在则更新value，插入到链表后，会看当前链表的节点个数，如果大于等于8，那么则会将该链表转成红黑树。</p></li></ul></blockquote><p><a href="https://blog.csdn.net/ajie_gt/article/details/123420816">HashMap源码（JDK1.8）深度分析-红黑树（插入）</a></p><ul><li>算法题：选一个自己会的算法写出来就行。（二分查找）</li></ul><h2 id="摩西科技一面"><a href="#摩西科技一面" class="headerlink" title="摩西科技一面"></a>摩西科技一面</h2><p>1.Kafka你怎么使用的？</p><blockquote><p>待整理</p></blockquote><p>2.Kafka丢失了消息该怎么办？</p><p>解决方案：</p><blockquote><p>保证消息不丢失需要三方的配合：生产者，broker，消费者</p><ol><li><p>生产者需要处理好broker的响应，无论同步还是异步都需要做好try catch的处理响应，如果返回写入失败则需要重新发送。当多次发送失败则需要进行报警处理，日志记录等操作。</p></li><li><p>Broker需要控制响应的时机，单机是消息刷盘后响应，集群多副本需要两个及两个以上的情况再返回响应。</p></li><li><p>消费者需要在执行完真正的逻辑之后再返回响应给Broker</p></li></ol><p>但是消息可靠性增强了性能就会下降，消息刷盘，集群副本复制等很消耗性能，所以一般日志传输的话丢个一两条问题不大。</p></blockquote><p>3.HashMap & Hashtable区别</p><p><img src="/%E9%9D%A2%E8%AF%95.assets/image-20220825143826972.png" alt="image-20220825143826972"></p><p>4.Redis你怎么使用的？（熟悉项目）</p><p>5.HashMap 1.7&1.8 HashMap 扩容机制</p><ul><li>HashMap jdk1.7与jdk1.8区别：</li></ul><p><img src="/%E9%9D%A2%E8%AF%95.assets/image-20220830083404633.png" alt="image-20220830083404633"></p><p><img src="/%E9%9D%A2%E8%AF%95.assets/image-20220830083422754.png" alt="image-20220830083422754"></p><p><a href="https://blog.csdn.net/qq_39480875/article/details/123423138">博客链接</a></p><ul><li>HashMap 扩容机制</li></ul><p><img src="/%E9%9D%A2%E8%AF%95.assets/format,png.png" alt="HashMap扩容"></p><p>6.ConcurrentHashMap 1.7&1.8</p><p><a href="https://blog.csdn.net/Mind_programmonkey/article/details/111035733">ConcurrentHashMap1.7和1.8详解对比</a></p><p><a href="https://javaguide.cn/java/collection/concurrent-hash-map-source-code.html#_1-concurrenthashmap-1-7">ConcurrentHashMap源码&底层数据结构</a></p><p>7.HashMap & ConcurrentHashMap</p><p><a href="https://www.php.cn/java/base/469764.html">HashMap & ConcurrentHashMap区别</a></p><p>8.ArrayLisy 1.7 & 1.8</p><blockquote><p>jdk1.7及以前版本中</p><p>ArrayList初始容量是10，当添加到11个元素时会扩容至原来的1.5倍，再将原来的数据赋值到新的数组中。</p><p>jdk1.8以后</p><p>ArrayList初始容量为0，当添加第一个元素的时候会初始化10个单位的容量，然后扩容也是在满的时候扩容至1.5倍。</p><p>优点：延迟数组的创建，节省内存。</p></blockquote><p>9.HashMap为什么引入红黑树，引入之后链表有什么用处？</p><p><a href="https://blog.csdn.net/weixin_44688973/article/details/125703073">HashMap为什么用链表加红黑树</a></p><p>10.ArrayList & LinkedList区别、底层</p><p><a href="https://javaguide.cn/java/collection/arraylist-source-code.html#arraylist-%E4%B8%8E-linkedlist-%E5%8C%BA%E5%88%AB">ArrayList & LinkedList区别</a></p><p>11.如果你的服务器内存不够，只能使用redis，MySQL，如何利用两个工具再去实现整个系统？</p><blockquote><p>查询十万条帖子，采用redis的hash+zset配合实现查询实现es，list实现kafka，</p></blockquote><p>12.Mybatis是半自动ORM还是全自动ORM，为什么？</p><blockquote><p>Mybatis在查询关联对象或关联集合对象时，需要手动编写sql来完成，所以，称之为半自动ORM映射工具。</p></blockquote><p>13.Mybatis中动态SQL的执行过程是如何的？</p><p><a href="https://blog.csdn.net/Pastxu/article/details/124338417">MyBatis的SQL执行流程</a></p><p>14.SQL题：userid，score（分数），time（耗时）<br>查找耗时最短，分数最高的用户</p><figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">select</span> userid,score,<span class="type">time</span></span><br><span class="line"><span class="keyword">from</span> <span class="keyword">user</span></span><br><span class="line"><span class="keyword">group</span> <span class="keyword">by</span> userid</span><br><span class="line"><span class="keyword">order</span> <span class="keyword">by</span> score <span class="keyword">desc</span>,<span class="type">time</span> <span class="keyword">asc</span></span><br><span class="line">limit <span class="number">1</span>;</span><br></pre></td></tr></table></figure><h2 id="杭州产链数字科技一面"><a href="#杭州产链数字科技一面" class="headerlink" title="杭州产链数字科技一面"></a>杭州产链数字科技一面</h2><ol><li><p>事务四个特性</p></li><li><p>@AutoWired和@Resource的区别</p><ol><li><p>Autowired是Spring提供的，Resource是JavaEE提供的</p></li><li><p>Autowired默认只采用的是类型注入</p></li><li><p>Resource默认采用的是名称注入</p><p><img src="/%E9%9D%A2%E8%AF%95.assets/image-20220904164719792.png" alt="image-20220904164719792"></p></li></ol></li><li><p>Spring中如何解决bean的循环依赖的？</p><p>Spring的三级缓存</p><p><a href="https://www.cnblogs.com/dw3306/p/15995834.html">Spring 如何解决循环依赖</a></p><p><a href="https://blog.csdn.net/java13992394428/article/details/124455127">Spring是如何解决循环依赖的？</a></p></li><li><p>Git的合并分支有哪些？</p></li><li><p>线程池的实现原理？</p></li><li><p>Redis的缓存击穿、缓存穿透了解过没？</p></li></ol><h2 id="乐刻运动Java"><a href="#乐刻运动Java" class="headerlink" title="乐刻运动Java"></a>乐刻运动Java</h2><h3 id="一面面经牛客可搜"><a href="#一面面经牛客可搜" class="headerlink" title="一面面经牛客可搜"></a>一面面经牛客可搜</h3><h3 id="二面崩盘"><a href="#二面崩盘" class="headerlink" title="二面崩盘"></a>二面崩盘</h3><h2 id="互时科技Java"><a href="#互时科技Java" class="headerlink" title="互时科技Java"></a>互时科技Java</h2>]]></content>
</entry>
<entry>
<title>LeetCode刷题篇(20)-二叉树最大宽度</title>
<link href="/2022/08/27/leetcode/LeetCode(20)/"/>
<url>/2022/08/27/leetcode/LeetCode(20)/</url>
<content type="html"><![CDATA[<h1 id="二叉树最大宽度"><a href="#二叉树最大宽度" class="headerlink" title="二叉树最大宽度"></a>二叉树最大宽度</h1><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><blockquote><p>给你一棵二叉树的根节点 root ，返回树的 最大宽度 。<br>树的 最大宽度 是所有层中最大的 宽度 。</p></blockquote><blockquote><p>每一层的 宽度 被定义为该层最左和最右的非空节点>（即，两个端点）之间的长度。将这个二叉树视作与满二叉>树结构相同，两端点间会出现一些延伸到这一层的 null >节点，这些 null 节点也计入长度。</p></blockquote><blockquote><p>题目数据保证答案将会在 32 位 带符号整数范围内。</p></blockquote><p>示例：</p><p><img src="https://assets.leetcode.com/uploads/2021/05/03/width1-tree.jpg" alt="示例"></p><blockquote><p>输入：root = [1,3,2,5,3,null,9]</p></blockquote><blockquote><p>输出：4</p></blockquote><blockquote><p>解释：最大宽度出现在树的第 3 层，宽度为 4 (5,3,null,9) 。</p></blockquote><h2 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h2><p>这道题是队列+规律</p><p>主要是首先采用队列层级遍历，其次找出当前节点的下一次索引下标<br>例如当前索引为<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="5.663ex" height="1.595ex" role="img" focusable="false" viewBox="0 -694 2503 705"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(345,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(945,0)"><path data-c="1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></g><g data-mml-node="mi" transform="translate(1465,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mi" transform="translate(1931,0)"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g></g></g></svg></mjx-container>，则当前节点的左节点下标应为$2<em>index<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.452ex;" xmlns="http://www.w3.org/2000/svg" width="15.837ex" height="2.149ex" role="img" focusable="false" viewBox="0 -750 7000 950"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><text data-variant="italic" transform="scale(1,-1)" font-size="884px" font-family="serif" font-style="italic">，</text></g><g data-mml-node="mi" transform="translate(1000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">右</text></g><g data-mml-node="mi" transform="translate(2000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">节</text></g><g data-mml-node="mi" transform="translate(3000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">点</text></g><g data-mml-node="mi" transform="translate(4000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">下</text></g><g data-mml-node="mi" transform="translate(5000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">标</text></g><g data-mml-node="mi" transform="translate(6000,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">为</text></g></g></g></svg></mjx-container>2</em>index+1$,那么这道题就好做了。<br>直接看代码！</p><h2 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h2><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment"> * Definition for a binary tree node.</span></span><br><span class="line"><span class="comment"> * public class TreeNode {</span></span><br><span class="line"><span class="comment"> * int val;</span></span><br><span class="line"><span class="comment"> * TreeNode left;</span></span><br><span class="line"><span class="comment"> * TreeNode right;</span></span><br><span class="line"><span class="comment"> * TreeNode() {}</span></span><br><span class="line"><span class="comment"> * TreeNode(int val) { this.val = val; }</span></span><br><span class="line"><span class="comment"> * TreeNode(int val, TreeNode left, TreeNode right) {</span></span><br><span class="line"><span class="comment"> * this.val = val;</span></span><br><span class="line"><span class="comment"> * this.left = left;</span></span><br><span class="line"><span class="comment"> * this.right = right;</span></span><br><span class="line"><span class="comment"> * }</span></span><br><span class="line"><span class="comment"> * }</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">widthOfBinaryTree</span><span class="params">(TreeNode root)</span> </span>{</span><br><span class="line"> Queue<TreeNode> queue = <span class="keyword">new</span> LinkedList<>();</span><br><span class="line"> LinkedList<Integer> list = <span class="keyword">new</span> LinkedList<>();</span><br><span class="line"> queue.offer(root);</span><br><span class="line"> list.add(<span class="number">1</span>);</span><br><span class="line"> <span class="keyword">int</span> size = <span class="number">1</span>,maxSize = <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">while</span>(!queue.isEmpty()){</span><br><span class="line"> size--;</span><br><span class="line"> TreeNode node = queue.poll();</span><br><span class="line"> <span class="keyword">int</span> index = list.removeFirst();</span><br><span class="line"> <span class="keyword">if</span>(node.left != <span class="keyword">null</span>){</span><br><span class="line"> queue.offer(node.left);</span><br><span class="line"> list.add(<span class="number">2</span> * index);<span class="comment">//左节点存在才计算下标</span></span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(node.right != <span class="keyword">null</span>){</span><br><span class="line"> queue.offer(node.right);</span><br><span class="line"> list.add(<span class="number">2</span> * index + <span class="number">1</span>);<span class="comment">//右节点存在才计算下标</span></span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(size == <span class="number">0</span>){</span><br><span class="line"> <span class="keyword">if</span>(list.size() >= <span class="number">2</span>){<span class="comment">//超过两个节点才计算宽度，一个节点默认为1</span></span><br><span class="line"> maxSize = Math.max(maxSize,list.getLast() - list.getFirst() + <span class="number">1</span>);</span><br><span class="line"> }</span><br><span class="line"> size = queue.size();</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> maxSize;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 队列 </tag>
<tag> 二叉树 </tag>
</tags>
</entry>
<entry>
<title>创邻科技-Java校招</title>
<link href="/2022/08/27/%E7%A7%8B%E6%8B%9B%E7%AC%94%E7%BB%8F/test02/"/>
<url>/2022/08/27/%E7%A7%8B%E6%8B%9B%E7%AC%94%E7%BB%8F/test02/</url>
<content type="html"><![CDATA[<h1 id="创邻科技-Java校招"><a href="#创邻科技-Java校招" class="headerlink" title="创邻科技-Java校招"></a>创邻科技-Java校招</h1><blockquote><p>这道题目不是难，主要是涉及到Java多线程操作，故有一定难度</p></blockquote><h1 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h1><p>输入m和n</p><p>n个线程交替输出m个数，从1开始1、2…m。且每个线程轮流输出一个数的循环操作。</p><h1 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h1><p><code>Semaphore</code>也是一个线程同步的辅助类,类似与操作系统中的信号量,可以维护当前访问自身的线程个数，并提供了同步机制。使用Semaphore可以控制同时访问资源的线程个数，例如，实现一个文件允许的并发访问数。</p><h1 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h1><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> java.util.*;</span><br><span class="line"><span class="keyword">import</span> java.util.concurrent.Semaphore;</span><br><span class="line"></span><br><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">Main</span> </span>{</span><br><span class="line"> <span class="keyword">private</span> <span class="keyword">static</span> Queue<Integer> queue = <span class="keyword">new</span> LinkedList<>();</span><br><span class="line"> <span class="keyword">private</span> <span class="keyword">static</span> List<Semaphore> list = <span class="keyword">new</span> ArrayList<>();</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">main</span><span class="params">(String[] args)</span> </span>{</span><br><span class="line"> Scanner sc = <span class="keyword">new</span> Scanner(System.in);</span><br><span class="line"> <span class="keyword">int</span> m = sc.nextInt();</span><br><span class="line"> <span class="keyword">int</span> n = sc.nextInt();</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i<=m;i++){</span><br><span class="line"> queue.offer(i);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<n;i++){</span><br><span class="line"> <span class="keyword">if</span>(i == <span class="number">0</span>) list.add(<span class="keyword">new</span> Semaphore(<span class="number">1</span>));<span class="comment">//信号量为1</span></span><br><span class="line"> <span class="keyword">else</span> list.add(<span class="keyword">new</span> Semaphore(<span class="number">0</span>));</span><br><span class="line"> <span class="keyword">new</span> Thread(<span class="keyword">new</span> MyRunnable(i)).start();<span class="comment">//并发处理</span></span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">static</span> <span class="class"><span class="keyword">class</span> <span class="title">MyRunnable</span> <span class="keyword">implements</span> <span class="title">Runnable</span></span>{</span><br><span class="line"> <span class="keyword">private</span> <span class="keyword">int</span> index = <span class="number">0</span>;</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="title">MyRunnable</span><span class="params">(<span class="keyword">int</span> i)</span></span>{</span><br><span class="line"> <span class="keyword">this</span>.index = i;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="function"><span class="keyword">private</span> Semaphore <span class="title">getNext</span><span class="params">()</span> </span>{<span class="comment">//取出下一个元素</span></span><br><span class="line"> <span class="keyword">if</span>(index == list.size() -<span class="number">1</span>) <span class="keyword">return</span> list.get(<span class="number">0</span>);</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">return</span> list.get(index + <span class="number">1</span>);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="meta">@Override</span></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">run</span><span class="params">()</span> </span>{</span><br><span class="line"> <span class="keyword">while</span>(!queue.isEmpty()){</span><br><span class="line"> <span class="keyword">try</span> {</span><br><span class="line"> list.get(index).acquire();<span class="comment">//获取一个公共资源，公共资源-1，如果公共资源<0阻塞等待</span></span><br><span class="line"> } <span class="keyword">catch</span> (InterruptedException e) {</span><br><span class="line"> <span class="keyword">throw</span> <span class="keyword">new</span> RuntimeException(e);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(queue.size() != <span class="number">0</span>){</span><br><span class="line"> System.out.println(queue.poll() + <span class="string">" "</span> + Thread.currentThread().getName());</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">this</span>.getNext().release();<span class="comment">//释放一个公共资源，公共资源+1</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<tags>
<tag> Java </tag>
<tag> 笔试 </tag>
</tags>
</entry>
<entry>
<title>NIO蔚来-Java后端</title>
<link href="/2022/08/23/%E7%A7%8B%E6%8B%9B%E7%AC%94%E7%BB%8F/test01/"/>
<url>/2022/08/23/%E7%A7%8B%E6%8B%9B%E7%AC%94%E7%BB%8F/test01/</url>
<content type="html"><![CDATA[<h1 id="NIO蔚来Java后端笔试（2022-8-22）"><a href="#NIO蔚来Java后端笔试（2022-8-22）" class="headerlink" title="NIO蔚来Java后端笔试（2022/8/22）"></a>NIO蔚来Java后端笔试（2022/8/22）</h1><h1 id="第一题"><a href="#第一题" class="headerlink" title="第一题"></a>第一题</h1><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><p>输入一个<code>n</code>，寻找一个数<code>i</code>使得<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="19.584ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 8656 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(567.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(1567.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2445.2,0)"><g data-mml-node="text"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="text" transform="translate(778,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g></g><g data-mml-node="mi" transform="translate(4279,0)"><path data-c="1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 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transform="translate(7067,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mo" transform="translate(7533,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(7922,0)"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(8267,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container>，输出一共有多少个<code>i</code>满足条件。</p><h2 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h2><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> java.util.*;</span><br><span class="line"></span><br><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">Main</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">main</span><span class="params">(String[] args)</span> </span>{</span><br><span class="line"> Scanner sc = <span class="keyword">new</span> Scanner(System.in);</span><br><span class="line"> <span class="keyword">long</span> n = sc.nextLong();</span><br><span class="line"> <span class="keyword">long</span> ans = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">if</span>(n >= <span class="number">6432746723</span>){</span><br><span class="line"> System.out.println(ans);</span><br><span class="line"> }<span class="keyword">else</span>{</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">long</span> i=<span class="number">0</span>;i<n;i++){</span><br><span class="line"> <span class="keyword">if</span>(i + n == reverse(i)){</span><br><span class="line"> ans++;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> System.out.println(ans);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">long</span> <span class="title">reverse</span><span class="params">(<span class="keyword">long</span> x)</span></span>{</span><br><span class="line"> <span class="keyword">long</span> sum=<span class="number">0</span>;</span><br><span class="line"> <span class="keyword">if</span>(x % <span class="number">10</span> == <span class="number">0</span>) <span class="keyword">return</span> sum;</span><br><span class="line"> <span class="keyword">while</span>(x!=<span class="number">0</span>){</span><br><span class="line"> sum = sum*<span class="number">10</span> + x%<span class="number">10</span>;</span><br><span class="line"> x = x/<span class="number">10</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> sum;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h1 id="第二题"><a href="#第二题" class="headerlink" title="第二题"></a>第二题</h1><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> java.util.*;</span><br><span class="line"></span><br><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">Main</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">main</span><span class="params">(String[] args)</span> </span>{</span><br><span class="line"> Scanner sc = <span class="keyword">new</span> Scanner(System.in);</span><br><span class="line"> <span class="keyword">int</span> N = sc.nextInt();</span><br><span class="line"> <span class="keyword">int</span>[] arr = <span class="keyword">new</span> <span class="keyword">int</span>[N];</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<N;i++){</span><br><span class="line"> arr[i] = sc.nextInt();</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">int</span> res = <span class="number">0</span>,t = <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<N;i++){</span><br><span class="line"> <span class="keyword">if</span>(arr[i] >= t) res += arr[i] - t;</span><br><span class="line"> t = arr[i];</span><br><span class="line"> }</span><br><span class="line"> System.out.println(res + <span class="number">1</span>);</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h1 id="第三题"><a href="#第三题" class="headerlink" title="第三题"></a>第三题</h1><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> java.util.*;</span><br><span class="line"></span><br><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">Main</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">main</span><span class="params">(String[] args)</span> </span>{</span><br><span class="line"> Scanner sc = <span class="keyword">new</span> Scanner(System.in);</span><br><span class="line"></span><br><span class="line"> String s = sc.nextLine();</span><br><span class="line"> <span class="keyword">int</span> p =sc.nextInt();</span><br><span class="line"> String[] arr1 = s.split(<span class="string">" "</span>);</span><br><span class="line"> <span class="keyword">int</span>[] arr = <span class="keyword">new</span> <span class="keyword">int</span>[arr1.length];</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<arr1.length;i++){</span><br><span class="line"> arr[i] = Integer.parseInt(arr1[i]);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">int</span> maxl = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<arr.length-<span class="number">1</span>;i++){</span><br><span class="line"> maxl = Math.max(maxl,arr[i]);</span><br><span class="line"> }</span><br><span class="line"> System.out.print(<span class="string">"["</span>);</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<arr.length;i++){</span><br><span class="line"> <span class="keyword">if</span>(i != arr.length-<span class="number">1</span>){</span><br><span class="line"> <span class="keyword">if</span>(arr[i] + p >= maxl){</span><br><span class="line"> System.out.print(<span class="string">"True, "</span>);</span><br><span class="line"> }<span class="keyword">else</span> System.out.print(<span class="string">"False, "</span>);</span><br><span class="line"> }<span class="keyword">else</span>{</span><br><span class="line"> <span class="keyword">if</span>(arr[i] + p >= maxl){</span><br><span class="line"> System.out.print(<span class="string">"True"</span>);</span><br><span class="line"> }<span class="keyword">else</span> System.out.print(<span class="string">"False"</span>);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> System.out.print(<span class="string">"]"</span>);</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<tags>
