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algorithm/acwing/code/ACWing.iml

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+<?xml version="1.0" encoding="UTF-8"?>
+<module type="JAVA_MODULE" version="4">
+  <component name="NewModuleRootManager" inherit-compiler-output="true">
+    <exclude-output />
+    <content url="file://$MODULE_DIR$">
+      <sourceFolder url="file://$MODULE_DIR$/src" isTestSource="false" />
+    </content>
+    <orderEntry type="inheritedJdk" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+</module>

algorithm/acwing/code/src/a_BinaryAlgorithm/T789.java

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+package a_BinaryAlgorithm;
+
+import java.io.BufferedReader;
+import java.io.InputStreamReader;
+import java.util.Scanner;
+
+/**
+ * @problem 789数的范围
+ * @idea 二分法查找
+ */
+public class T789 {
+    public static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
+    public static final Scanner sc =new Scanner(System.in);
+    public static int n, q;
+    public static void main(String[] args) throws Exception{
+        n = sc.nextInt();
+        q = sc.nextInt();
+        int k;
+        int[] arr = new int[n];
+        String[] nums = br.readLine().split(" ");
+        for (int i = 0; i < n; i++) {
+            arr[i] = Integer.parseInt(nums[i]);
+        }
+        for (int i = 0; i < q; i++) {
+            k = sc.nextInt();
+            startToEnd(arr, k);
+        }
+    }
+
+    public static void startToEnd(int[] arr, int k){
+        int l = 0, r = n - 1;
+        while (l < r){
+            int mid = (l + r) / 2;
+            if (arr[mid] >= k) r = mid;
+            else l = mid + 1;
+        }
+        if(arr[l] != k) System.out.println("-1 -1");
+        else {
+            System.out.println(l + " ");
+            l = 0;
+            r = n - 1;
+            while (l < r){
+                int mid = (l + r + 1) / 2;
+                if(arr[mid] <= k) l = mid;
+                else r = mid - 1;
+            }
+            System.out.println(l);
+        }
+    }
+}

algorithm/acwing/code/src/a_BinaryAlgorithm/T790.java

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+package a_BinaryAlgorithm;
+
+import java.util.Scanner;
+
+/**
+ * @problem 790数的三次方根
+ * @idea 二分法
+ */
+public class T790 {
+    public static void main(String[] args) {
+        double n = new Scanner(System.in).nextDouble();
+        cubeRoot(n);
+    }
+
+    private static void cubeRoot(double n) {
+        double l, r;
+        double abs_n = Math.abs(n);
+        if(abs_n <= 1){
+            l = abs_n;
+            r = 1;
+        }else {
+            l = 1;
+            r = abs_n;
+        }
+        while (r - l > 1e-8){
+            double mid = (l + r) / 2;
+            if(mid * mid * mid <= abs_n) l = mid;
+            else r = mid;
+        }
+        System.out.println(String.format("%.6f", n >= 0 ? l : -l));
+    }
+}

algorithm/acwing/code/src/a_BinaryAlgorithm/Template.java

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+package a_BinaryAlgorithm;
+
+public class Template {
+    /**
+     * 检查x是够满足某种性质
+     * @param x
+     * @return
+     */
+    public static<E> boolean check(E x){
+        /*...*/
+        return true;
+    }
+
+    /**
+     * 区间[l, r]被划分成[l, mid]和[mid + 1, r]时使用。用于确定最左端的位置
+     * @param l
+     * @param r
+     * @return
+     */
+    public static int bSearchLeft(int l, int r){
+        while (l < r){
+            int mid = l + r >> 1;
+            if(check(mid)) r = mid;
+            else l = mid + 1;
+        }
+        return l;
+    }
+
+    /**
+     * 区间[l, r]被划分成[l, mid - 1]和[mid, r]时使用。用于确定最右端的位置
+     * @param l
+     * @param r
+     * @return
+     */
+    public static int bSearchRight(int l, int r){
+        while (l < r){
+            int mid = l + r + 1 >> 1;
+            if(check(mid)) l = mid;
+            else r = mid - 1;
+        }
+        return l;
+    }
+}

