add: 统计整数数目

Author: yi-ge

.vscode/settings.json

@@ -196,6 +196,7 @@
     "DCMAKE",
     "dearmour",
     "deque",
+    "dlimit",
     "dupenv",
     "efcfe",
     "egcfe",

README.md

@@ -850,3 +850,7 @@ C++标准库提供的数据结构实在是太多了，参考[C++标准库头文
 - [被列覆盖的最多行数](src/math/maximum_rows_covered_by_columns.cpp)  [位运算, 数组, 回溯, 枚举, 矩阵]
 
   - LeetCode 2397. 被列覆盖的最多行数 <https://leetcode.cn/problems/maximum-rows-covered-by-columns>
+
+- [统计整数数目](src/math/count_of_integers.cpp)  [数学, 字符串, 动态规划]
+
+  - LeetCode 2719. 统计整数数目 <https://leetcode.cn/problems/count-of-integers>

images/math/count_of_integers.jpeg

@@ -0,0 +1,44 @@
+// 统计整数数目
+// https://leetcode.cn/problems/count-of-integers
+// INLINE  ../../images/math/count_of_integers.jpeg
+
+#include <headers.hpp>
+
+class Solution {
+public:
+  int count(string num1, string num2, int min_sum, int max_sum) {
+    const int mod = 1000000007;
+    int m = num2.length();
+    std::vector<int> up_limit, down_limit;
+    for (char c : num2)
+      up_limit.push_back(c - '0');
+    num1 = std::string(std::max(0, m - static_cast<int>(num1.length())), '0') +
+           num1;
+    for (char c : num1)
+      down_limit.push_back(c - '0');
+
+    std::function<int(int, int, bool, bool, bool)> f;
+    std::unordered_map<long long, int> memo;
+
+    f = [&](int i, int s, bool valid, bool dlimit, bool ulimit) -> int {
+      if (i == m) {
+        return valid && min_sum <= s && s <= max_sum ? 1 : 0;
+      }
+      long long key =
+          i + 71LL * (s + 71LL * (valid + 2LL * (dlimit + 2LL * ulimit)));
+      if (memo.count(key))
+        return memo[key];
+      int down = dlimit ? down_limit[i] : 0;
+      int up = ulimit ? up_limit[i] : 9;
+      int ans = 0;
+      for (int d = down; d <= up; ++d) {
+        ans = (ans + f(i + 1, s + d, valid || d != 0, dlimit && d == down,
+                       ulimit && d == up)) %
+              mod;
+      }
+      return memo[key] = ans;
+    };
+
+    return f(0, 0, false, true, true);
+  }
+};

src/math/count_of_integers.cpp

@@ -1,4 +1,4 @@
-// 执行编译时间：2024-01-13 14:28:48
+// 执行编译时间：2024-01-16 09:18:43
 #include <gtest/gtest.h>
 #include <lib.hpp>
 

test/lib/lib_test.cpp

@@ -0,0 +1,26 @@
+#include <math/count_of_integers.cpp>
+
+TEST(统计整数数目, count) {
+  Solution solution;
+  // 示例 1：
+  // 输入：num1 = "1", num2 = "12", min_num = 1, max_num = 8
+  // 输出：11
+  // 解释：总共有 11 个整数的数位和在 1 到 8 之间，分别是 1,2,3,4,5,6,7,8,10,11
+  // 和 12 。所以我们返回 11 。
+  string num1 = "1";
+  string num2 = "12";
+  int min_sum = 1;
+  int max_sum = 8;
+  EXPECT_EQ(solution.count(num1, num2, min_sum, max_sum), 11);
+
+  // 示例 2：
+  // 输入：num1 = "1", num2 = "5", min_num = 1, max_num = 5
+  // 输出：5
+  // 解释：数位和在 1 到 5 之间的 5 个整数分别为 1,2,3,4 和 5 。所以我们返回 5
+  // 。
+  num1 = "1";
+  num2 = "5";
+  min_sum = 1;
+  max_sum = 5;
+  EXPECT_EQ(solution.count(num1, num2, min_sum, max_sum), 5);
+}