add: 参加考试的最大学生数

README.md

@@ -790,3 +790,7 @@ 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
 - [不浪费原料的汉堡制作方案](src/math/number_of_burgers_with_no_waste_of_ingredients.cpp)  [数学]
 
   - LeetCode 1276. 不浪费原料的汉堡制作方案 <https://leetcode.cn/problems/number-of-burgers-with-no-waste-of-ingredients>
+
+- [参加考试的最大学生数](src/math/maximum_students_taking_exam.cpp)  [位运算, 数组, 动态规划, 状态压缩, 矩阵]
+
+  - LeetCode 1349. 参加考试的最大学生数 <https://leetcode.cn/problems/maximum-students-taking-exam>

src/math/maximum_students_taking_exam.cpp

@@ -0,0 +1,44 @@
+// 参加考试的最大学生数
+// https://leetcode.cn/problems/maximum-students-taking-exam
+// INLINE  ../../images/math/maximum_students_taking_exam.jpeg
+
+#include <headers.hpp>
+
+class Solution {
+public:
+  int maxStudents(vector<vector<char>> &seats) {
+    int m = seats.size();
+    int n = seats[0].size();
+    vector<int> ss(m);
+    vector<vector<int>> f(1 << n, vector<int>(m, -1));
+    for (int i = 0; i < m; ++i) {
+      for (int j = 0; j < n; ++j) {
+        if (seats[i][j] == '.') {
+          ss[i] |= 1 << j;
+        }
+      }
+    }
+    function<int(int, int)> dfs = [&](int seat, int i) -> int {
+      if (f[seat][i] != -1) {
+        return f[seat][i];
+      }
+      int ans = 0;
+      for (int mask = 0; mask < 1 << n; ++mask) {
+        if ((seat | mask) != seat || (mask & (mask << 1)) != 0) {
+          continue;
+        }
+        int cnt = __builtin_popcount(mask);
+        if (i == m - 1) {
+          ans = max(ans, cnt);
+        } else {
+          int nxt = ss[i + 1];
+          nxt &= ~(mask >> 1);
+          nxt &= ~(mask << 1);
+          ans = max(ans, cnt + dfs(nxt, i + 1));
+        }
+      }
+      return f[seat][i] = ans;
+    };
+    return dfs(ss[0], 0);
+  }
+};

test/lib/lib_test.cpp

@@ -1,4 +1,4 @@
-// 执行编译时间：2023-12-25 10:21:30
+// 执行编译时间：2023-12-26 10:04:16
 #include <gtest/gtest.h>
 #include <lib.hpp>
 

test/math/maximum_students_taking_exam_test.cpp

@@ -0,0 +1,41 @@
+#include <math/maximum_students_taking_exam.cpp>
+
+TEST(参加考试的最大学生数, maxStudents) {
+  Solution solution;
+  // 示例 1：
+  // 输入：seats = [["#",".","#","#",".","#"],
+  //               [".","#","#","#","#","."],
+  //               ["#",".","#","#",".","#"]]
+  // 输出：4
+  // 解释：教师可以让 4 个学生坐在可用的座位上，这样他们就无法在考试中作弊。
+  vector<vector<char>> seats = {{'#', '.', '#', '#', '.', '#'},
+                                {'.', '#', '#', '#', '#', '.'},
+                                {'#', '.', '#', '#', '.', '#'}};
+  EXPECT_EQ(solution.maxStudents(seats), 4);
+
+  // 示例 2：
+  // 输入：seats = [[".","#"],
+  //               ["#","#"],
+  //               ["#","."],
+  //               ["#","#"],
+  //               [".","#"]]
+  // 输出：3
+  // 解释：让所有学生坐在可用的座位上。
+  seats = {{'.', '#'}, {'#', '#'}, {'#', '.'}, {'#', '#'}, {'.', '#'}};
+  EXPECT_EQ(solution.maxStudents(seats), 3);
+
+  // 示例 3：
+  // 输入：seats = [["#",".",".",".","#"],
+  //               [".","#",".","#","."],
+  //               [".",".","#",".","."],
+  //               [".","#",".","#","."],
+  //               ["#",".",".",".","#"]]
+  // 输出：10
+  // 解释：让学生坐在第 1、3 和 5 列的可用座位上。
+  seats = {{'#', '.', '.', '.', '#'},
+           {'.', '#', '.', '#', '.'},
+           {'.', '.', '#', '.', '.'},
+           {'.', '#', '.', '#', '.'},
+           {'#', '.', '.', '.', '#'}};
+  EXPECT_EQ(solution.maxStudents(seats), 10);
+}