<tag> Java </tag>
<tag> 笔试 </tag>
</tags>
</entry>
<entry>
<title>LeetCode刷题篇(19)-二叉树的右视图</title>
<link href="/2022/08/20/leetcode/LeetCode(19)/"/>
<url>/2022/08/20/leetcode/LeetCode(19)/</url>
<content type="html"><![CDATA[<h1 id="二叉树的右视图"><a href="#二叉树的右视图" class="headerlink" title="二叉树的右视图"></a>二叉树的右视图</h1><blockquote><p>字节跳动飞书后端一面算法题</p></blockquote><hr><p><a href="https://leetcode.cn/problems/WNC0Lk/">题目链接</a></p><hr><h1 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h1><p>给定一个二叉树的 根节点<code>root</code>，想象自己站在它的右侧，按照从顶部到底部的顺序，返回从右侧所能看到的节点值。</p><p><img src="https://assets.leetcode.com/uploads/2021/02/14/tree.jpg" alt="示例"></p><h1 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h1><p>这道题第一次见是在飞书后端一面上遇到，第一眼就知道这是层序遍历可以解出，但是奈何自己的Java中队列数据结构使用不熟悉导致一直出不来结果。</p><p>本题主要解题思路是层序遍历，每一层遍历完了后，最后一个节点进行保存，最后输出即可。</p><ul><li>Queue<e> queue = new LinkedList<e>();<ul><li>offer()：队列尾部添加元素</li><li>poll()：检索并删除队列头部第一个元素</li><li>peek()：检索但不删除头部第一个元素</li><li>contains(Object o)：检测队列是否包含此元素</li></ul></e></e></li></ul><h1 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h1><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment"> * Definition for a binary tree node.</span></span><br><span class="line"><span class="comment"> * public class TreeNode {</span></span><br><span class="line"><span class="comment"> * int val;</span></span><br><span class="line"><span class="comment"> * TreeNode left;</span></span><br><span class="line"><span class="comment"> * TreeNode right;</span></span><br><span class="line"><span class="comment"> * TreeNode() {}</span></span><br><span class="line"><span class="comment"> * TreeNode(int val) { this.val = val; }</span></span><br><span class="line"><span class="comment"> * TreeNode(int val, TreeNode left, TreeNode right) {</span></span><br><span class="line"><span class="comment"> * this.val = val;</span></span><br><span class="line"><span class="comment"> * this.left = left;</span></span><br><span class="line"><span class="comment"> * this.right = right;</span></span><br><span class="line"><span class="comment"> * }</span></span><br><span class="line"><span class="comment"> * }</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> List<Integer> <span class="title">rightSideView</span><span class="params">(TreeNode root)</span> </span>{</span><br><span class="line"> List<Integer> list = <span class="keyword">new</span> ArrayList<>();</span><br><span class="line"> <span class="keyword">if</span>(root == <span class="keyword">null</span>) <span class="keyword">return</span> list;</span><br><span class="line"> Queue<TreeNode> queue = <span class="keyword">new</span> LinkedList<>();</span><br><span class="line"> queue.offer(root);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span>(!queue.isEmpty()){</span><br><span class="line"> <span class="keyword">int</span> size = queue.size();</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<size;i++){</span><br><span class="line"> TreeNode node = queue.poll();</span><br><span class="line"> <span class="keyword">if</span>(node.left != <span class="keyword">null</span>) queue.offer(node.left);</span><br><span class="line"> <span class="keyword">if</span>(node.right != <span class="keyword">null</span>) queue.offer(node.right);</span><br><span class="line"> <span class="keyword">if</span>(i == size - <span class="number">1</span>) list.add(node.val); </span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> list;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 队列 </tag>
<tag> 二叉树 </tag>
</tags>
</entry>
<entry>
<title>LeetCode刷题篇(18)-最大二叉树</title>
<link href="/2022/08/20/leetcode/LeetCode(18)/"/>
<url>/2022/08/20/leetcode/LeetCode(18)/</url>
<content type="html"><![CDATA[<h1 id="最大二叉树"><a href="#最大二叉树" class="headerlink" title="最大二叉树"></a>最大二叉树</h1><blockquote><p>2022/8/20-每日一题</p></blockquote><hr><p><a href="https://leetcode.cn/problems/maximum-binary-tree/">题目链接</a></p><hr><h1 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h1><p>给定一个不重复的整数数组<code>nums</code>。 最大二叉树 可以用下面的算法从<code>nums</code>递归地构建:</p><blockquote><p>创建一个根节点，其值为<code>nums</code>中的最大值。<br>递归地在最大值<strong>左边</strong>的子数组前缀上构建左子树。<br>递归地在最大值<strong>右边</strong>的子数组后缀上构建右子树。</p></blockquote><p>返回 nums 构建的<strong>最大二叉树</strong></p><h1 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h1><p>题目本身就是不断在区间找最大值然后分叉，题目本身要求不高，所以检索最大值只需要暴力找就行。标准做法是dfs（深搜）。</p><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line">TreeNode root = <span class="keyword">new</span> TreeNode(nums[mid]);<span class="comment">//mid是当前区间最大值下标</span></span><br><span class="line">root.left = maxTree(nums,left,mid-<span class="number">1</span>);<span class="comment">//深搜左边区域</span></span><br><span class="line">root.right = maxTree(nums,mid+<span class="number">1</span>,right);<span class="comment">//深搜右边区域</span></span><br></pre></td></tr></table></figure><h1 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h1><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment"> * Definition for a binary tree node.</span></span><br><span class="line"><span class="comment"> * public class TreeNode {</span></span><br><span class="line"><span class="comment"> * int val;</span></span><br><span class="line"><span class="comment"> * TreeNode left;</span></span><br><span class="line"><span class="comment"> * TreeNode right;</span></span><br><span class="line"><span class="comment"> * TreeNode() {}</span></span><br><span class="line"><span class="comment"> * TreeNode(int val) { this.val = val; }</span></span><br><span class="line"><span class="comment"> * TreeNode(int val, TreeNode left, TreeNode right) {</span></span><br><span class="line"><span class="comment"> * this.val = val;</span></span><br><span class="line"><span class="comment"> * this.left = left;</span></span><br><span class="line"><span class="comment"> * this.right = right;</span></span><br><span class="line"><span class="comment"> * }</span></span><br><span class="line"><span class="comment"> * }</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> TreeNode <span class="title">constructMaximumBinaryTree</span><span class="params">(<span class="keyword">int</span>[] nums)</span> </span>{</span><br><span class="line"> <span class="keyword">return</span> maxTree(nums,<span class="number">0</span>,nums.length-<span class="number">1</span>);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//建树</span></span><br><span class="line"> <span class="function"><span class="keyword">public</span> TreeNode <span class="title">maxTree</span><span class="params">(<span class="keyword">int</span>[] nums,<span class="keyword">int</span> left,<span class="keyword">int</span> right)</span></span>{</span><br><span class="line"> <span class="keyword">if</span>(left > right) <span class="keyword">return</span> <span class="keyword">null</span>;</span><br><span class="line"> <span class="keyword">int</span> mid = findMax(nums,left,right);</span><br><span class="line"> TreeNode root = <span class="keyword">new</span> TreeNode(nums[mid]);</span><br><span class="line"> root.left = maxTree(nums,left,mid-<span class="number">1</span>);</span><br><span class="line"> root.right = maxTree(nums,mid+<span class="number">1</span>,right);</span><br><span class="line"> <span class="keyword">return</span> root;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//检索区间最大值下标</span></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">findMax</span><span class="params">(<span class="keyword">int</span>[] nums,<span class="keyword">int</span> left,<span class="keyword">int</span> right)</span></span>{</span><br><span class="line"> <span class="keyword">int</span> max = Integer.MIN_VALUE,index = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=left;i<=right;i++){</span><br><span class="line"> <span class="keyword">if</span>(nums[i] > max){</span><br><span class="line"> max = nums[i];</span><br><span class="line"> index = i;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> index;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 深度优先搜索 </tag>
</tags>
</entry>
<entry>
<title>LeetCode刷题篇(17)-4.寻找两个正序数组的中位数</title>
<link href="/2022/08/06/leetcode/LeetCode(17)/"/>
<url>/2022/08/06/leetcode/LeetCode(17)/</url>
<content type="html"><![CDATA[<h1 id="寻找两个正序数组的中位数"><a href="#寻找两个正序数组的中位数" class="headerlink" title="寻找两个正序数组的中位数"></a>寻找两个正序数组的中位数</h1><hr><h2 id="题目链接"><a href="#题目链接" class="headerlink" title="题目链接"></a><a href="https://leetcode.cn/problems/median-of-two-sorted-arrays/">题目链接</a></h2><hr><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><p>给定两个大小分别为<code>m</code>和<code>n</code>的正序（从小到大）数组<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="6.83ex" height="1.532ex" role="img" focusable="false" viewBox="0 -666 3019 677"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(600,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1172,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(2050,0)"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g><g data-mml-node="mn" transform="translate(2519,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g></g></g></svg></mjx-container>和<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="6.83ex" height="1.532ex" role="img" focusable="false" viewBox="0 -666 3019 677"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(600,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1172,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(2050,0)"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g><g data-mml-node="mn" transform="translate(2519,0)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g></g></svg></mjx-container>请你找出并返回这两个正序数组的中位数。</p><p>算法的时间复杂度应该为<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="14.207ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 6279.4 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1152,0)"><path data-c="1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path></g><g data-mml-node="mi" transform="translate(1450,0)"><path data-c="1D45C" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"></path></g><g data-mml-node="mi" transform="translate(1935,0)"><path data-c="1D454" d="M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z"></path></g><g data-mml-node="mo" transform="translate(2412,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2801,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3901.2,0)"><path data-c="2B" d="M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z"></path></g><g data-mml-node="mi" transform="translate(4901.4,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5501.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5890.4,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container>.</p><p>样例：</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line">输入：nums1 = [1,3], nums2 = [2]</span><br><span class="line">输出：2.00000</span><br><span class="line">解释：合并数组 = [1,2,3] ，中位数 2</span><br></pre></td></tr></table></figure><h2 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h2><blockquote><p>主要利用的是一种划分数组的思想</p></blockquote><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"> left_part | right_part</span><br><span class="line">A[0], A[1], ..., A[i-1] | A[i], A[i+1], ..., A[m-1]</span><br><span class="line">B[0], B[1], ..., B[j-1] | B[j], B[j+1], ..., B[n-1]</span><br></pre></td></tr></table></figure><p>A、B都是正序数组，故<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="7.784ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3440.4 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D434" d="M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z"></path></g><g data-mml-node="mo" transform="translate(750,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mi" transform="translate(1028,0)"><path data-c="1D457" d="M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z"></path></g><g data-mml-node="mo" transform="translate(1662.2,0)"><path data-c="2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path></g><g data-mml-node="mn" transform="translate(2662.4,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g><g data-mml-node="mo" transform="translate(3162.4,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container>是A数组中left_part最大的，<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="3.887ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1718 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D434" d="M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z"></path></g><g data-mml-node="mo" transform="translate(750,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mi" transform="translate(1028,0)"><path data-c="1D457" d="M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z"></path></g><g data-mml-node="mo" transform="translate(1440,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container>是A数组中right_part最小的。</p><p>同理B数组一样,故我们只需要将数组划分为数量相同（如果两数组长度之和为奇数则只需要左边多一个即可）的两部分，且左边最大值小于等于右边最小值，然后就可以找出中位数。</p><p>看代码即可</p><h2 id="代码实现"><a href="#代码实现" class="headerlink" title="代码实现"></a>代码实现</h2><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">double</span> <span class="title">findMedianSortedArrays</span><span class="params">(<span class="keyword">int</span>[] nums1, <span class="keyword">int</span>[] nums2)</span> </span>{</span><br><span class="line"> <span class="keyword">if</span>(nums1.length > nums2.length){<span class="comment">//使第一个数组长度始终小于等于第二个数组</span></span><br><span class="line"> <span class="keyword">int</span>[] tmp = nums1;</span><br><span class="line"> nums1 = nums2;</span><br><span class="line"> nums2 = tmp;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">int</span> m = nums1.length;</span><br><span class="line"> <span class="keyword">int</span> n = nums2.length;</span><br><span class="line"> <span class="keyword">int</span> totalLeft = (m + n + <span class="number">1</span>)/<span class="number">2</span>;</span><br><span class="line"></span><br><span class="line"> <span class="keyword">int</span> left = <span class="number">0</span>,right = m;</span><br><span class="line"> <span class="keyword">while</span>(left < right){</span><br><span class="line"> <span class="keyword">int</span> i = left + (right - left + <span class="number">1</span>)/<span class="number">2</span>;</span><br><span class="line"> <span class="keyword">int</span> j = totalLeft - i;</span><br><span class="line"> <span class="keyword">if</span>(nums1[i-<span class="number">1</span>] > nums2[j]){<span class="comment">//上分割线左边最后一个值始终小于下分割线右边第一个值</span></span><br><span class="line"> right = i - <span class="number">1</span>;<span class="comment">//变更分割线</span></span><br><span class="line"> }<span class="keyword">else</span>{</span><br><span class="line"> left = i;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">int</span> i = left;</span><br><span class="line"> <span class="keyword">int</span> j = totalLeft - i;</span><br><span class="line"> <span class="keyword">int</span> nums1LeftMax = i == <span class="number">0</span> ? Integer.MIN_VALUE : nums1[i-<span class="number">1</span>];<span class="comment">//上分割线左边最后一个值</span></span><br><span class="line"> <span class="keyword">int</span> nums1RightMin = i == m ? Integer.MAX_VALUE : nums1[i];<span class="comment">//上分割线右边第一个值</span></span><br><span class="line"> <span class="keyword">int</span> nums2LeftMax = j == <span class="number">0</span> ? Integer.MIN_VALUE : nums2[j-<span class="number">1</span>];<span class="comment">//下分割线左边最后一个值</span></span><br><span class="line"> <span class="keyword">int</span> nums2RightMin = j == n ? Integer.MAX_VALUE : nums2[j];<span class="comment">//下分割线右边第一个值</span></span><br><span class="line"></span><br><span class="line"> <span class="keyword">if</span>((m + n) % <span class="number">2</span> == <span class="number">1</span>){<span class="comment">//两数组长度之和为奇数</span></span><br><span class="line"> <span class="keyword">return</span> Math.max(nums1LeftMax,nums2LeftMax);</span><br><span class="line"> }<span class="keyword">else</span>{</span><br><span class="line"> <span class="keyword">return</span> (<span class="keyword">double</span>) ((Math.max(nums1LeftMax,nums2LeftMax) + Math.min(nums1RightMin,nums2RightMin))) / <span class="number">2</span>;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 分治 </tag>
</tags>
</entry>
<entry>
<title>LeetCode刷题篇(16)-189.轮转数组</title>
<link href="/2022/07/28/leetcode/LeetCode(16)/"/>
<url>/2022/07/28/leetcode/LeetCode(16)/</url>
<content type="html"><![CDATA[<h1 id="轮转数组"><a href="#轮转数组" class="headerlink" title="轮转数组"></a>轮转数组</h1><hr><h2 id="题目链接"><a href="#题目链接" class="headerlink" title="题目链接"></a><a href="https://leetcode.cn/problems/rotate-array/">题目链接</a></h2><hr><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><p>给你一个数组，将数组中的元素向右轮转<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.179ex" height="1.595ex" role="img" focusable="false" viewBox="0 -694 521 705"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></g></g></g></svg></mjx-container>个位置，其中<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.179ex" height="1.595ex" role="img" focusable="false" viewBox="0 -694 521 705"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></g></g></g></svg></mjx-container>是非负数。</p><h2 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h2><p><mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="4.844ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2141 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1152,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1752,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container>时间，<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="4.618ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2041 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(1152,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g><g data-mml-node="mo" transform="translate(1652,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container>空间的做法很多<br>目前只掌握一种</p><blockquote><p>要想循环，且右移循环<code>k</code>位，需要对前<code>n-k</code>位进行<code>reverse</code>，后<code>k</code>位进行<code>reverse</code>，最后整体<code>reverse</code>就行<br>这个方法属于一种比较奇特的思路，且应该是本题的最优解</p></blockquote><h2 id="代码实现"><a href="#代码实现" class="headerlink" title="代码实现"></a>代码实现</h2><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">rotate</span><span class="params">(<span class="keyword">int</span>[] nums, <span class="keyword">int</span> k)</span> </span>{</span><br><span class="line"> k = k % nums.length;</span><br><span class="line"> reverse(nums,<span class="number">0</span>,nums.length-k-<span class="number">1</span>);</span><br><span class="line"> reverse(nums,nums.length-k,nums.length-<span class="number">1</span>);</span><br><span class="line"> reverse(nums,<span class="number">0</span>,nums.length-<span class="number">1</span>);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">reverse</span><span class="params">(<span class="keyword">int</span>[] nums,<span class="keyword">int</span> left,<span class="keyword">int</span> right)</span></span>{</span><br><span class="line"> <span class="keyword">while</span>(left < right){</span><br><span class="line"> swap(nums,left,right);</span><br><span class="line"> left++;</span><br><span class="line"> right--;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">swap</span><span class="params">(<span class="keyword">int</span>[] nums,<span class="keyword">int</span> i,<span class="keyword">int</span> j)</span></span>{<span class="comment">//异或就可以解决交换</span></span><br><span class="line"> <span class="keyword">if</span>(i == j) <span class="keyword">return</span>;</span><br><span class="line"> nums[i] = nums[i] ^ nums[j];</span><br><span class="line"> nums[j] = nums[i] ^ nums[j];</span><br><span class="line"> nums[i] = nums[i] ^ nums[j];</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