algorithm/acwing/code/src/b_MergeAlgorithm/T788.java

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+package b_MergeAlgorithm;
+
+import java.io.BufferedReader;
+import java.io.IOException;
+import java.io.InputStreamReader;
+
+/**
+ * @problem 788逆序对的数量
+ * @Idea 归并排序
+ */
+public class T788 {
+    public static int n;
+    public static int[] arrTemp = new int[100010];
+    public static long rp = 0;
+    public static final BufferedReader br = new BufferedReader(new InputStreamReader((System.in)));
+    public static void main(String[] args) throws IOException {
+        n = Integer.parseInt(br.readLine());
+        int[] arr = new int[n];
+        String[] nums = br.readLine().split(" ");
+        for (int i = 0; i < n; i++) {
+            arr[i] = Integer.parseInt(nums[i]);
+        }
+        reversePairs(arr, 0, n - 1);
+        System.out.println(rp);
+        br.close();
+    }
+
+    public static void reversePairs(int[] arr, int low, int high){
+        if(low < high){
+            int mid = (low + high) / 2;
+            reversePairs(arr, low, mid);
+            reversePairs(arr, mid + 1, high);
+            for (int i = low; i <= high; i++) {
+                arrTemp[i] = arr[i];
+            }
+            int i = low, j = mid + 1;
+            int k = low;
+            while (i <= mid && j <=high){
+                if (arrTemp[i] <= arrTemp[j]) arr[k++] = arrTemp[i++];
+                else {
+                    arr[k++] = arrTemp[j++];
+                    rp += mid - i + 1;
+                }
+            }
+            while (i <= mid) arr[k++] = arrTemp[i++];
+            while (j <= high) arr[k++] = arrTemp[j++];
+        }
+    }
+}

algorithm/acwing/code/src/c_PrefixSum/T795.java

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+package c_PrefixSum;
+
+import java.util.Scanner;
+
+/**
+ * @problem 795.一维前缀和
+ * @idea 前缀和算法
+ */
+public class T795 {
+    public static void main(String[] args) {
+        Scanner sc = new Scanner(System.in);
+        int n = sc.nextInt();
+        int m = sc.nextInt();
+        int[] num = new int[n];
+        int[] s = new int[n + 1];
+        for (int i = 0; i < n; i++) {
+            num[i] = sc.nextInt();
+            s[i + 1] = s[i] + num[i];
+        }
+        while (m > 0){
+            int l = sc.nextInt();
+            int r = sc.nextInt();
+            System.out.println(s[r] - s[l - 1]);
+            --m;
+        }
+    }
+}

algorithm/acwing/code/src/c_PrefixSum/T796.java

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+package c_PrefixSum;
+
+import java.util.Scanner;
+/**
+ * @problem 796.二维前缀和
+ * @idea 前缀和算法
+ */
+public class T796 {
+    public static void main(String[] args) {
+        Scanner sc = new Scanner(System.in);
+        int n = sc.nextInt();
+        int m = sc.nextInt();
+        int q = sc.nextInt();
+        int[][] num = new int[n + 1][m + 1];
+        int[][] s = new int[n + 1][m + 1];
+        for (int i = 1; i <= n; i++) {
+            for (int j = 1; j <= m; j++) {
+                num[i][j] = sc.nextInt();
+                s[i][j] = s[i - 1][j] + s[i][j - 1] - s[i - 1][j - 1] + num[i][j];
+            }
+        }
+        while (q > 0){
+            int x1 = sc.nextInt();
+            int y1 = sc.nextInt();
+            int x2 = sc.nextInt();
+            int y2 = sc.nextInt();
+            System.out.println(s[x2][y2] - s[x2][y1 - 1] - s[x1 - 1][y2] + s[x1 - 1][y1 - 1]);
+            --q;
+        }
+    }
+}