</tags>
</entry>
<entry>
<title>基数排序</title>
<link href="/2022/07/28/sort/sort(9)/"/>
<url>/2022/07/28/sort/sort(9)/</url>
<content type="html"><![CDATA[<h1 id="基数排序"><a href="#基数排序" class="headerlink" title="基数排序"></a>基数排序</h1><blockquote><p>首先先看一个动图：</p></blockquote><p><img src="/img/radix_sort.gif" alt="基数排序"></p><p>待更</p><h2 id="代码实现"><a href="#代码实现" class="headerlink" title="代码实现"></a>代码实现</h2><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">Main</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">main</span><span class="params">(String[] args)</span> </span>{</span><br><span class="line"> <span class="keyword">int</span>[] arr = <span class="keyword">new</span> <span class="keyword">int</span> []{<span class="number">6</span>,<span class="number">2</span>,<span class="number">9</span>,<span class="number">7</span>,<span class="number">4</span>,<span class="number">10</span>,<span class="number">5</span>,<span class="number">8</span>,<span class="number">3</span>,<span class="number">1</span>};</span><br><span class="line"> <span class="keyword">int</span> max = Math.abs(arr[<span class="number">0</span>]);</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i<arr.length;i++){</span><br><span class="line"> max = Math.max(max,Math.abs(arr[i]));<span class="comment">//求最大值</span></span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">int</span> maxDigitLen = <span class="number">0</span>,base = <span class="number">10</span>;<span class="comment">//maxDigitLen表示最大位数，base表示基数(进制)</span></span><br><span class="line"> <span class="keyword">while</span>(max != <span class="number">0</span>){</span><br><span class="line"> maxDigitLen++;</span><br><span class="line"> max /= base;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">int</span>[] sortedArr = <span class="keyword">new</span> <span class="keyword">int</span>[arr.length];</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<maxDigitLen;i++){</span><br><span class="line"> <span class="keyword">int</span>[] countArr = <span class="keyword">new</span> <span class="keyword">int</span>[<span class="number">19</span>];<span class="comment">//将-9~9的数字分别存储在countArr[0]~countArr[18]中</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j=<span class="number">0</span>;j<arr.length;j++){</span><br><span class="line"> <span class="keyword">int</span> bucketIdx = (arr[j] % base) / (base / <span class="number">10</span>) + <span class="number">9</span>;<span class="comment">//+9:考虑负数</span></span><br><span class="line"> countArr[bucketIdx]++;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j = <span class="number">1</span>;j< countArr.length;j++){</span><br><span class="line"> countArr[j] += countArr[j-<span class="number">1</span>];</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j = arr.length - <span class="number">1</span>;j>=<span class="number">0</span>;j--){</span><br><span class="line"> <span class="keyword">int</span> thisBase = (arr[j] % base) / (base / <span class="number">10</span>) + <span class="number">9</span>;<span class="comment">//+9:考虑负数</span></span><br><span class="line"> sortedArr[countArr[thisBase] - <span class="number">1</span>] = arr[j];</span><br><span class="line"> countArr[thisBase]--;</span><br><span class="line"> }</span><br><span class="line"> arr = Arrays.copyOf(sortedArr,sortedArr.length);</span><br><span class="line"> base *= <span class="number">10</span>;</span><br><span class="line"> }</span><br><span class="line"> System.out.println(Arrays.toString(arr));</span><br><span class="line"> <span class="comment">//[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]</span></span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> 排序算法 </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 基数排序 </tag>
</tags>
</entry>
<entry>
<title>Redis知识点</title>
<link href="/2022/07/26/%E9%A1%B9%E7%9B%AE/redis(2)/"/>
<url>/2022/07/26/%E9%A1%B9%E7%9B%AE/redis(2)/</url>
<content type="html"><![CDATA[<h1 id="概要"><a href="#概要" class="headerlink" title="概要"></a>概要</h1><blockquote><p>Redis知识点肯定繁多，需要每日看上一小时<br>当然我可能记的不全，如若访客看出错误或者补充，评论即可，或者联系我！</p></blockquote><h1 id="Redis数据类型"><a href="#Redis数据类型" class="headerlink" title="Redis数据类型"></a>Redis数据类型</h1><ul><li>string</li></ul><p>string结构底层是一个简单<code>动态字符串</code>，支持扩容。存储<code>字符串、数字和二进制数据</code>,除了值可以是String以外,所有的键也可以是string,string最大可以存储大小为<code>2M</code>的数据。</p><ul><li>list（有序可重复）</li></ul><p>list存储<code>线性有序且可重复</code>的元素，底层数据结构可以是双向链表/压缩列表。可以当作简单的<code>消息队列</code>使用,一个list最多可以存储2^32-1个元素</p><ul><li>set（不可重复）</li></ul><p>set存储<code>不可重复</code>的元素，一般用于求交集、差集等，底层数据结构可以是hash和整数数组。一个set最多可以存储2^32-1个元素</p><ul><li>zset（有序不可重复）</li></ul><p>zset存储的是<code>有序不可重复</code>的元素，zset为每个元素添加了一个score属性作为排序依据，底层数据结构可以是ziplist和跳表。zset数据类型中成员是唯一不可重复的，但评分不是。</p><ul><li>hash（存键值对）</li></ul><p>hash类型存储的是键值对，底层数据结构是ziplist和hash。</p><h1 id="主从复制"><a href="#主从复制" class="headerlink" title="主从复制"></a>主从复制</h1><h1 id="哨兵模式"><a href="#哨兵模式" class="headerlink" title="哨兵模式"></a>哨兵模式</h1><h1 id="缓存"><a href="#缓存" class="headerlink" title="缓存"></a>缓存</h1><h2 id="缓存穿透"><a href="#缓存穿透" class="headerlink" title="缓存穿透"></a>缓存穿透</h2><h2 id="缓存击穿"><a href="#缓存击穿" class="headerlink" title="缓存击穿"></a>缓存击穿</h2><h2 id="缓存雪崩"><a href="#缓存雪崩" class="headerlink" title="缓存雪崩"></a>缓存雪崩</h2><h1 id="分布式锁"><a href="#分布式锁" class="headerlink" title="分布式锁"></a>分布式锁</h1><h1 id="持久化策略"><a href="#持久化策略" class="headerlink" title="持久化策略"></a>持久化策略</h1>]]></content>
<categories>
<category> 项目开发 </category>
</categories>
<tags>
<tag> 待更新 </tag>
<tag> Java </tag>
<tag> Springboot </tag>
<tag> Redis </tag>
</tags>
</entry>
<entry>
<title>MySQL&LeetCode刷题篇(2)</title>
<link href="/2022/07/26/SQL/mysql_05/"/>
<url>/2022/07/26/SQL/mysql_05/</url>
<content type="html"><![CDATA[<h1 id="按日期分组销售产品"><a href="#按日期分组销售产品" class="headerlink" title="按日期分组销售产品"></a>按日期分组销售产品</h1><h2 id="题目链接"><a href="#题目链接" class="headerlink" title="题目链接"></a><a href="https://leetcode.cn/problems/group-sold-products-by-the-date/">题目链接</a></h2><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><p>编写一个 SQL 查询来查找每个日期、销售的不同产品的数量及其名称。<br>每个日期的销售产品名称应按词典序排列。<br>返回按<code>sell_date</code>排序的结果表。<br>查询结果格式如下例所示。</p><blockquote><p>解释：<br>对于2020-05-30，出售的物品是 (Headphone, Basketball, T-shirt)，按词典序排列，并用逗号 ‘,’ 分隔。<br>对于2020-06-01，出售的物品是 (Pencil, Bible)，按词典序排列，并用逗号分隔。<br>对于2020-06-02，出售的物品是 (Mask)，只需返回该物品名。</p></blockquote><h2 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h2><p>第一次接触这个函数所以记录一下，词典序排列</p><ul><li><p><code>group_concat()</code></p><ul><li>如果只想用<code>,</code>相隔，则直接将相应的字段放入即可</li><li>如果想用<code>;</code>相隔，需要写成这种格式<code>group_concat(name separator ';')</code></li></ul></li></ul><h2 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h2><figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"># Write your MySQL query statement below</span><br><span class="line"><span class="keyword">select</span> sell_date, </span><br><span class="line"> <span class="built_in">count</span>(<span class="keyword">distinct</span> product) <span class="keyword">as</span> num_sold,</span><br><span class="line"> GROUP_CONCAT(<span class="keyword">distinct</span> product <span class="keyword">order</span> <span class="keyword">by</span> product <span class="keyword">asc</span>) <span class="keyword">as</span> products</span><br><span class="line"><span class="keyword">from</span> Activities</span><br><span class="line"><span class="keyword">group</span> <span class="keyword">by</span> sell_date</span><br><span class="line"><span class="keyword">order</span> <span class="keyword">by</span> sell_date <span class="keyword">asc</span>;</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> MySQL </category>
</categories>
<tags>
<tag> MySQL </tag>
<tag> LeetCode </tag>
</tags>
</entry>
<entry>
<title>LeetCode刷题篇(15)-剑指OfferII094.最少回文分割</title>
<link href="/2022/07/24/leetcode/LeetCode(15)/"/>
<url>/2022/07/24/leetcode/LeetCode(15)/</url>
<content type="html"><![CDATA[<h1 id="最少回文分割"><a href="#最少回文分割" class="headerlink" title="最少回文分割"></a>最少回文分割</h1><hr><h2 id="题目链接"><a href="#题目链接" class="headerlink" title="题目链接"></a><a href="https://leetcode.cn/problems/omKAoA/">题目链接</a></h2><hr><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><p>给定一个字符串<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.023ex;" xmlns="http://www.w3.org/2000/svg" width="1.061ex" height="1.023ex" role="img" focusable="false" viewBox="0 -442 469 452"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 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58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g></g></g></svg></mjx-container>分割成一些子串，使每个子串都是回文串。<br>返回符合要求的 最少分割次数 。</p><blockquote><p>输入：s = “aab”<br>输出：1</p></blockquote><h2 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h2><p>动态规划经典题<br><mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.543ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2892 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></g><g data-mml-node="mi" transform="translate(520,0)"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(1023,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mi" transform="translate(1301,0)"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1646,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g><g data-mml-node="mo" transform="translate(1924,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mi" transform="translate(2202,0)"><path data-c="1D457" d="M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z"></path></g><g data-mml-node="mo" transform="translate(2614,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container>是回文串需要满足两个条件</p><ul><li><mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="14.337ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 6336.9 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 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-125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z"></path></g><g data-mml-node="mo" transform="translate(4558.7,0)"><path data-c="2212" d="M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z"></path></g><g data-mml-node="mn" transform="translate(5558.9,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g><g data-mml-node="mo" transform="translate(6058.9,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container>是回文串</li><li><mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="11.128ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4918.6 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g><g data-mml-node="mo" transform="translate(469,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mi" transform="translate(747,0)"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1092,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g><g data-mml-node="mo" transform="translate(1647.8,0)"><g data-mml-node="text"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g 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-0.566ex;" xmlns="http://www.w3.org/2000/svg" width="33.406ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 14765.6 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D451" d="M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></g><g data-mml-node="mi" 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396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g><g data-mml-node="mo" transform="translate(13320.6,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mn" transform="translate(13598.6,0)"><path data-c="36" d="M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 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55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></g><g data-mml-node="mi" transform="translate(520,0)"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g><g data-mml-node="mo" transform="translate(1023,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mn" transform="translate(1301,0)"><path data-c="33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></g><g data-mml-node="mo" transform="translate(1801,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g><g data-mml-node="mo" transform="translate(2079,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mn" transform="translate(2357,0)"><path data-c="35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z"></path></g><g data-mml-node="mo" transform="translate(2857,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container>为false，所以就算是回文串也会被误判</p></blockquote><p>后面处理分割次数那就是贪心套路</p><h2 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h2><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">minCut</span><span class="params">(String s)</span> </span>{<span class="comment">//dp</span></span><br><span class="line"> <span class="keyword">int</span> n = s.length();</span><br><span class="line"> <span class="keyword">boolean</span>[][] dp = <span class="keyword">new</span> <span class="keyword">boolean</span>[n][n];</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<n;i++){</span><br><span class="line"> Arrays.fill(dp[i],<span class="keyword">true</span>);<span class="comment">//全部赋值为true</span></span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=n-<span class="number">1</span>;i>=<span class="number">0</span>;i--){<span class="comment">//从后往前处理</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j=i + <span class="number">1</span>;j<n;j++){</span><br><span class="line"> dp[i][j] = dp[i+<span class="number">1</span>][j-<span class="number">1</span>] && (s.charAt(i) == s.charAt(j));<span class="comment">//i -> j : i+1 -> j-1&&s[i]==s[j]</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">int</span>[] ans = <span class="keyword">new</span> <span class="keyword">int</span>[n];</span><br><span class="line"> Arrays.fill(ans,Integer.MAX_VALUE);</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<n;i++){</span><br><span class="line"> <span class="keyword">if</span>(dp[<span class="number">0</span>][i]) ans[i] = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">else</span>{</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j=<span class="number">0</span>;j<i;j++){</span><br><span class="line"> <span class="keyword">if</span>(dp[j+<span class="number">1</span>][i]) ans[i] = Math.min(ans[i],ans[j]+<span class="number">1</span>);<span class="comment">//0->i : 0->j + (j+1 -> i)</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> <span class="keyword">return</span> ans[n-<span class="number">1</span>]; </span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 动态规划 </tag>
</tags>
</entry>
<entry>
<title>LeetCode刷题篇(14)-剑指Offer59-I.滑动窗口的最大值</title>
<link href="/2022/07/24/leetcode/LeetCode(14)/"/>
<url>/2022/07/24/leetcode/LeetCode(14)/</url>
<content type="html"><![CDATA[<h1 id="滑动窗口最大值"><a href="#滑动窗口最大值" class="headerlink" title="滑动窗口最大值"></a>滑动窗口最大值</h1><hr><h2 id="题目链接"><a href="#题目链接" class="headerlink" title="题目链接"></a><a href="https://leetcode.cn/problems/hua-dong-chuang-kou-de-zui-da-zhi-lcof/">题目链接</a></h2><hr><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><p>给定一个数组 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="5.699ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 2519 453"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(600,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1172,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(2050,0)"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g></g></g></svg></mjx-container> 和滑动窗口的大小 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.179ex" height="1.595ex" role="img" focusable="false" viewBox="0 -694 521 705"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></g></g></g></svg></mjx-container>，请找出所有滑动窗口里的最大值</p><blockquote><p>输入: nums = [1,3,-1,-3,5,3,6,7], 和 k = 3<br>输出: [3,3,5,5,6,7] </p></blockquote><h2 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h2><p>今天看了题解才知道咋做这种题的，以为跟之前树状数组维护单调区间一样去做，可能用到线段树求极值？？不太懂。<br>这道题主要用到的是双端队列，既可以处理头部，又可以处理尾部<br>双端队列头部主要存放最大值，每次进来一个值之前先处理完队列尾部，最大值的下标放入头部（分析完毕）。</p><h2 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h2><blockquote><p>放代码之前先熟悉几个api</p></blockquote><ul><li><p><code>ArrayDeque</code>：双端队列</p><ul><li>peekLast()<blockquote><p>查看队列最后一个值，但不出队列。</p></blockquote></li><li>peekFirst()<blockquote><p>查看队列第一个值，但不会出队列</p></blockquote></li><li>pollFirst()<blockquote><p>删除队列第一个值</p></blockquote></li><li>pollLast()<blockquote><p>删除队列最后一个值</p></blockquote></li></ul></li></ul><p> 哈哈哈今天学到一个新东西，<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="10.242ex" height="2.084ex" role="img" focusable="false" viewBox="0 -716 4527 921"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D434" d="M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z"></path></g><g data-mml-node="mi" transform="translate(750,0)"><path data-c="1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1201,0)"><path data-c="1D45F" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1652,0)"><path data-c="1D44E" d="M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z"></path></g><g data-mml-node="mi" transform="translate(2181,0)"><path data-c="1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(2671,0)"><path data-c="1D43F" d="M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z"></path></g><g data-mml-node="mi" transform="translate(3352,0)"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(3697,0)"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g><g data-mml-node="mi" transform="translate(4166,0)"><path data-c="1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></g></g></g></svg></mjx-container>转<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="4.213ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1862 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(345,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(945,0)"><path data-c="1D461" d="M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z"></path></g><g data-mml-node="mo" transform="translate(1306,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mo" transform="translate(1584,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container>，利用JDK8 的<code>Intstream</code></p><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="keyword">public</span> <span class="keyword">int</span>[] maxSlidingWindow(<span class="keyword">int</span>[] nums, <span class="keyword">int</span> k) {</span><br><span class="line"> <span class="keyword">int</span> n = nums.length;</span><br><span class="line"> List<Integer> arr = <span class="keyword">new</span> ArrayList<Integer>();</span><br><span class="line"> <span class="keyword">if</span>(k <= n && k!=<span class="number">0</span>){</span><br><span class="line"> ArrayDeque<Integer> queue = <span class="keyword">new</span> ArrayDeque<Integer>();<span class="comment">//双端队列</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<k;i++){<span class="comment">//处理第一个窗口</span></span><br><span class="line"> <span class="keyword">while</span>(!queue.isEmpty() && nums[queue.peekLast()] < nums[i]){</span><br><span class="line"> queue.pollLast();</span><br><span class="line"> }</span><br><span class="line"> queue.add(i);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = k;i<n;i++){</span><br><span class="line"> arr.add(nums[queue.peekFirst()]);</span><br><span class="line"> <span class="keyword">while</span>(!queue.isEmpty() && queue.peekFirst() < i-k+<span class="number">1</span>){<span class="comment">//依次退出之前处理完的窗口值</span></span><br><span class="line"> queue.pollFirst();</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">while</span>(!queue.isEmpty() && nums[queue.peekLast()] < nums[i]){<span class="comment">//处理当前窗口</span></span><br><span class="line"> queue.pollLast();</span><br><span class="line"> }</span><br><span class="line"> queue.add(i);</span><br><span class="line"> }</span><br><span class="line"> arr.add(nums[queue.peekFirst()]);<span class="comment">//最后处理完的窗口加入</span></span><br><span class="line"> }</span><br><span class="line"> <span class="comment">// int[] a = new int[arr.size()];</span></span><br><span class="line"> <span class="comment">// for(int i=0;i<arr.size();i++){</span></span><br><span class="line"> <span class="comment">// a[i] = arr.get(i);</span></span><br><span class="line"> <span class="comment">// }</span></span><br><span class="line"> <span class="keyword">return</span> arr.stream().mapToInt(Integer::valueOf).toArray();</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 单调队列 </tag>
</tags>
</entry>
<entry>
<title>LeetCode刷题篇(13)-剑指OfferII 115.重建序列</title>
<link href="/2022/07/23/leetcode/LeetCode(13)/"/>
<url>/2022/07/23/leetcode/LeetCode(13)/</url>
<content type="html"><![CDATA[<h1 id="重建序列"><a href="#重建序列" class="headerlink" title="重建序列"></a>重建序列</h1><hr><h2 id="题目链接"><a href="#题目链接" class="headerlink" title="题目链接"></a><a href="https://leetcode.cn/problems/ur2n8P/">题目链接</a></h2><hr><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><p>给定一个长度为 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg></mjx-container> 的整数数组<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="5.699ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 2519 453"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(600,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1172,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(2050,0)"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g></g></g></svg></mjx-container> ，其中<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="5.699ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 2519 453"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(600,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1172,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(2050,0)"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g></g></g></svg></mjx-container> 是范围为<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.009ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2656 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mn" transform="translate(278,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g><g data-mml-node="mi" transform="translate(778,0)"><text data-variant="italic" transform="scale(1,-1)" font-size="884px" font-family="serif" font-style="italic">，</text></g><g data-mml-node="mi" transform="translate(1778,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(2378,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container>的整数的排列。还提供了一个 2D 整数数组 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.439ex;" xmlns="http://www.w3.org/2000/svg" width="9.957ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 4401 636"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g><g data-mml-node="mi" transform="translate(469,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mi" transform="translate(935,0)"><path data-c="1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></g><g data-mml-node="mi" transform="translate(1395,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1967,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mi" transform="translate(2433,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(3033,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mi" transform="translate(3466,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mi" transform="translate(3932,0)"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g></g></g></svg></mjx-container> ，其中 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="11.995ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 5302 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g><g data-mml-node="mi" transform="translate(469,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mi" transform="translate(935,0)"><path data-c="1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></g><g data-mml-node="mi" 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404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5024,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container> 是 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="5.699ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 2519 453"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(600,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1172,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 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21 287Z"></path></g><g data-mml-node="mi" transform="translate(2050,0)"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g></g></g></svg></mjx-container> 是否是唯一的最短 超序列 。最短 超序列 是 长度最短 的序列，并且所有序列<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="11.995ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 5302 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" 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120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g><g data-mml-node="mo" transform="translate(4401,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mi" transform="translate(4679,0)"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(5024,0)"><path data-c="5D" d="M22 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326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></g><g data-mml-node="mi" transform="translate(1395,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1967,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mi" transform="translate(2433,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(3033,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mi" transform="translate(3466,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mi" transform="translate(3932,0)"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g></g></g></svg></mjx-container>，可能存在多个有效的 超序列 。</p><blockquote><p>例如，对于 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="24.291ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 10736.6 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g><g data-mml-node="mi" transform="translate(469,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mi" transform="translate(935,0)"><path data-c="1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></g><g data-mml-node="mi" transform="translate(1395,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1967,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mi" transform="translate(2433,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(3033,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z"></path></g><g data-mml-node="mi" transform="translate(3466,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mi" transform="translate(3932,0)"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g><g data-mml-node="mo" transform="translate(4678.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(5734.6,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mo" transform="translate(6012.6,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mn" transform="translate(6290.6,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g><g data-mml-node="mo" transform="translate(6790.6,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mn" transform="translate(7235.2,0)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g><g data-mml-node="mo" transform="translate(7735.2,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g><g data-mml-node="mo" transform="translate(8013.2,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mo" transform="translate(8457.9,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mn" transform="translate(8735.9,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g><g data-mml-node="mo" transform="translate(9235.9,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mn" transform="translate(9680.6,0)"><path data-c="33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></g><g data-mml-node="mo" transform="translate(10180.6,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g><g data-mml-node="mo" transform="translate(10458.6,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container> ，有两个最短的 超序列 ，<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.664ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2945.3 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mn" transform="translate(278,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g><g data-mml-node="mo" transform="translate(778,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mn" transform="translate(1222.7,0)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g><g data-mml-node="mo" transform="translate(1722.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mn" transform="translate(2167.3,0)"><path data-c="33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></g><g data-mml-node="mo" transform="translate(2667.3,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container> 和 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.664ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2945.3 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mn" transform="translate(278,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g><g data-mml-node="mo" transform="translate(778,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mn" transform="translate(1222.7,0)"><path data-c="33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></g><g data-mml-node="mo" transform="translate(1722.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mn" transform="translate(2167.3,0)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g><g data-mml-node="mo" transform="translate(2667.3,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container> 。<br>而对于<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="31.961ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 14126.6 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g><g data-mml-node="mi" transform="translate(469,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mi" transform="translate(935,0)"><path data-c="1D45E" d="M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z"></path></g><g data-mml-node="mi" transform="translate(1395,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 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120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g><g data-mml-node="mo" transform="translate(4678.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mo" transform="translate(5734.6,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mo" transform="translate(6012.6,0)"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mn" transform="translate(6290.6,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 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transform="translate(13070.6,0)"><path data-c="33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></g><g data-mml-node="mo" transform="translate(13570.6,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g><g data-mml-node="mo" transform="translate(13848.6,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container>，唯一可能的最短 超序列 是 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="6.664ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2945.3 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mn" transform="translate(278,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g><g data-mml-node="mo" transform="translate(778,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 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17Z"></path></g><g data-mml-node="mn" transform="translate(2167.3,0)"><path data-c="33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></g><g data-mml-node="mo" transform="translate(2667.3,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container> 。<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="8.801ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3890 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><path data-c="5B" d="M118 -250V750H255V710H158V-210H255V-250H118Z"></path></g><g data-mml-node="mn" transform="translate(278,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g><g data-mml-node="mo" transform="translate(778,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mn" transform="translate(1222.7,0)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g><g data-mml-node="mo" transform="translate(1722.7,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mn" transform="translate(2167.3,0)"><path data-c="33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></g><g data-mml-node="mo" transform="translate(2667.3,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mn" transform="translate(3112,0)"><path data-c="34" d="M462 0Q444 3 333 3Q217 3 199 0H190V46H221Q241 46 248 46T265 48T279 53T286 61Q287 63 287 115V165H28V211L179 442Q332 674 334 675Q336 677 355 677H373L379 671V211H471V165H379V114Q379 73 379 66T385 54Q393 47 442 46H471V0H462ZM293 211V545L74 212L183 211H293Z"></path></g><g data-mml-node="mo" transform="translate(3612,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container> 是可能的超序列，但不是最短的。<br>如果<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="5.699ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 2519 453"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(600,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1172,0)"><path data-c="1D45A" d="M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(2050,0)"><path data-c="1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z"></path></g></g></g></svg></mjx-container>是序列的唯一最短 超序列 ，则返回 <code>true</code> ，否则返回<code>false</code>。<br>子序列 是一个可以通过从另一个序列中删除一些元素或不删除任何元素，而不改变其余元素的顺序的<code>序列</code>。</p></blockquote><hr><h2 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h2><p>这题开始做的时候一点思路都没有，之前了解过一点拓扑排序，拓扑排序中重要的是存放节点的入度，队列维护，在这个题目中同样是这样的。拓扑排序建立链表，队列存放下一数字的所有可能</p><ul><li>下一数字的数量大于一，表示当前不符合唯一性要求，返回<code>false</code></li><li>下一数字的数量等于一，继续遍历序列，知道队列为空。</li></ul><blockquote><p>例如<mjx-container 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26 290 98L298 109L352 326Z"></path></g><g data-mml-node="mi" transform="translate(1395,0)"><path data-c="1D462" d="M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1967,0)"><path data-c="1D452" d="M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z"></path></g><g data-mml-node="mi" transform="translate(2433,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(3033,0)"><path data-c="1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 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transform="translate(11681.2,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mn" transform="translate(12125.9,0)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g><g data-mml-node="mo" transform="translate(12625.9,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mn" transform="translate(13070.6,0)"><path data-c="33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></g><g data-mml-node="mo" transform="translate(13570.6,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g><g data-mml-node="mo" transform="translate(13848.6,0)"><path data-c="5D" d="M22 710V750H159V-250H22V-210H119V710H22Z"></path></g></g></g></svg></mjx-container><br>根据拓扑排序建立链表</p></blockquote><p>①1->2，当前1的入度为0，2的入度为1<br>②1->3，当前1的入度为0，3的入度为1<br>③2->3，当前2的入度为1，3的入度为2<br>将度为0的节点放入队列，循环遍历队列中元素的链表，并及时将入度为0的节点加入到队列。</p><hr><h2 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h2><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">boolean</span> <span class="title">sequenceReconstruction</span><span class="params">(<span class="keyword">int</span>[] nums, <span class="keyword">int</span>[][] sequences)</span> </span>{</span><br><span class="line"> <span class="keyword">int</span> n = nums.length;</span><br><span class="line"> <span class="keyword">int</span>[] inde = <span class="keyword">new</span> <span class="keyword">int</span>[n+<span class="number">1</span>];<span class="comment">//存放每个元素的入度</span></span><br><span class="line"> Set<Integer>[] graph = <span class="keyword">new</span> Set[n+<span class="number">1</span>];<span class="comment">//存放有向边关系</span></span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i<=n;i++){</span><br><span class="line"> graph[i] = <span class="keyword">new</span> HashSet<Integer>();</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span>[] sequence : sequences){</span><br><span class="line"> <span class="keyword">int</span> size = sequence.length;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i<size;i++){</span><br><span class="line"> <span class="keyword">int</span> prev = sequence[i-<span class="number">1</span>],next = sequence[i];<span class="comment">//有向边的起始和终点</span></span><br><span class="line"> <span class="keyword">if</span>(graph[prev].add(next)){</span><br><span class="line"> inde[next]++;<span class="comment">//能加入则该元素入度加一</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> Queue<Integer> queue = <span class="keyword">new</span> ArrayDeque<Integer>();</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i<=n;i++){</span><br><span class="line"> <span class="keyword">if</span>(inde[i] == <span class="number">0</span>) queue.offer(i);<span class="comment">//遍历数组，将入度为0的数加入队列</span></span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span>(!queue.isEmpty()){</span><br><span class="line"> <span class="keyword">if</span>(queue.size() > <span class="number">1</span>) <span class="keyword">return</span> <span class="keyword">false</span>;</span><br><span class="line"> <span class="keyword">int</span> num = queue.poll();</span><br><span class="line"> Set<Integer> set = graph[num];</span><br><span class="line"> <span class="keyword">for</span> (<span class="keyword">int</span> next : set){<span class="comment">//遍历有向边，所有入度减一</span></span><br><span class="line"> inde[next]--;</span><br><span class="line"> <span class="keyword">if</span>(inde[next] == <span class="number">0</span>) queue.offer(next);<span class="comment">//入度为0加入队列末尾</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="keyword">true</span>;</span><br><span class="line"></span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 拓扑排序 </tag>
</tags>
</entry>
<entry>
<title>LeetCode刷题篇(12)-最大间距</title>
<link href="/2022/07/22/leetcode/LeetCode(12)/"/>
<url>/2022/07/22/leetcode/LeetCode(12)/</url>
<content type="html"><![CDATA[<h1 id="最大间距"><a href="#最大间距" class="headerlink" title="最大间距"></a>最大间距</h1><h2 id="题目链接"><a href="#题目链接" class="headerlink" title="题目链接"></a><a href="https://leetcode.cn/problems/maximum-gap/">题目链接</a></h2><hr><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><blockquote><p>给定一个无序的数组<code>nums</code>，返回 数组在排序之后，相邻元素之间最大的差值 。如果数组元素个数小于 2，则返回 0 。<br>您必须编写一个在「线性时间」内运行并使用「线性额外空间」的算法。</p></blockquote><hr><h2 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h2><p>由桶排序的算法我们可以知道，桶排序的过程中每次都是选取一定范围内的值塞进了同一个桶，所以根据这个题我们可以知道，利用桶排序的算法可以解决这个最大间距的问题，每一个桶中的最小值与前一个桶的最大值相比较，寻找差值的最大值即是最大间距。</p><p>时间复杂度：<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="4.844ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2141 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1152,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1752,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container><br>空间复杂度：<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="4.844ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2141 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1152,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1752,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container></p><hr><h2 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h2><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">maximumGap</span><span class="params">(<span class="keyword">int</span>[] nums)</span> </span>{</span><br><span class="line"> <span class="keyword">int</span> n = nums.length;</span><br><span class="line"> <span class="keyword">if</span>(nums.length < <span class="number">2</span>) <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">int</span> min = Arrays.stream(nums).min().getAsInt();<span class="comment">//利用流找最小值</span></span><br><span class="line"> <span class="keyword">int</span> max = Arrays.stream(nums).max().getAsInt();<span class="comment">//最大值</span></span><br><span class="line"> <span class="keyword">int</span> interval = Math.max((max - min) / (n - <span class="number">1</span>),<span class="number">1</span>);<span class="comment">//桶的大小</span></span><br><span class="line"> <span class="keyword">int</span> bucketSize = (max - min) / interval + <span class="number">1</span>;<span class="comment">//桶的个数</span></span><br><span class="line"> </span><br><span class="line"> <span class="keyword">int</span>[][] buckets = <span class="keyword">new</span> <span class="keyword">int</span>[bucketSize][<span class="number">2</span>];</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">0</span>; i < bucketSize;++i){</span><br><span class="line"> Arrays.fill(buckets[i], -<span class="number">1</span>);<span class="comment">//全部赋值-1</span></span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span> (<span class="keyword">int</span> num : nums) {</span><br><span class="line"> <span class="keyword">int</span> index = (num - min) / interval;</span><br><span class="line"> <span class="keyword">if</span>(buckets[index][<span class="number">0</span>] == -<span class="number">1</span>) {</span><br><span class="line"> buckets[index][<span class="number">0</span>] = buckets[index][<span class="number">1</span>] = num;</span><br><span class="line"> }<span class="keyword">else</span> {</span><br><span class="line"> buckets[index][<span class="number">0</span>] = Math.min(buckets[index][<span class="number">0</span>], num);<span class="comment">//桶的最小值</span></span><br><span class="line"> buckets[index][<span class="number">1</span>] = Math.max(buckets[index][<span class="number">1</span>], num);<span class="comment">//桶的最大值</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">int</span> maxGap = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">int</span> pre = -<span class="number">1</span>;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">1</span>; i < buckets.length; i++) {</span><br><span class="line"> <span class="keyword">if</span>(buckets[i][<span class="number">0</span>] == -<span class="number">1</span>) <span class="keyword">continue</span>;</span><br><span class="line"> <span class="keyword">if</span>(pre != -<span class="number">1</span>){</span><br><span class="line"> maxGap = Math.max(maxGap, buckets[i][<span class="number">0</span>] - buckets[pre][<span class="number">1</span>]);</span><br><span class="line"> }</span><br><span class="line"> pre = i;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> maxGap;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 桶排序 </tag>