algorithm/acwing/code/src/d_DifferenceMethod/T797.java

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+package d_DifferenceMethod;
+
+import java.util.Scanner;
+
+public class T797 {
+    public static void main(String[] args) {
+        Scanner sc = new Scanner(System.in);
+        int n = sc.nextInt();
+        int m = sc.nextInt();
+        int[] a = new int[n + 1];
+        int[] b = new int[n + 1];
+        for (int i = 1; i <= n; ++i){
+            a[i] = sc.nextInt();
+            b[i] = a[i] - a[i - 1];
+        }
+        while (m > 0){
+            int l = sc.nextInt();
+            int r = sc.nextInt();
+            int c = sc.nextInt();
+            b[l] += c;
+            if(r < n) b[r + 1] -= c;
+            --m;
+        }
+        for (int i = 1; i <= n; i++) {
+            a[i] = a[i - 1] + b[i];
+            System.out.print(a[i] + " ");
+        }
+    }
+}

algorithm/acwing/notes/1前缀和.md

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+## 前缀和
+
+---
+
+### 一维前缀和  
+
+#### 一维前缀和是什么
+原数组: a[1], a[2], a[3], a[4], a[5], …, a[n]
+
+前缀和 S[i]为数组的前 i 项和
+
+前缀和: S[i] = a[1] + a[2] + a[3] + … + a[i]
+
+**注意：前缀和的下标从1开始，s[0]=0;**
+
+> s[0] = 0
+> s[1] = s[0] + a[1]
+>
+> s[2] = s[1] + a[2]
+>
+> ......
+>
+> s[i] = s[i - 1] + a[i]
+
+**前缀和的作用**
+快速求出元素组中某段区间的和
+
+**一维数组求解前缀和(Si)**
+
+1. for循环求出 每个S[i] (将 S[0] 定义为 0, 避免下标的转换)
+2. 求 [l, r]中的和, 即为 **==S[r] - S[l-1]==**
+```java
+public class Main {
+    public static void main(String[] args) {
+        Scanner sc = new Scanner(System.in);
+        int n = sc.nextInt();
+        int m = sc.nextInt();
+        int[] num = new int[n];
+        int[] s = new int[n + 1];
+        s[0] = 0;
+        for (int i = 0; i < n; i++) {
+            num[i] = sc.nextInt();
+            s[i + 1] = s[i] + num[i];
+        }
+        while (m > 0){
+            int l = sc.nextInt();
+            int r = sc.nextInt();
+            System.out.println(s[r] - s[l - 1]);
+            --m;
+        }
+    }
+}
+```
+
+### 二维前缀和  
+
+#### 二位前缀和是什么
+
+在一维前缀和的基础上，将一维数组改为了矩阵
+
+前缀和`S[i][j]`表示二维数组的前 i 行、前 j 列的和
+
+![<img src="https://img-blog.csdnimg.cn/20201214201734653.png"   width="10%">](https://img-blog.csdnimg.cn/20201217174700577.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80NTYyOTI4NQ==,size_16,color_FFFFFF,t_70)
+
+紫色面积是指(1,1)左上角到(i, j-1)右下角的矩形面积, 绿色面积是指(1,1)左上角到(i-1, j )右下角的矩形面积。
+
+*每一个颜色的矩形面积都代表了它所包围元素的和。*
+
+从图中我们很容易看出，整个外围蓝色矩形面积s[i][j] = 绿色面积`s[i-1][j]` + 紫色面积`s[i][j-1]` - 重复加的红色的面积`s[i-1][j-1]`+小方块的面积`a[i][j]`;
+
+**注意：前缀和的下标从i=1, j=1开始，`s[0][i]=0、s[j][0]=0`;**
+
+
+
+#### 公式
+
+==**`s[i][j] = s[i - 1][j] + s[i][j - 1] + a[i][j] - s[i - 1][j - 1]`**==
+
+以`(x1, y1)`为左上角，`(x2, y2)`为右下角的矩阵的和为：**==`s[x2][y2] - s[x1 -1][y2] - s[x2][y1 - 1] + s[x1 - 1][y1 - 1]`==**
+
+![<img src="https://img-blog.csdnimg.cn/2020121717185394.png"   width="80%">](https://img-blog.csdnimg.cn/20201217174751639.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80NTYyOTI4NQ==,size_16,color_FFFFFF,t_70)
+
+
+
+---
+
+**相关题目:**
+
+***AcWing 795 https://www.acwing.com/activity/content/problem/content/829/***
+
+***AcWing 796 https://www.acwing.com/activity/content/problem/content/830/***