</tags>
</entry>
<entry>
<title>桶排序</title>
<link href="/2022/07/22/sort/sort(8)/"/>
<url>/2022/07/22/sort/sort(8)/</url>
<content type="html"><![CDATA[<h1 id="桶排序"><a href="#桶排序" class="headerlink" title="桶排序"></a>桶排序</h1><blockquote><p>首先先看一个动图：</p></blockquote><p><img src="/img/bucket_sort.gif" alt="桶排序"></p><h2 id="原理"><a href="#原理" class="headerlink" title="原理"></a>原理</h2><p>桶排序将原数组划分到称为 「桶」 的多个区间中，然后对每个桶单独进行排序，之后再按桶序和桶内序输出结果。<br>适合于分布较均匀的数据。</p><blockquote><p>怎么把元素均匀的划分到每个桶里面去呢？</p></blockquote><p>答案是根据元素的大小在数组中最小值与最大值之间占的位置而定。</p><ol><li>首先是找出数组最小值与最大值，</li><li>创建桶，因为桶排序的复杂度公式，所以建议将桶的数量设置为<code>(数组大小 / 3)</code>，</li><li>将元素均匀的加入到每一个桶里面去，</li><li>最后对每一个桶进行排序就可以了。</li></ol><blockquote><p>桶排序的时间复杂度取决于排序每一个桶的时候的时间复杂度，可以使用Java内置排序<code>Collections.sort()</code></p></blockquote><h2 id="复杂度分析"><a href="#复杂度分析" class="headerlink" title="复杂度分析"></a>复杂度分析</h2><p>时间复杂度：找最大最小值和分配桶均耗费 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="4.844ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2141 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1152,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1752,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container>，之后的复杂度取决于每个桶内的排序算法复杂度之和。假设有<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.179ex" height="1.595ex" role="img" focusable="false" viewBox="0 -694 521 705"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></g></g></g></svg></mjx-container>个桶，且数据分布均匀</p><ul><li>若采用 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="5.975ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2641 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1152,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(1752,0)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g><g data-mml-node="mo" transform="translate(2252,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container>的排序算法，那么总排序时间复杂度为 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="8.142ex" height="2.452ex" role="img" focusable="false" viewBox="0 -833.9 3598.6 1083.9"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="msup" transform="translate(1152,0)"><g data-mml-node="mi"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(633,363) scale(0.707)"><path data-c="32" d="M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z"></path></g></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(2188.6,0)"><g data-mml-node="mo"><path data-c="2F" d="M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z"></path></g></g><g data-mml-node="mi" transform="translate(2688.6,0)"><path data-c="1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></g><g data-mml-node="mo" transform="translate(3209.6,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container>，</li><li>若采用 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="9.052ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4001 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1152,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1752,0)"><path data-c="1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path></g><g data-mml-node="mi" transform="translate(2050,0)"><path data-c="1D45C" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"></path></g><g data-mml-node="mi" transform="translate(2535,0)"><path data-c="1D454" d="M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z"></path></g><g data-mml-node="mi" transform="translate(3012,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3612,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container>的排序算法，总排序时间复杂度为 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="18.371ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 8120 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g 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353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></g><g data-mml-node="mo" transform="translate(1673,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(2062,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 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354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></g><g data-mml-node="mo" transform="translate(3683,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g 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477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></g><g data-mml-node="mo" transform="translate(7342,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 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216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1152,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1752,0)"><path data-c="1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path></g><g data-mml-node="mi" transform="translate(2050,0)"><path data-c="1D45C" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"></path></g><g data-mml-node="mi" transform="translate(2535,0)"><path data-c="1D454" d="M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z"></path></g><g data-mml-node="mo" transform="translate(3012,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(3401,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(4001,0)"><g data-mml-node="mo"><path data-c="2F" d="M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z"></path></g></g><g data-mml-node="mi" transform="translate(4501,0)"><path data-c="1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></g><g data-mml-node="mo" transform="translate(5022,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g><g data-mml-node="mo" transform="translate(5411,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container>。</li></ul><blockquote><p>若桶内排序采用<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="9.052ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4001 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1152,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1752,0)"><path data-c="1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path></g><g data-mml-node="mi" transform="translate(2050,0)"><path data-c="1D45C" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"></path></g><g data-mml-node="mi" transform="translate(2535,0)"><path data-c="1D454" d="M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z"></path></g><g data-mml-node="mi" transform="translate(3012,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3612,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container>算法，且<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.179ex" height="1.595ex" role="img" focusable="false" viewBox="0 -694 521 705"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></g></g></g></svg></mjx-container>的大小适当，例如<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="7.823ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3457.6 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path></g><g data-mml-node="mo" transform="translate(798.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="mi" transform="translate(1854.6,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(2454.6,0)"><g data-mml-node="mo"><path data-c="2F" d="M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z"></path></g></g><g data-mml-node="mi" transform="translate(2954.6,0)"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g></g></g></svg></mjx-container>，<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.439ex;" xmlns="http://www.w3.org/2000/svg" width="1.138ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 503 636"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D45D" d="M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z"></path></g></g></g></svg></mjx-container>是一个较小的数例如2，3等。那么整体的时间复杂度大约为<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="4.844ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2141 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1152,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(1752,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container>。<br>虽然形式上为线性复杂度，但其n的系数较大，未必优于<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="9.052ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4001 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1152,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1752,0)"><path data-c="1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path></g><g data-mml-node="mi" transform="translate(2050,0)"><path data-c="1D45C" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"></path></g><g data-mml-node="mi" transform="translate(2535,0)"><path data-c="1D454" d="M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z"></path></g><g data-mml-node="mi" transform="translate(3012,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3612,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container>的排序算法。</p></blockquote><h2 id="代码实现"><a href="#代码实现" class="headerlink" title="代码实现"></a>代码实现</h2><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">Main</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">main</span><span class="params">(String[] args)</span> </span>{</span><br><span class="line"> <span class="keyword">int</span>[] arr = <span class="keyword">new</span> <span class="keyword">int</span> []{<span class="number">6</span>,<span class="number">2</span>,<span class="number">9</span>,<span class="number">7</span>,<span class="number">4</span>,<span class="number">10</span>,<span class="number">5</span>,<span class="number">8</span>,<span class="number">3</span>,<span class="number">1</span>};</span><br><span class="line"> <span class="keyword">int</span> n = arr.length;</span><br><span class="line"> <span class="keyword">int</span> minl = arr[<span class="number">0</span>];</span><br><span class="line"> <span class="keyword">int</span> maxl = arr[<span class="number">0</span>];</span><br><span class="line"> List<ArrayList<Integer>> buckets = <span class="keyword">new</span> ArrayList<>(n/<span class="number">3</span>);<span class="comment">//桶的个数</span></span><br><span class="line"> <span class="keyword">for</span> (<span class="keyword">int</span> i=<span class="number">1</span>;i<n;i++){</span><br><span class="line"> minl = Math.min(minl,arr[i]);</span><br><span class="line"> maxl = Math.max(maxl,arr[i]);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<n;i++){</span><br><span class="line"> buckets.add(<span class="keyword">new</span> ArrayList<>());</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span> (<span class="keyword">int</span> j : arr) {</span><br><span class="line"> <span class="keyword">int</span> re = (maxl - minl) / (n - <span class="number">1</span>);<span class="comment">//每个桶的宽度</span></span><br><span class="line"> <span class="keyword">int</span> index = (j - minl) / re;<span class="comment">//桶的索引</span></span><br><span class="line"> buckets.get(index).add(j);<span class="comment">//添加到桶中</span></span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span> (ArrayList<Integer> integers : buckets) {</span><br><span class="line"> Collections.sort(integers);<span class="comment">//排序</span></span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">int</span> index = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span>(ArrayList<Integer> bucket : buckets){<span class="comment">//遍历桶</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> val : bucket){</span><br><span class="line"> arr[index++] = val;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> System.out.println(Arrays.toString(arr));</span><br><span class="line"> <span class="comment">//[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]</span></span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> 排序算法 </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 桶排序 </tag>
</tags>
</entry>
<entry>
<title>计数排序</title>
<link href="/2022/07/22/sort/sort(7)/"/>
<url>/2022/07/22/sort/sort(7)/</url>
<content type="html"><![CDATA[<h1 id="计数排序"><a href="#计数排序" class="headerlink" title="计数排序"></a>计数排序</h1><blockquote><p>首先先看一个动图：</p></blockquote><p><img src="/img/count_sort.gif" alt="计数排序"></p><p>待更</p><h2 id="代码实现"><a href="#代码实现" class="headerlink" title="代码实现"></a>代码实现</h2>]]></content>
<categories>
<category> 排序算法 </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 计数排序 </tag>
</tags>
</entry>
<entry>
<title>堆排序</title>
<link href="/2022/07/22/sort/sort(6)/"/>
<url>/2022/07/22/sort/sort(6)/</url>
<content type="html"><![CDATA[<h1 id="堆排序"><a href="#堆排序" class="headerlink" title="堆排序"></a>堆排序</h1><p>待更</p>]]></content>
<categories>
<category> 排序算法 </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 堆排序 </tag>
</tags>
</entry>
<entry>
<title>快速排序</title>
<link href="/2022/07/22/sort/sort(5)/"/>
<url>/2022/07/22/sort/sort(5)/</url>
<content type="html"><![CDATA[<h1 id="快速排序"><a href="#快速排序" class="headerlink" title="快速排序"></a>快速排序</h1><blockquote><p>先看一个动图</p></blockquote><p><img src="/img/quick_sort.gif" alt="快速排序"></p><h2 id="原理"><a href="#原理" class="headerlink" title="原理"></a>原理</h2><ul><li>个人理解</li></ul><blockquote><p>快速排序每次是选取数组中的一个值进行”处理”<br>处理主要是将这个元素放在数组中的某个位置，使得该元素左边的元素都小于<br>或等于该元素，右边的元素都大于或等于该元素。</p></blockquote><p>最后依次对处理完的元素位置左边和右边的元素</p><p>综上所述：</p><p>时间复杂度:<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="9.052ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 4001 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1152,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mi" transform="translate(1752,0)"><path data-c="1D459" d="M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z"></path></g><g data-mml-node="mi" transform="translate(2050,0)"><path data-c="1D45C" d="M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z"></path></g><g data-mml-node="mi" transform="translate(2535,0)"><path data-c="1D454" d="M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z"></path></g><g data-mml-node="mi" transform="translate(3012,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(3612,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container><br>空间复杂度:<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="4.618ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2041 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mn" transform="translate(1152,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g><g data-mml-node="mo" transform="translate(1652,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container></p><h2 id="代码实现"><a href="#代码实现" class="headerlink" title="代码实现"></a>代码实现</h2><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">quickSort</span><span class="params">(<span class="keyword">int</span>[] arr,<span class="keyword">int</span> left,<span class="keyword">int</span> right)</span></span>{</span><br><span class="line"> <span class="keyword">if</span>(left < right){</span><br><span class="line"> <span class="keyword">int</span> pos = partition(arr,left,right);</span><br><span class="line"> quickSort(arr,left,pos-<span class="number">1</span>);<span class="comment">//对左边进行处理</span></span><br><span class="line"> quickSort(arr,pos+<span class="number">1</span>,right);<span class="comment">//对右边进行处理</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//对arr[right]找到数组中合适的位置</span></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">partition</span><span class="params">(<span class="keyword">int</span>[] arr,<span class="keyword">int</span> left,<span class="keyword">int</span> right)</span></span>{</span><br><span class="line"> <span class="keyword">int</span> po = arr[right];<span class="comment">//暂存arr[right]</span></span><br><span class="line"> <span class="keyword">while</span>(left < right){</span><br><span class="line"> <span class="keyword">while</span>(left < right && arr[left] < po){</span><br><span class="line"> left++;</span><br><span class="line"> }</span><br><span class="line"> arr[right] = arr[left];<span class="comment">//依据arr[right]记录左边的临界点</span></span><br><span class="line"> <span class="keyword">while</span>(left < right && arr[right] >= po){</span><br><span class="line"> right--;</span><br><span class="line"> }</span><br><span class="line"> arr[left] = arr[right];<span class="comment">//依据arr[left]记录右边的临界点</span></span><br><span class="line"> }</span><br><span class="line"> arr[left] = po;</span><br><span class="line"> <span class="keyword">return</span> left;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> 排序算法 </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 快速排序 </tag>
</tags>
</entry>
<entry>
<title>归并排序</title>
<link href="/2022/07/22/sort/sort(4)/"/>
<url>/2022/07/22/sort/sort(4)/</url>
<content type="html"><![CDATA[<h1 id="归并排序"><a href="#归并排序" class="headerlink" title="归并排序"></a>归并排序</h1><p>待更</p>]]></content>
<categories>
<category> 排序算法 </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 归并排序 </tag>
</tags>
</entry>
<entry>
<title>插入排序</title>
<link href="/2022/07/22/sort/sort(3)/"/>
<url>/2022/07/22/sort/sort(3)/</url>
<content type="html"><![CDATA[<h1 id="插入排序"><a href="#插入排序" class="headerlink" title="插入排序"></a>插入排序</h1><p>待更</p>]]></content>
<categories>
<category> 排序算法 </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 插入排序 </tag>
</tags>
</entry>
<entry>
<title>选择排序</title>
<link href="/2022/07/22/sort/sort(2)/"/>
<url>/2022/07/22/sort/sort(2)/</url>
<content type="html"><![CDATA[<h1 id="选择排序"><a href="#选择排序" class="headerlink" title="选择排序"></a>选择排序</h1><p>待更</p>]]></content>
<categories>
<category> 排序算法 </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 选择排序 </tag>
</tags>
</entry>
<entry>
<title>冒泡排序</title>
<link href="/2022/07/22/sort/sort(1)/"/>
<url>/2022/07/22/sort/sort(1)/</url>
<content type="html"><![CDATA[<h1 id="冒泡排序"><a href="#冒泡排序" class="headerlink" title="冒泡排序"></a>冒泡排序</h1><p>待更</p><h2 id="冒泡优化版1"><a href="#冒泡优化版1" class="headerlink" title="冒泡优化版1"></a>冒泡优化版1</h2><h3 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h3><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="keyword">public</span> <span class="keyword">int</span>[] sortArray(<span class="keyword">int</span>[] nums) {</span><br><span class="line"> <span class="keyword">int</span> len = nums.length;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<len;i++){</span><br><span class="line"> <span class="keyword">boolean</span> flag = <span class="keyword">false</span>;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j = <span class="number">1</span>;j<len-i;j++){</span><br><span class="line"> <span class="keyword">if</span>(nums[j] < nums[j-<span class="number">1</span>]){</span><br><span class="line"> swap(nums,j,j-<span class="number">1</span>);</span><br><span class="line"> flag = <span class="keyword">true</span>;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(!flag) <span class="keyword">break</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> nums;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">swap</span><span class="params">(<span class="keyword">int</span>[] arr,<span class="keyword">int</span> i,<span class="keyword">int</span> j)</span></span>{</span><br><span class="line"> <span class="keyword">if</span>(i == j) <span class="keyword">return</span>;</span><br><span class="line"> arr[i] = arr[i] ^ arr[j];</span><br><span class="line"> arr[j] = arr[i] ^ arr[j];</span><br><span class="line"> arr[i] = arr[i] ^ arr[j];</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h2 id="冒泡优化版2"><a href="#冒泡优化版2" class="headerlink" title="冒泡优化版2"></a>冒泡优化版2</h2><h3 id="代码-1"><a href="#代码-1" class="headerlink" title="代码"></a>代码</h3><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="keyword">public</span> <span class="keyword">int</span>[] sortArray(<span class="keyword">int</span>[] nums) {</span><br><span class="line"> <span class="keyword">boolean</span> swaped = <span class="keyword">true</span>;</span><br><span class="line"> <span class="keyword">int</span> len = nums.length;</span><br><span class="line"> <span class="keyword">int</span> lastIndex = len - <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">int</span> swapIndex = -<span class="number">1</span>;</span><br><span class="line"> <span class="keyword">while</span>(swaped){</span><br><span class="line"> swaped = <span class="keyword">false</span>;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<lastIndex;i++){</span><br><span class="line"> <span class="keyword">if</span>(nums[i] > nums[i+<span class="number">1</span>]){</span><br><span class="line"> swap(nums,i,i+<span class="number">1</span>);</span><br><span class="line"> swaped = <span class="keyword">true</span>;<span class="comment">//标记已出现交换</span></span><br><span class="line"> swapIndex = i;<span class="comment">//记录最后交换位置</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> lastIndex = swapIndex;<span class="comment">//上限为最后一次交换位置</span></span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> nums;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">swap</span><span class="params">(<span class="keyword">int</span>[] arr,<span class="keyword">int</span> i,<span class="keyword">int</span> j)</span></span>{<span class="comment">//异或可以实现原地交换</span></span><br><span class="line"> <span class="keyword">if</span>(i == j) <span class="keyword">return</span>;</span><br><span class="line"> arr[i] = arr[i] ^ arr[j];</span><br><span class="line"> arr[j] = arr[i] ^ arr[j];</span><br><span class="line"> arr[i] = arr[i] ^ arr[j];</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> 排序算法 </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 排序 </tag>
</tags>
</entry>
<entry>
<title>LeetCode刷题篇(11)-四数之和</title>
<link href="/2022/07/20/leetcode/LeetCode(11)/"/>
<url>/2022/07/20/leetcode/LeetCode(11)/</url>
<content type="html"><![CDATA[<h1 id="四数之和"><a href="#四数之和" class="headerlink" title="四数之和"></a>四数之和</h1><h2 id="题目链接"><a href="#题目链接" class="headerlink" title="题目链接"></a><a href="https://leetcode.cn/problems/4sum/">题目链接</a></h2><hr><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><p>给你一个由<code> n</code> 个整数组成的数组 <code>nums</code> ，和一个目标值 <code>target</code> 。请你找出并返回满足下述全部条件且不重复的四元组<code>[nums[a], nums[b], nums[c], nums[d]]</code>（若两个四元组元素一一对应，则认为两个四元组重复）：</p><ul><li><code>0 <= a, b, c, d < n</code></li><li><code>a</code>、<code>b</code>、<code>c</code> 和 <code>d</code> 互不相同</li><li><code>nums[a] + nums[b] + nums[c] + nums[d] == target</code></li></ul><blockquote><p>示例：</p></blockquote><blockquote><p>输入：nums = [1,0,-1,0,-2,2], target = 0<br>输出：[[-2,-1,1,2],[-2,0,0,2],[-1,0,0,1]]</p></blockquote><hr><h2 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h2><p>leetcode题目其实有点意思的，两数之和，三数之和，四数之和，还有之前13届蓝桥杯B组国赛的十数之和，那个题是真的头疼，后续给出题解。<br>同样的四数之和与三数之和类似，第一重循环锁定一个数，第二种继续锁定一个数，第三重就是双指针，排序+双指针可以减少一重循环，但是官网好像最优就是<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="5.975ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2641 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z"></path></g><g data-mml-node="mo" transform="translate(763,0)"><path data-c="28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path></g><g data-mml-node="mi" transform="translate(1152,0)"><path data-c="1D45B" d="M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mn" transform="translate(1752,0)"><path data-c="33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path></g><g data-mml-node="mo" transform="translate(2252,0)"><path data-c="29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></g></g></g></svg></mjx-container>，暂时我还不知道最优答案是什么方法，另外就是根据一些特点可以排除一些四元组，具体看代码。</p><hr><h2 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h2><p>由于最近找实习，代码全部由Java语言编写</p><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="keyword">public</span> List<List<Integer>> fourSum(<span class="keyword">int</span>[] nums, <span class="keyword">int</span> target) {</span><br><span class="line"> List<List<Integer>> list = <span class="keyword">new</span> ArrayList<List<Integer>>();</span><br><span class="line"> <span class="keyword">if</span>(nums == <span class="keyword">null</span> || nums.length < <span class="number">4</span>) <span class="keyword">return</span> list;</span><br><span class="line"> Arrays.sort(nums);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<nums.length - <span class="number">3</span>;i++){</span><br><span class="line"> <span class="keyword">if</span>(i > <span class="number">0</span> && nums[i] == nums[i-<span class="number">1</span>]) <span class="keyword">continue</span>;<span class="comment">//重复跳过</span></span><br><span class="line"> <span class="comment">//从当前数往后四个数大于则不用循环，因为后面的数更大</span></span><br><span class="line"> <span class="keyword">if</span>((<span class="keyword">long</span>) nums[i] + nums[i+<span class="number">1</span>] + nums[i+<span class="number">2</span>] + nums[i+<span class="number">3</span>] > target) <span class="keyword">break</span>;</span><br><span class="line"> <span class="comment">//当前数加上最大的三个数还要小于目标，则继续后移</span></span><br><span class="line"> <span class="keyword">if</span>((<span class="keyword">long</span>) nums[i] + nums[nums.length-<span class="number">3</span>] + nums[nums.length-<span class="number">2</span>] + nums[nums.length-<span class="number">1</span>] < target) <span class="keyword">continue</span>;</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j = i+<span class="number">1</span>;j<nums.length - <span class="number">2</span>;j++){</span><br><span class="line"> <span class="keyword">if</span>(j > i+<span class="number">1</span> && nums[j] == nums[j-<span class="number">1</span>]) <span class="keyword">continue</span>;</span><br><span class="line"> <span class="keyword">if</span>((<span class="keyword">long</span>) nums[i] + nums[j] + nums[j+<span class="number">1</span>] + nums[j+<span class="number">2</span>] > target) <span class="keyword">break</span>;</span><br><span class="line"> <span class="keyword">if</span>((<span class="keyword">long</span>) nums[i] + nums[j] + nums[nums.length-<span class="number">2</span>] + nums[nums.length-<span class="number">1</span>] < target) <span class="keyword">continue</span>;</span><br><span class="line"> <span class="keyword">int</span> left = j+<span class="number">1</span>,right = nums.length - <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">while</span>(left < right){<span class="comment">//双指针遍历</span></span><br><span class="line"> <span class="keyword">int</span> sum = nums[i] + nums[j] + nums[left] + nums[right];</span><br><span class="line"> <span class="keyword">if</span>(sum == target){<span class="comment">//目标值锁定</span></span><br><span class="line"> list.add(Arrays.asList(nums[i],nums[j],nums[left],nums[right]));</span><br><span class="line"> <span class="keyword">while</span>(left < right && nums[left] == nums[left+<span class="number">1</span>]) left++;</span><br><span class="line"> left++;</span><br><span class="line"> <span class="keyword">while</span>(left < right && nums[right] == nums[right - <span class="number">1</span>]) right--;</span><br><span class="line"> right--;</span><br><span class="line"> }<span class="keyword">else</span> <span class="keyword">if</span>(sum < target){</span><br><span class="line"> left++;</span><br><span class="line"> }<span class="keyword">else</span>{</span><br><span class="line"> right--;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> list;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 双指针 </tag>
</tags>
</entry>
<entry>
<title>LeetCode刷题篇(10)-三数之和</title>
<link href="/2022/07/20/leetcode/LeetCode(10)/"/>
<url>/2022/07/20/leetcode/LeetCode(10)/</url>
<content type="html"><![CDATA[<h1 id="三数之和"><a href="#三数之和" class="headerlink" title="三数之和"></a>三数之和</h1><h2 id="题目链接"><a href="#题目链接" class="headerlink" title="题目链接"></a><a href="https://leetcode.cn/problems/3sum/">题目链接</a></h2><hr><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><p>给你一个包含 <code>n</code>个整数的数组 <code>nums</code>，判断 <code>nums</code> 中是否存在三个元素 <code>a</code>，<code>b</code>，<code>c</code> ，使得 <code>a + b + c = 0</code> ？请你找出所有和为 <code>0</code> 且不重复的三元组。</p><p><strong>注意：</strong> 答案中不可以包含重复的三元组。</p><blockquote><p>示例：</p></blockquote><blockquote><p>输入：nums = [-1,0,1,2,-1,-4]<br>输出：[[-1,-1,2],[-1,0,1]]</p></blockquote><hr><h2 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h2><p>题目和两数之和很相似，具有共同之处，排序+双指针就可以解出，从头至尾循环数组，固定到某一位置后，对数组后面部分进行双指针左右开始遍历找出三元组，代码即可出炉。</p><hr><h2 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h2><p>由于最近找实习，代码全部由Java语言编写</p><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="keyword">public</span> List<List<Integer>> threeSum(<span class="keyword">int</span>[] nums) {</span><br><span class="line"> List<List<Integer>> list = <span class="keyword">new</span> ArrayList<List<Integer>>();</span><br><span class="line"> <span class="keyword">int</span> len = nums.length;</span><br><span class="line"> <span class="keyword">if</span>(len < <span class="number">3</span>) <span class="keyword">return</span> list;<span class="comment">//数组长度小于三直接被排除</span></span><br><span class="line"> Arrays.sort(nums);<span class="comment">//升序排序</span></span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<len-<span class="number">2</span>;i++){</span><br><span class="line"> <span class="keyword">int</span> sum = <span class="number">0</span> - nums[i];<span class="comment">//便于后面双指针遍历</span></span><br><span class="line"> <span class="keyword">if</span>(sum < <span class="number">0</span>) <span class="keyword">break</span>;</span><br><span class="line"> <span class="keyword">if</span>(i > <span class="number">0</span> && nums[i] == nums[i-<span class="number">1</span>]) <span class="keyword">continue</span>;<span class="comment">//三元组不能有重复</span></span><br><span class="line"></span><br><span class="line"> <span class="keyword">int</span> a = i+<span class="number">1</span>,b = len-<span class="number">1</span>;</span><br><span class="line"> <span class="keyword">while</span>(a < b){<span class="comment">//左指针始终小于右指针</span></span><br><span class="line"> <span class="keyword">if</span>(sum == nums[a] + nums[b]){<span class="comment">//找到三元组</span></span><br><span class="line"> list.add(Arrays.asList(nums[i],nums[a],nums[b]));</span><br><span class="line"> a++;</span><br><span class="line"> b--;<span class="comment">//左右指针同时移动，只移动任何一个后面都无法找出三元组</span></span><br><span class="line"> <span class="keyword">while</span>(a < b && nums[a] == nums[a-<span class="number">1</span>]) a++;<span class="comment">//重复跳过</span></span><br><span class="line"> <span class="keyword">while</span>(a < b && nums[b] == nums[b+<span class="number">1</span>]) b--;</span><br><span class="line"> }<span class="keyword">else</span> <span class="keyword">if</span>(sum > nums[a] + nums[b]){<span class="comment">//和偏小，左指针右移</span></span><br><span class="line"> a++;</span><br><span class="line"> }<span class="keyword">else</span>{<span class="comment">//和偏大，右指针左移</span></span><br><span class="line"> b--;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> list;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 双指针 </tag>
</tags>
</entry>
<entry>
<title>LeetCode刷题篇(9)-两数相加</title>
<link href="/2022/07/16/leetcode/LeetCode(9)/"/>
<url>/2022/07/16/leetcode/LeetCode(9)/</url>
<content type="html"><![CDATA[<h1 id="两数相加"><a href="#两数相加" class="headerlink" title="两数相加"></a>两数相加</h1><h2 id="题目链接"><a href="#题目链接" class="headerlink" title="题目链接"></a><a href="https://leetcode.cn/problems/add-two-numbers/">题目链接</a></h2><hr><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><blockquote><p>给你两个非空的链表，表示两个非负的整数。它们每位数字都是按照逆序的方式存储的，并且每个节点只能存储一位数字。<br>请你将两个数相加，并以相同形式返回一个表示和的链表。<br>你可以假设除了数字 0 之外，这两个数都不会以 0 开头。</p></blockquote><blockquote><p>输入：l1 = [2,4,3], l2 = [5,6,4]<br>输出：[7,0,8]<br>解释：342 + 465 = 807.</p></blockquote><hr><h2 id="题解"><a href="#题解" class="headerlink" title="题解"></a>题解</h2><p><strong>主要思路是加法进制，进位需要单独保留，头节点需要保存，尾节点跟随两个节点一起移动，代码即可出炉</strong></p><hr><h2 id="代码如下"><a href="#代码如下" class="headerlink" title="代码如下"></a>代码如下</h2><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment"> * Definition for singly-linked list.</span></span><br><span class="line"><span class="comment"> * public class ListNode {</span></span><br><span class="line"><span class="comment"> * int val;</span></span><br><span class="line"><span class="comment"> * ListNode next;</span></span><br><span class="line"><span class="comment"> * ListNode() {}</span></span><br><span class="line"><span class="comment"> * ListNode(int val) { this.val = val; }</span></span><br><span class="line"><span class="comment"> * ListNode(int val, ListNode next) { this.val = val; this.next = next; }</span></span><br><span class="line"><span class="comment"> * }</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> ListNode <span class="title">addTwoNumbers</span><span class="params">(ListNode l1, ListNode l2)</span> </span>{</span><br><span class="line"> ListNode head = <span class="keyword">null</span>;</span><br><span class="line"> ListNode tail = <span class="keyword">null</span>;</span><br><span class="line"> <span class="keyword">int</span> cnt = <span class="number">0</span>;<span class="comment">//进位</span></span><br><span class="line"> <span class="keyword">while</span>(l1!=<span class="keyword">null</span> && l2 != <span class="keyword">null</span>){<span class="comment">//保证两个链表都不为空，后续可以根据链表长度不一致单独遍历</span></span><br><span class="line"> <span class="keyword">if</span>(head == <span class="keyword">null</span>){</span><br><span class="line"> head = tail = <span class="keyword">new</span> ListNode((l1.val + l2.val + cnt) % <span class="number">10</span>);<span class="comment">//保存头节点</span></span><br><span class="line"> }<span class="keyword">else</span>{</span><br><span class="line"> tail.next = <span class="keyword">new</span> ListNode((l1.val + l2.val + cnt) % <span class="number">10</span>);<span class="comment">//尾节点移动</span></span><br><span class="line"> tail = tail.next;</span><br><span class="line"> }</span><br><span class="line"> cnt = (cnt + l1.val + l2.val) / <span class="number">10</span>;<span class="comment">//保存进位</span></span><br><span class="line"> l1 = l1.next;</span><br><span class="line"> l2 = l2.next;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">while</span>(l1==<span class="keyword">null</span> && l2!=<span class="keyword">null</span>){<span class="comment">//遍历没有跑完的l2</span></span><br><span class="line"> tail.next = <span class="keyword">new</span> ListNode((l2.val + cnt) % <span class="number">10</span>);</span><br><span class="line"> cnt = (l2.val + cnt) /<span class="number">10</span>;</span><br><span class="line"> tail = tail.next;</span><br><span class="line"> l2 = l2.next;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span>(l2==<span class="keyword">null</span> && l1!=<span class="keyword">null</span>){<span class="comment">//遍历没有跑完的l1</span></span><br><span class="line"> tail.next = <span class="keyword">new</span> ListNode((l1.val + cnt) % <span class="number">10</span>);</span><br><span class="line"> cnt = (l1.val + cnt) /<span class="number">10</span>;</span><br><span class="line"> tail = tail.next;</span><br><span class="line"> l1 = l1.next;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(cnt != <span class="number">0</span>){</span><br><span class="line"> tail.next = <span class="keyword">new</span> ListNode(cnt);</span><br><span class="line"> tail = tail.next;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> head;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 链表 </tag>
</tags>
</entry>
<entry>
<title>LeetCode刷题篇(8)-滑动窗口的平均值</title>
<link href="/2022/07/16/leetcode/LeetCode(8)/"/>
<url>/2022/07/16/leetcode/LeetCode(8)/</url>
<content type="html"><![CDATA[<h1 id="滑动窗口的平均值"><a href="#滑动窗口的平均值" class="headerlink" title="滑动窗口的平均值"></a>滑动窗口的平均值</h1><h2 id="题目链接"><a href="#题目链接" class="headerlink" title="题目链接"></a><a href="https://leetcode.cn/problems/qIsx9U/">题目链接</a></h2><hr><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><blockquote><p>给定一个整数数据流和一个窗口大小，根据该滑动窗口的大小，计算滑动窗口里所有数字的平均值。</p></blockquote><p>代码如下：</p><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">MovingAverage</span> </span>{</span><br><span class="line"></span><br><span class="line"> Queue<Integer> queue;</span><br><span class="line"> <span class="keyword">int</span> size;</span><br><span class="line"> <span class="keyword">int</span> sum;</span><br><span class="line"></span><br><span class="line"> <span class="comment">/** Initialize your data structure here. */</span></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="title">MovingAverage</span><span class="params">(<span class="keyword">int</span> size)</span> </span>{</span><br><span class="line"> queue = <span class="keyword">new</span> ArrayDeque<Integer>();</span><br><span class="line"> <span class="keyword">this</span>.size = size;</span><br><span class="line"> sum = <span class="number">0</span>;</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">double</span> <span class="title">next</span><span class="params">(<span class="keyword">int</span> val)</span> </span>{</span><br><span class="line"> <span class="keyword">if</span>(size == queue.size()){</span><br><span class="line"> sum -= queue.poll();</span><br><span class="line"> }</span><br><span class="line"> queue.offer(val);</span><br><span class="line"> sum += val;</span><br><span class="line"> <span class="keyword">return</span> (<span class="keyword">double</span>) sum / queue.size();</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment"> * Your MovingAverage object will be instantiated and called as such:</span></span><br><span class="line"><span class="comment"> * MovingAverage obj = new MovingAverage(size);</span></span><br><span class="line"><span class="comment"> * double param_1 = obj.next(val);</span></span><br><span class="line"><span class="comment"> */</span></span><br></pre></td></tr></table></figure><hr><h2 id="Java代码方法解释"><a href="#Java代码方法解释" class="headerlink" title="Java代码方法解释"></a>Java代码方法解释</h2><ul><li><p><code>ArrayDeque</code></p><ul><li><p><code>poll</code></p><blockquote><p>检索并删除由此<code>deque</code>表示的队列的头部（换句话说，该<code>deque</code>的第一个元素），如果此<code>deque</code>为空，则返回<code>null</code> 。</p></blockquote></li><li><p><code>offer</code></p><blockquote><p>在此<code>deque</code>的末尾插入指定的元素。</p></blockquote></li><li><p><code>size</code></p><blockquote><p>返回此<code>deque</code>中的元素数。 </p></blockquote></li></ul></li></ul>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
</tags>
</entry>
<entry>
<title>牛客刷题篇(7)-数组中的逆序对</title>
<link href="/2022/07/12/leetcode/LeetCode(7)/"/>
<url>/2022/07/12/leetcode/LeetCode(7)/</url>
<content type="html"><![CDATA[<h1 id="数组中的逆序对"><a href="#数组中的逆序对" class="headerlink" title="数组中的逆序对"></a>数组中的逆序对</h1><h2 id="题目链接"><a href="#题目链接" class="headerlink" title="题目链接"></a><a href="https://www.nowcoder.com/practice/96bd6684e04a44eb80e6a68efc0ec6c5?tpId=295&tqId=23260&ru=/exam/oj&qru=/ta/format-top101/question-ranking">题目链接</a></h2><hr><h2 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h2><p>在数组中的两个数字，如果前面一个数字大于后面的数字，则这两个数字组成一个逆序对。输入一个数组,求出这个数组中的逆序对的总数P。并将P对1000000007取模的结果输出。 即输出P <code>mod</code> 1000000007</p><blockquote><p>要求：空间复杂度 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="4.844ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2141 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D442" d="M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 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src="https://img-blog.csdnimg.cn/img_convert/107ac48d38cee761ceaea434819f7494.png" alt="归并排序"></p><hr><h2 id="代码如下："><a href="#代码如下：" class="headerlink" title="代码如下："></a>代码如下：</h2><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="keyword">int</span> count = <span class="number">0</span>;</span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">InversePairs</span><span class="params">(<span class="keyword">int</span> [] array)</span> </span>{</span><br><span class="line"> <span class="keyword">if</span>(array.length < <span class="number">2</span>) <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line"> mergeSort(array,<span class="number">0</span>,array.length-<span class="number">1</span>);</span><br><span class="line"> <span class="keyword">return</span> count;</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">mergeSort</span><span class="params">(<span class="keyword">int</span>[] arr,<span class="keyword">int</span> left,<span class="keyword">int</span> right)</span></span>{</span><br><span class="line"> <span class="keyword">if</span>(left == right) <span class="keyword">return</span>;</span><br><span class="line"> <span class="keyword">int</span> mid = (left + right) / <span class="number">2</span>;</span><br><span class="line"> mergeSort(arr,left,mid);<span class="comment">//处理左半部分</span></span><br><span class="line"> mergeSort(arr,mid+<span class="number">1</span>,right);<span class="comment">//处理右半部分</span></span><br><span class="line"> merge(arr,left,mid,right);<span class="comment">//合并</span></span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">merge</span><span class="params">(<span class="keyword">int</span>[] arr,<span class="keyword">int</span> left,<span class="keyword">int</span> mid,<span class="keyword">int</span> right)</span></span>{</span><br><span class="line"> <span class="keyword">int</span>[] array = <span class="keyword">new</span> <span class="keyword">int</span>[right-left+<span class="number">1</span>];</span><br><span class="line"> <span class="keyword">int</span> c = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">int</span> i = left;</span><br><span class="line"> <span class="keyword">int</span> l = left;</span><br><span class="line"> <span class="keyword">int</span> r = mid+<span class="number">1</span>;</span><br><span class="line"> <span class="keyword">while</span>(l <= mid && r <= right){<span class="comment">//左部分和右部分进行大小比对，并装入新数组array</span></span><br><span class="line"> <span class="keyword">if</span>(arr[l] < arr[r]){</span><br><span class="line"> array[c++] = arr[l++];</span><br><span class="line"> }<span class="keyword">else</span>{</span><br><span class="line"> array[c++] = arr[r++];</span><br><span class="line"> count += mid+<span class="number">1</span> - l;</span><br><span class="line"> count %= <span class="number">1000000007</span>;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">while</span>(l<=mid){<span class="comment">//处理左部分没处理完的</span></span><br><span class="line"> array[c++] = arr[l++];</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">while</span>(r<=right){<span class="comment">//处理右部分没处理完的</span></span><br><span class="line"> array[c++] = arr[r++];</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> num:array){<span class="comment">//最后再复制回原数组</span></span><br><span class="line"> arr[i++] = num;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 归并排序 </tag>
</tags>
</entry>
<entry>
<title>Redis在Springboot中的扩展</title>
<link href="/2022/07/07/%E9%A1%B9%E7%9B%AE/redis(1)/"/>
<url>/2022/07/07/%E9%A1%B9%E7%9B%AE/redis(1)/</url>
<content type="html"><![CDATA[<h1 id="Redis"><a href="#Redis" class="headerlink" title="Redis"></a>Redis</h1><h2 id="简要介绍"><a href="#简要介绍" class="headerlink" title="简要介绍"></a>简要介绍</h2><p><code>Redis</code>是完全开源的，遵守<code>BSD</code>协议，是一个高性能的<code>key</code>-<code>value</code>数据库。</p><p><code>Redis</code>与其他<code>key</code>-<code>value</code>缓存产品有以下三个特点：</p><ul><li><p><code>Redis</code>支持数据的持久化，可以将内存中的数据保存在磁盘中，重启的时候可以再次加载进行使用。</p></li><li><p><code>Redis</code>不仅仅支持简单的<code>key</code>-<code>value</code>类型的数据，同时还提供<code>list</code>，<code>set</code>，<code>zset</code>，<code>hash</code>等数据结构的存储。</p></li><li><p><code>Redis</code>支持数据的备份，即<code>master</code>-<code>slave</code>模式的数据备份。</p></li></ul><h2 id="基本命令"><a href="#基本命令" class="headerlink" title="基本命令"></a>基本命令</h2><blockquote><p>客户端</p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">redis-cli</span><br></pre></td></tr></table></figure><blockquote><p>服务器</p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">redis-server</span><br></pre></td></tr></table></figure><blockquote><p><code>redis</code>一共<code>16</code>个库(<code>0</code>-<code>15</code>)，选择库(示例选择第一个库)</p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">select 0</span><br></pre></td></tr></table></figure><blockquote><p>建立键值对（<code>key</code>: <code>test:count</code>, <code>value</code>: <code>1</code>）</p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">set test:count 1</span><br></pre></td></tr></table></figure><blockquote><p>根据键值得到键值对的值</p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">get test:count</span><br></pre></td></tr></table></figure><blockquote><p>对值(数字)加一</p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">incr test:count</span><br></pre></td></tr></table></figure><blockquote><p>对值(数字)减一</p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">decr test:count</span><br></pre></td></tr></table></figure><blockquote><p>查询库里一共有哪些<code>key</code></p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">key * </span><br></pre></td></tr></table></figure><blockquote><p>模糊查询库里<code>test</code>开头的<code>key</code>有哪些</p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">keys test*</span><br></pre></td></tr></table></figure><blockquote><p>查看某个<code>key</code>是什么类型(<code>test:user</code>是一个<code>key</code>)</p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">type test:user</span><br></pre></td></tr></table></figure><blockquote><p>查看某个key存不存在(<code>test:user</code>是一个<code>key</code>)</p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">exists test:user</span><br></pre></td></tr></table></figure><blockquote><p>删掉某个key(<code>test:user</code>是一个<code>key</code>)</p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">del test:user</span><br></pre></td></tr></table></figure><blockquote><p>设置key的过期时间，过期自动删除，最后的数字是代表秒数(<code>test:user</code>是一个<code>key</code>)</p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">expire test:user 10</span><br></pre></td></tr></table></figure><ul><li>哈希相关命令</li></ul><blockquote><p>建立哈希，示例一个<code>test:user</code>对象</p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">></span><span class="bash">hset <span class="built_in">test</span>:user id 1</span></span><br><span class="line">(integer) 1</span><br><span class="line"><span class="meta">></span><span class="bash">hset <span class="built_in">test</span>:user name zwz</span></span><br><span class="line">(integer) 1</span><br></pre></td></tr></table></figure><blockquote><p>取哈希值</p></blockquote><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">></span><span class="bash">hget <span class="built_in">test</span>:user id</span></span><br><span class="line">"1"</span><br><span class="line"><span class="meta">></span><span class="bash">hget <span class="built_in">test</span>:user name</span></span><br><span class="line">"zwz"</span><br></pre></td></tr></table></figure><ul><li>栈相关命令（左进右出）</li></ul><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">></span><span class="bash">lpush <span class="built_in">test</span>:ids 101 102 103 //从左边插入</span></span><br><span class="line">顺序("103" "102" "101")</span><br><span class="line"><span class="meta">></span><span class="bash">len <span class="built_in">test</span>:ids //长度</span></span><br><span class="line">(integer) 3</span><br><span class="line"><span class="meta">></span><span class="bash">lindex <span class="built_in">test</span>:ids 0 //查询下标0的value</span></span><br><span class="line">"103"</span><br><span class="line"><span class="meta">></span><span class="bash">lindex <span class="built_in">test</span>:ids 2 //查询下标2的value</span></span><br><span class="line">"101"</span><br><span class="line"><span class="meta">></span><span class="bash">lrange <span class="built_in">test</span>:ids 0 2</span></span><br><span class="line">"103"</span><br><span class="line">"102"</span><br><span class="line">"101"</span><br><span class="line"><span class="meta">></span><span class="bash">rpop <span class="built_in">test</span>:ids</span></span><br><span class="line">"101"</span><br><span class="line"><span class="meta">></span><span class="bash">rpop <span class="built_in">test</span>:ids</span></span><br><span class="line">"102"</span><br></pre></td></tr></table></figure><ul><li>集合相关命令（<code>Set</code>）</li></ul><p>集合中的元素无序</p><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">></span><span class="bash">sadd <span class="built_in">test</span>:teachers aaa bbb ccc ddd eee //添加命令</span></span><br><span class="line">(integer) 5</span><br><span class="line"><span class="meta">></span><span class="bash">scard <span class="built_in">test</span>:teachers //统计集合中有多少个元素</span></span><br><span class="line">(integer) 5</span><br><span class="line"><span class="meta">></span><span class="bash">spop <span class="built_in">test</span>:teachers //从集合中随机的弹出一个元素</span></span><br><span class="line">"ccc"</span><br><span class="line"><span class="meta">></span><span class="bash">smembers <span class="built_in">test</span>:teachers //查看集合中有多少个元素</span></span><br><span class="line">1) "aaa"</span><br><span class="line">2) "bbb"</span><br><span class="line">3) "ddd"</span><br><span class="line">4) "eee"</span><br></pre></td></tr></table></figure><ul><li>有序集合</li></ul><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">></span><span class="bash">zadd <span class="built_in">test</span>:students 10 aaa 20 bbb 30 ccc 40 ddd 50 eee</span></span><br><span class="line">(integer) 5</span><br><span class="line"><span class="meta">></span><span class="bash">zcard <span class="built_in">test</span>:students</span></span><br><span class="line">(integer) 5</span><br><span class="line"><span class="meta">></span><span class="bash">zscore <span class="built_in">test</span>:students ccc</span></span><br><span class="line">"30"</span><br><span class="line"><span class="meta">></span><span class="bash">zrank <span class="built_in">test</span>:students ccc //按分数值递增(从小到大)顺序排列</span></span><br><span class="line">(integer) 2</span><br><span class="line"><span class="meta">></span><span class="bash">zrange <span class="built_in">test</span>:students 0 2 //成员的位置按分数值递增(从小到大)来排序</span></span><br><span class="line">1) "aaa"</span><br><span class="line">2) "bbb"</span><br><span class="line">3) "ccc"</span><br></pre></td></tr></table></figure><h2 id="Spring整合Redis"><a href="#Spring整合Redis" class="headerlink" title="Spring整合Redis"></a>Spring整合Redis</h2><h3 id="导包"><a href="#导包" class="headerlink" title="导包"></a>导包</h3><p><code>pop.xml</code></p><figure class="highlight xml"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment"><!--redis(2.1.7.RELEASE)--></span></span><br><span class="line"><span class="comment"><!-- https://mvnrepository.com/artifact/org.springframework.boot/spring-boot-starter-data-redis --></span></span><br><span class="line"><span class="tag"><<span class="name">dependency</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">groupId</span>></span>org.springframework.boot<span class="tag"></<span class="name">groupId</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">artifactId</span>></span>spring-boot-starter-data-redis<span class="tag"></<span class="name">artifactId</span>></span></span><br><span class="line"><span class="tag"></<span class="name">dependency</span>></span></span><br></pre></td></tr></table></figure><h3 id="redis配置类"><a href="#redis配置类" class="headerlink" title="redis配置类"></a>redis配置类</h3><p><code>RedisConfig.java</code></p><blockquote><p><code>Springboot</code>自身有针对<code>redis</code>的配置类，但是<code>key</code>是<code>Object</code>类型，故可以自己根据<code>key</code>的类型需要设计一个<code>redis</code>配置类</p></blockquote><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">@Configuration</span></span><br><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">RedisConfig</span> </span>{</span><br><span class="line"> <span class="meta">@Bean</span></span><br><span class="line"> <span class="function"><span class="keyword">public</span> RedisTemplate<String, Object> <span class="title">redisTemplate</span><span class="params">(RedisConnectionFactory factory)</span> </span>{<span class="comment">//Redis工厂</span></span><br><span class="line"> RedisTemplate<String, Object> template = <span class="keyword">new</span> RedisTemplate<>();</span><br><span class="line"> template.setConnectionFactory(factory);</span><br><span class="line"></span><br><span class="line"> <span class="comment">//设置key序列化方式</span></span><br><span class="line"> template.setKeySerializer(RedisSerializer.string());</span><br><span class="line"></span><br><span class="line"> <span class="comment">//设置value序列化方式</span></span><br><span class="line"> template.setValueSerializer(RedisSerializer.json());</span><br><span class="line"></span><br><span class="line"> <span class="comment">//设置hash key序列化方式</span></span><br><span class="line"> template.setHashKeySerializer(RedisSerializer.string());</span><br><span class="line"></span><br><span class="line"> <span class="comment">//设置hash value序列化方式</span></span><br><span class="line"> template.setHashValueSerializer(RedisSerializer.json());</span><br><span class="line"></span><br><span class="line"> <span class="comment">//设置做完后触发生效</span></span><br><span class="line"> template.afterPropertiesSet();</span><br><span class="line"> <span class="keyword">return</span> template;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h3 id="redis工具类"><a href="#redis工具类" class="headerlink" title="redis工具类"></a>redis工具类</h3><p><code>RedisKeyUtil.java</code></p><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="class"><span class="keyword">class</span> <span class="title">RedisKeyUtil</span> </span>{</span><br><span class="line"></span><br><span class="line"> <span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">final</span> String SPILT = <span class="string">":"</span>;</span><br><span class="line"> <span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">final</span> String PREFIX_ENTITY_LIKE = <span class="string">"like:entity"</span>;<span class="comment">//点赞实体</span></span><br><span class="line"> <span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">final</span> String PREFIX_USER_LIKE = <span class="string">"like:user"</span>;<span class="comment">//点赞用户</span></span><br><span class="line"> <span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">final</span> String PREFIX_FOLLOWEE = <span class="string">"followee"</span>;<span class="comment">//关注</span></span><br><span class="line"> <span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">final</span> String PREFIX_FOLLOWER = <span class="string">"follower"</span>;<span class="comment">//粉丝</span></span><br><span class="line"> <span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">final</span> String PREFIX_KAPTCHA = <span class="string">"kaptcha"</span>;<span class="comment">//验证码</span></span><br><span class="line"> <span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">final</span> String PREFIX_TICKET = <span class="string">"ticket"</span>;<span class="comment">//凭证</span></span><br><span class="line"> <span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">final</span> String PREFIX_USER = <span class="string">"user"</span>;<span class="comment">//用户</span></span><br><span class="line"></span><br><span class="line"> <span class="comment">// 实体点赞key</span></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> String <span class="title">getEntityLikeKey</span><span class="params">(<span class="keyword">int</span> entityType, <span class="keyword">int</span> entityId)</span> </span>{<span class="comment">// entityType:entityId</span></span><br><span class="line"> <span class="keyword">return</span> PREFIX_ENTITY_LIKE + SPILT + entityType + SPILT + entityId;<span class="comment">// 例如-> like:entity:1:2</span></span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//某个用户的赞</span></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> String <span class="title">getUserLikeKey</span><span class="params">(<span class="keyword">int</span> userId)</span> </span>{</span><br><span class="line"> <span class="keyword">return</span> PREFIX_USER_LIKE + SPILT + userId;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//某个用户关注的实体</span></span><br><span class="line"> <span class="comment">// followee:userId:entityType -> zset(entityId, now)</span></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> String <span class="title">getFolloweeKey</span><span class="params">(<span class="keyword">int</span> userId, <span class="keyword">int</span> entityType)</span> </span>{</span><br><span class="line"> <span class="keyword">return</span> PREFIX_FOLLOWEE + SPILT + userId + SPILT + entityType;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//某个实体的粉丝</span></span><br><span class="line"> <span class="comment">// follower:entityType:entityId -> zset(userId, now)</span></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> String <span class="title">getFollowerKey</span><span class="params">(<span class="keyword">int</span> entityType, <span class="keyword">int</span> entityId)</span> </span>{</span><br><span class="line"> <span class="keyword">return</span> PREFIX_FOLLOWER + SPILT + entityType + SPILT + entityId;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//登录验证码</span></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> String <span class="title">getKaptchaKey</span><span class="params">(String owner)</span> </span>{</span><br><span class="line"> <span class="keyword">return</span> PREFIX_KAPTCHA + SPILT + owner;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//登陆凭证</span></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> String <span class="title">getTicketKey</span><span class="params">(String ticket)</span> </span>{</span><br><span class="line"> <span class="keyword">return</span> PREFIX_TICKET + SPILT + ticket;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//用户信息</span></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">static</span> String <span class="title">getUserKey</span><span class="params">(<span class="keyword">int</span> userId)</span> </span>{</span><br><span class="line"> <span class="keyword">return</span> PREFIX_USER + SPILT + userId;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line">}</span><br></pre></td></tr></table></figure><h3 id="点赞服务"><a href="#点赞服务" class="headerlink" title="点赞服务"></a>点赞服务</h3><p>service中点赞代码示例</p><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">@Autowired</span></span><br><span class="line"><span class="keyword">private</span> RedisTemplate redisTemplate;</span><br><span class="line"></span><br><span class="line"><span class="comment">// 点赞</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">like</span><span class="params">(<span class="keyword">int</span> userId, <span class="keyword">int</span> entityType, <span class="keyword">int</span> entityId, <span class="keyword">int</span> entityUserId)</span> </span>{</span><br><span class="line"> redisTemplate.execute(<span class="keyword">new</span> SessionCallback() {</span><br><span class="line"> <span class="meta">@Override</span></span><br><span class="line"> <span class="function"><span class="keyword">public</span> Object <span class="title">execute</span><span class="params">(RedisOperations operations)</span> <span class="keyword">throws</span> DataAccessException </span>{</span><br><span class="line"> String entityLikeKey = RedisKeyUtil.getEntityLikeKey(entityType, entityId);<span class="comment">//获取实体点赞key</span></span><br><span class="line"> String userLikeKey = RedisKeyUtil.getUserLikeKey(entityUserId);<span class="comment">//获取用户点赞key</span></span><br><span class="line"></span><br><span class="line"> <span class="keyword">boolean</span> isMember = operations.opsForSet().isMember(entityLikeKey, userId);<span class="comment">//获取当前用户是否点赞</span></span><br><span class="line"> operations.multi();<span class="comment">//开启事务</span></span><br><span class="line"> <span class="keyword">if</span> (isMember) {<span class="comment">//已点赞则再点就是取消点赞，数量减一</span></span><br><span class="line"> operations.opsForSet().remove(entityLikeKey, userId);</span><br><span class="line"> operations.opsForValue().decrement(userLikeKey);</span><br><span class="line"> } <span class="keyword">else</span> {<span class="comment">//没有点赞则再点就是点赞，数量加一</span></span><br><span class="line"> operations.opsForSet().add(entityLikeKey, userId);</span><br><span class="line"> operations.opsForValue().increment(userLikeKey);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> operations.exec();<span class="comment">//事务提交</span></span><br><span class="line"> }</span><br><span class="line"> });</span><br><span class="line">}</span><br></pre></td></tr></table></figure><p>其余代码请看<a href="https://github.com/2455781639/nowcoder_project">项目</a></p>]]></content>
<categories>
<category> 项目开发 </category>
</categories>
<tags>
<tag> 待更新 </tag>
<tag> Java </tag>
<tag> Springboot </tag>
<tag> Redis </tag>
</tags>
</entry>
<entry>
<title>nowcoderProject</title>
<link href="/2022/07/07/%E9%A1%B9%E7%9B%AE/nowcoder_project/"/>
<url>/2022/07/07/%E9%A1%B9%E7%9B%AE/nowcoder_project/</url>
<content type="html"><![CDATA[<h1 id="待更，等项目全部完善后更新"><a href="#待更，等项目全部完善后更新" class="headerlink" title="待更，等项目全部完善后更新"></a>待更，等项目全部完善后更新</h1>]]></content>
<categories>
<category> 项目开发 </category>
</categories>
<tags>
<tag> 待更新 </tag>
<tag> Java </tag>
<tag> Springboot </tag>
<tag> Redis </tag>
<tag> Kafka </tag>
<tag> Elastisearch </tag>
</tags>
</entry>
<entry>
<title>LeetCode刷题篇(6)-每日一题</title>
<link href="/2022/06/24/leetcode/LeetCode(6)/"/>
<url>/2022/06/24/leetcode/LeetCode(6)/</url>
<content type="html"><![CDATA[<p><a href="https://leetcode.cn/problems/find-largest-value-in-each-tree-row/">题目链接</a></p><h1 id="题意"><a href="#题意" class="headerlink" title="题意"></a>题意</h1><h2 id="给定一棵二叉树的根节点root，请找出该二叉树中每一层的最大值。"><a href="#给定一棵二叉树的根节点root，请找出该二叉树中每一层的最大值。" class="headerlink" title="给定一棵二叉树的根节点root，请找出该二叉树中每一层的最大值。"></a>给定一棵二叉树的根节点<code>root</code>，请找出该二叉树中每一层的最大值。</h2><blockquote><p>cin:<br>root = [1,3,2,5,3,null,9]</p><p>cout:<br>[1,3,9]</p></blockquote><h1 id="题解代码"><a href="#题解代码" class="headerlink" title="题解代码"></a>题解代码</h1><blockquote><p>leetcode以后均为java编写</p></blockquote><ul><li>深度优先搜索</li></ul><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> List<Integer> <span class="title">largestValues</span><span class="params">(TreeNode root)</span> </span>{</span><br><span class="line"> <span class="keyword">if</span>(root == <span class="keyword">null</span>){</span><br><span class="line"> <span class="keyword">return</span> <span class="keyword">new</span> ArrayList<Integer>();</span><br><span class="line"> }</span><br><span class="line"> List<Integer> list = <span class="keyword">new</span> ArrayList<Integer>();</span><br><span class="line"> selectMax(list,root,<span class="number">0</span>);</span><br><span class="line"> <span class="keyword">return</span> list;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="function"><span class="keyword">public</span> <span class="keyword">void</span> <span class="title">selectMax</span><span class="params">(List<Integer> list, TreeNode node, <span class="keyword">int</span> height)</span></span>{</span><br><span class="line"> <span class="keyword">if</span>(height == list.size()){</span><br><span class="line"> list.add(node.val);</span><br><span class="line"> }<span class="keyword">else</span>{</span><br><span class="line"> list.set(height,Math.max(node.val,list.get(height)));</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(node.left != <span class="keyword">null</span>){</span><br><span class="line"> selectMax(list,node.left,height+<span class="number">1</span>);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(node.right != <span class="keyword">null</span>){</span><br><span class="line"> selectMax(list,node.right,height+<span class="number">1</span>);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><ul><li>广度优先搜索</li></ul><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>{</span><br><span class="line"> <span class="function"><span class="keyword">public</span> List<Integer> <span class="title">largestValues</span><span class="params">(TreeNode root)</span> </span>{</span><br><span class="line"> <span class="keyword">if</span>(root == <span class="keyword">null</span>){</span><br><span class="line"> <span class="keyword">return</span> <span class="keyword">new</span> ArrayList<Integer>();</span><br><span class="line"> }</span><br><span class="line"> List<Integer> list = <span class="keyword">new</span> ArrayList<Integer>();</span><br><span class="line"> Queue<TreeNode> queue = <span class="keyword">new</span> ArrayDeque<TreeNode>();</span><br><span class="line"> queue.offer(root);</span><br><span class="line"> <span class="keyword">while</span>(!queue.isEmpty()){</span><br><span class="line"> <span class="keyword">int</span> len = queue.size();</span><br><span class="line"> <span class="keyword">int</span> max_ = Integer.MIN_VALUE;</span><br><span class="line"> <span class="keyword">while</span>(len > <span class="number">0</span>){</span><br><span class="line"> len--;</span><br><span class="line"> TreeNode tree = queue.poll();</span><br><span class="line"> max_ = Math.max(tree.val,max_);</span><br><span class="line"> <span class="keyword">if</span>(tree.left != <span class="keyword">null</span>){</span><br><span class="line"> queue.offer(tree.left);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(tree.right != <span class="keyword">null</span>){</span><br><span class="line"> queue.offer(tree.right);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> list.add(max_);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> list;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><blockquote><p>此题目中调用的方法以及使用的数据结构详细如下：</p></blockquote><ol><li><code>List<Integer> list = new ArrayList<Integer>();</code></li></ol><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br></pre></td><td class="code"><pre><span class="line">List(接口):</span><br><span class="line"> 1. List集合类中元素有序(添加顺序和取出顺序一致)，且可重复</span><br><span class="line"> 2. List集合中每个元素都有其对应的顺序索引，即支持索引</span><br><span class="line"> 3. List容器中元素都对应一个整数型的序号记载其在容器中的位置，可以根据序号取容器中的元素</span><br><span class="line"> 4. JDK API中List接口的实现类非常多，常用的有ArrayList，Set，Vector</span><br><span class="line"></span><br><span class="line">ArrayList(数组队列):</span><br><span class="line"> 1. 继承了 AbstractList并实现了List接口</span><br><span class="line"> 2. ArrayList支持可以根据需要增长的动态数组</span><br><span class="line"> 方法:</span><br><span class="line"> add():向集合中添加相应的元素，依次添加。Collection - ArrayList 源码解析</span><br></pre></td></tr></table></figure><p><a href="https://www.pdai.tech/md/java/collection/java-collection-ArrayList.html#collection---arraylist-%E6%BA%90%E7%A0%81%E8%A7%A3%E6%9E%90">Collection - ArrayList 源码解析</a></p><ol start="2"><li><code>Queue<TreeNode> queue = new ArrayDeque<TreeNode>();</code></li></ol><p><a href="https://www.pdai.tech/md/java/collection/java-collection-Queue&Stack.html#queue">Queue</a></p><p><a href="https://www.pdai.tech/md/java/collection/java-collection-Queue&Stack.html#deque">Deque</a></p>]]></content>
<categories>
<category> LeetCode </category>
</categories>
<tags>
<tag> Java </tag>
<tag> 深度搜索 </tag>
<tag> 广度搜索 </tag>
</tags>
</entry>
<entry>
<title>蓝桥杯刷题_09_板子&结束</title>
<link href="/2022/06/12/%E8%93%9D%E6%A1%A5%E6%9D%AF/lanqiao_09/"/>
<url>/2022/06/12/%E8%93%9D%E6%A1%A5%E6%9D%AF/lanqiao_09/</url>
<content type="html"><![CDATA[<h1 id="快速幂"><a href="#快速幂" class="headerlink" title="快速幂"></a>快速幂</h1><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><bits/stdc++.h></span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"><span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">long</span> ll;</span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> mod 1000000007</span></span><br><span class="line"><span class="keyword">int</span> dp[<span class="number">10000005</span>];</span><br><span class="line"></span><br><span class="line"><span class="function">ll <span class="title">qqow</span><span class="params">(ll a,ll b)</span></span>{</span><br><span class="line"> ll ans=<span class="number">1</span>,base = a;</span><br><span class="line"> <span class="keyword">while</span>(b > <span class="number">0</span>){</span><br><span class="line"> <span class="keyword">if</span>(b&<span class="number">1</span> != <span class="number">0</span>){</span><br><span class="line"> ans = (ans*base)%mod;</span><br><span class="line"> }</span><br><span class="line"> base = (base*base)%mod;</span><br><span class="line"> b>>=<span class="number">1</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> ans;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> cout<<<span class="built_in">qqow</span>(<span class="number">2</span>,<span class="number">10</span>);</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h1 id="结束"><a href="#结束" class="headerlink" title="结束"></a>结束</h1><p>伴随着2022/6/18结束，我的蓝桥之旅结束。</p><p><img src="/img/lanqiao/lanqiao1.jpg" alt="考场"></p><p><img src="/img/lanqiao/lanqiao2.png" alt="结束"></p><p><img src="/img/lanqiao/lanqiao3.jpg" alt="战服正面"></p><p><img src="/img/lanqiao/lanqiao4.jpg" alt="战服反面"></p>]]></content>
<categories>
<category> 蓝桥杯 </category>
</categories>
<tags>
<tag> C/C++ </tag>
<tag> 蓝桥杯 </tag>
</tags>
</entry>
<entry>
<title>项目开发感触</title>
<link href="/2022/05/12/own/"/>
<url>/2022/05/12/own/</url>
<content type="html"><![CDATA[<h1 id="第一个Springboot项目-员工管理系统-有感而发"><a href="#第一个Springboot项目-员工管理系统-有感而发" class="headerlink" title="第一个Springboot项目(员工管理系统)有感而发"></a>第一个Springboot项目(员工管理系统)有感而发</h1><hr><p><a href="https://github.com/2455781639/first_Springboot_project">项目链接</a></p><blockquote><p> 首先这个项目具体是在b站狂神说Java中跟着学的一个项目，静态资源与后端的联系非常紧密，可以说是非常的密切，友好的连接后端和前端静态资源最完美的方法我觉得现如今是Thymeleaf模板引擎，thymeleaf可以很完美的将前端跳转到后端并传输相应的数据，同样的后端也可以完美的将数据通过Model、httpSession等封装传给前端，前后端分离中间的缝合就是由Thymeleaf完成。</p><p> 但是Thymeleaf要学的东西很多很多，如果我掌握甚至说精通Thymeleaf，那么我也可以说我什么系统以后能够拿下，至于其中的实现难度或者说逻辑难度另说，首要要做的还是要熟悉Thymeleaf的语法，其次是Mybatis/MybatisPlus与Springboot的整合，业务逻辑都是由Dao层实现，但是每一个业务逻辑我们作为一个成年人是很容易构想出来的，但是实现呢？实现的过程呢？，这是个问题，不仅仅跳转来回就能实现，主要还是考察我SQL代码的编写能力以及数据库中表字段，表与表之间的联系以及Mybatis/MybatisPlus的熟练运用，这是很关键也是很致命的一步，如果这一步解决的话那么其他的代码编写那就没有任何问题（单单指的是业务代码）。</p><p> 那么对于上面所说到的SQL以及Mybatis整合，考察的还是SQL编程能力，不仅仅是CRUD，还要尽可能的实现系统该实现的所有的业务，不能畏难，要勇于直前，尽可能的挖掘项目系统中所有可以想到的业务并把它实现。（SQL学习）</p><p> 一个项目系统的实现肯定不仅仅是有增删改查，很多数据的呈现，数据的整理，数据的更改都有着一定的规律/规定，并且项目系统的安全也是必须要考量的，系统的安全这就涉及到系统的普通用户和管理员的权限问题，以及可能涉及到的游客或者系统中存在其他低权限管理员（高级用户）等用户的存在，所以必须考虑安全问题。</p><p> 总结：第一次的Springboot项目缺点很多，但是给了我足够多的知识、信心和让我知道了我有多么的不足，让我更有信心去往更深层次的项目开展。</p><p>日期： 2022/5/12 18:14 作者：张文卓</p></blockquote>]]></content>
</entry>
<entry>
<title>Springboot学习&Model数据经过重定向丢失</title>
<link href="/2022/05/12/Springboot%E5%AD%A6%E4%B9%A0/Springboot002/"/>
<url>/2022/05/12/Springboot%E5%AD%A6%E4%B9%A0/Springboot002/</url>
<content type="html"><![CDATA[<h1 id="Model数据经过重定向丢失"><a href="#Model数据经过重定向丢失" class="headerlink" title="Model数据经过重定向丢失"></a>Model数据经过重定向丢失</h1><p>在这里说明一下有两种解决方案</p><blockquote><p>重定向不改变</p></blockquote><h2 id="第一种解决方案"><a href="#第一种解决方案" class="headerlink" title="第一种解决方案"></a>第一种解决方案</h2><p><code>Model</code> 换成 <code>RedirectAttributesModelMap</code></p><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">RedirectAttributesModelMap model;</span><br><span class="line">model.addAttribute(<span class="string">"department"</span>,list);</span><br></pre></td></tr></table></figure><h2 id="第二种解决方案"><a href="#第二种解决方案" class="headerlink" title="第二种解决方案"></a>第二种解决方案</h2><p>利用session传输数据</p><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">HttpSession session;</span><br><span class="line">session.setAttribute(<span class="string">"department"</span>,list);</span><br></pre></td></tr></table></figure>]]></content>
<categories>
<category> Springboot </category>
</categories>
<tags>
<tag> Java </tag>
<tag> Spring </tag>
<tag> Springboot </tag>
</tags>
</entry>
<entry>
<title>JavaScript表单验证</title>
<link href="/2022/05/12/Springboot%E5%AD%A6%E4%B9%A0/js_form/"/>
<url>/2022/05/12/Springboot%E5%AD%A6%E4%B9%A0/js_form/</url>
<content type="html"><![CDATA[<h1 id="JavaScript-校验表单弹框"><a href="#JavaScript-校验表单弹框" class="headerlink" title="JavaScript 校验表单弹框"></a>JavaScript 校验表单弹框</h1><h1 id="1"><a href="#1" class="headerlink" title="1"></a>1</h1><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">function</span> <span class="title">alertBox</span>(<span class="params">message, callback</span>) </span>{</span><br><span class="line"> <span class="keyword">if</span> (!message) <span class="keyword">return</span> <span class="literal">false</span>;</span><br><span class="line"></span><br><span class="line"> <span class="keyword">var</span> template_alert_box =</span><br><span class="line"> <span class="string">'<div class="modal" id="alert-box" tabindex="-1" role="dialog">'</span>+</span><br><span class="line"> <span class="string">'<div class="modal-dialog" role="document" style="margin:100px auto;">'</span>+</span><br><span class="line"> <span class="string">'<div class="modal-content">'</span>+</span><br><span class="line"> <span class="string">'<div class="modal-header">'</span>+</span><br><span class="line"> <span class="string">'<h5 class="modal-title">提示</h5>'</span>+</span><br><span class="line"> <span class="string">'<button type="button" class="close" data-dismiss="modal" aria-label="Close">'</span>+</span><br><span class="line"> <span class="string">'<span aria-hidden="true">&times;</span>'</span>+</span><br><span class="line"> <span class="string">'</button>'</span>+</span><br><span class="line"> <span class="string">'</div>'</span>+</span><br><span class="line"> <span class="string">'<div class="modal-body">'</span>+</span><br><span class="line"> <span class="string">'<p id="alert-box-message"></p>'</span>+</span><br><span class="line"> <span class="string">'</div>'</span>+</span><br><span class="line"> <span class="string">'<div class="modal-footer">'</span>+</span><br><span class="line"> <span class="string">'<button type="button" class="btn btn-primary" data-dismiss="modal">确定</button>'</span>+</span><br><span class="line"> <span class="string">'</div>'</span>+</span><br><span class="line"> <span class="string">'</div>'</span>+</span><br><span class="line"> <span class="string">'</div>'</span>+</span><br><span class="line"> <span class="string">'</div>'</span>;</span><br><span class="line"></span><br><span class="line"> <span class="keyword">if</span> ($(<span class="string">"#alert-box"</span>)) $(<span class="string">"#alert-box"</span>).remove();</span><br><span class="line"></span><br><span class="line"> <span class="keyword">var</span> $box = $(template_alert_box);</span><br><span class="line"> $box.find(<span class="string">"#alert-box-message"</span>).text(message);</span><br><span class="line"> $box.modal({<span class="attr">backdrop</span>:<span class="string">"static"</span>, <span class="attr">show</span>:<span class="literal">true</span>});</span><br><span class="line"> <span class="keyword">if</span> (callback) $box.on(<span class="string">'hidden.bs.modal'</span>, callback);</span><br><span class="line"> $(<span class="string">"body"</span>).append($box);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="literal">true</span>;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">function</span> <span class="title">checkEmail</span>(<span class="params"></span>)</span>{</span><br><span class="line"> <span class="keyword">const</span> strEmail = <span class="built_in">document</span>.add.email.value;</span><br><span class="line"> <span class="keyword">const</span> strRegex = <span class="regexp">/^(\w-*\.*)+@(\w-?)+(\.\w{2,})+$/</span>;</span><br><span class="line"> <span class="keyword">if</span> (strEmail.length===<span class="number">0</span>)</span><br><span class="line"> {</span><br><span class="line"> alertBox(<span class="string">"电子邮件不能为空!"</span>);</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(!strRegex.test(strEmail)){</span><br><span class="line"> alertBox(<span class="string">"邮箱输入有误!"</span>)</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">true</span>;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">function</span> <span class="title">checkDate</span>(<span class="params"></span>)</span>{</span><br><span class="line"> <span class="keyword">const</span> date__ = <span class="built_in">document</span>.add.birth.value;</span><br><span class="line"> <span class="keyword">const</span> re =<span class="regexp">/^(\d{4})-(\d{2})-(\d{2})$/</span>;</span><br><span class="line"> <span class="keyword">if</span>(!re.test(date__)){</span><br><span class="line"> <span class="comment">//判断日期格式为YYYY-MM-DD标准</span></span><br><span class="line"> alertBox(<span class="string">"日期校验格式有误，例如2022-10-10"</span>);</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">true</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><blockquote><p>样式如下</p></blockquote><p><img src="/img/SpringBoot/js_form_001.jpg" alt="弹框样式"></p><hr><font color="red"><p> 你好</p></font>]]></content>
<categories>
<category> Springboot </category>
</categories>
<tags>
<tag> 待更新 </tag>
<tag> JavaScript </tag>
</tags>
</entry>
<entry>
<title>MySQL&LeetCode刷题篇(1)</title>
<link href="/2022/05/02/SQL/mysql_04/"/>
<url>/2022/05/02/SQL/mysql_04/</url>
<content type="html"><![CDATA[<h2 id="LeetCode例题"><a href="#LeetCode例题" class="headerlink" title="LeetCode例题"></a>LeetCode例题</h2><h2 id="题目链接"><a href="#题目链接" class="headerlink" title="题目链接"></a><a href="https://leetcode-cn.com/problems/rank-scores/">题目链接</a></h2><p>题目意思是对分数做出排名，排名有要求</p><p><strong>例如</strong></p><table><thead><tr><th align="center">score</th><th align="center">rank</th></tr></thead><tbody><tr><td align="center"></td><td align="center"></td></tr><tr><td align="center">4.00</td><td align="center">1</td></tr><tr><td align="center"></td><td align="center"></td></tr><tr><td align="center">4.00</td><td align="center">1</td></tr><tr><td align="center"></td><td align="center"></td></tr><tr><td align="center">3.85</td><td align="center">2</td></tr><tr><td align="center"></td><td align="center"></td></tr><tr><td align="center">3.65</td><td align="center">3</td></tr><tr><td align="center"></td><td align="center"></td></tr><tr><td align="center">3.65</td><td align="center">3</td></tr><tr><td align="center"></td><td align="center"></td></tr><tr><td align="center">3.50</td><td align="center">4</td></tr></tbody></table><p>对于这种格式的排名首先可以想到：</p><blockquote><p>对于当前分数的名次应该是表中大于等于该分数的去重后的数量</p></blockquote><p>由此思路可以写出以下</p><figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">select</span> a.score <span class="keyword">as</span> score,</span><br><span class="line">(<span class="keyword">select</span> <span class="built_in">count</span>(<span class="keyword">distinct</span> b.score) <span class="keyword">from</span> Scores <span class="keyword">as</span> b <span class="keyword">where</span> b.score <span class="operator">>=</span> a.score) <span class="keyword">as</span> <span class="string">'rank'</span></span><br><span class="line"><span class="keyword">from</span> Scores <span class="keyword">as</span> a</span><br><span class="line"><span class="keyword">order</span> <span class="keyword">by</span> a.score <span class="keyword">desc</span>;</span><br></pre></td></tr></table></figure><p>代码中需要注意的是</p><blockquote><p>Rank之所以也加``（反单引号），是因为它也是MySQL的转义字符</p><p>它是对数据库名、表名、字段名、索引名和别名做的特殊处理</p><p>避免和 MySQL 本身的关键字发生冲突。</p></blockquote><p>但是运行时间会过于缓慢</p><h2 id="使用窗口函数dense-rank-over"><a href="#使用窗口函数dense-rank-over" class="headerlink" title="使用窗口函数dense_rank() over"></a>使用窗口函数<code>dense_rank() over</code></h2><figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">select</span> a.score <span class="keyword">as</span> score,</span><br><span class="line"><span class="built_in">dense_rank</span>() <span class="keyword">over</span>(<span class="keyword">order</span> <span class="keyword">by</span> score <span class="keyword">desc</span>) <span class="keyword">as</span> <span class="string">'rank'</span></span><br><span class="line"><span class="keyword">from</span> Scores <span class="keyword">as</span> a;</span><br></pre></td></tr></table></figure><p><code>dense_rank() over</code>: 并列排序，不会跳过重复序号</p><p>有关MySQL中rank的函数讲解：</p><p><a href="https://blog.csdn.net/qq_41057885/article/details/109176014">MySQL rank() over、dense_rank() over、row_number() over 用法介绍</a></p><p><a href="https://blog.csdn.net/java123456111/article/details/123784084">MySQL - 自动排序函数(dense_rank() over)</a></p>]]></content>
<categories>
<category> MySQL </category>
</categories>
<tags>
<tag> MySQL </tag>
<tag> LeetCode </tag>
</tags>
</entry>
<entry>
<title>JSR303校验</title>
<link href="/2022/04/23/Springboot%E5%AD%A6%E4%B9%A0/JSR303/"/>