add: 参加考试的最大学生数

README.md

@@ -728,3 +728,7 @@ Rust标准库`std::collections`提供了4种通用容器类型，包含一下8
 - [不浪费原料的汉堡制作方案](src/math/number_of_burgers_with_no_waste_of_ingredients.rs)  [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.rs)  [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.rs

@@ -0,0 +1,54 @@
+// 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
+
+pub struct Solution;
+
+impl Solution {
+    pub fn max_students(seats: Vec<Vec<char>>) -> i32 {
+        fn dfs(
+            seat: usize,
+            i: usize,
+            f: &mut Vec<Vec<i32>>,
+            ss: &Vec<usize>,
+            m: usize,
+            n: usize,
+        ) -> i32 {
+            if f[seat][i] != -1 {
+                return f[seat][i];
+            }
+            let mut ans = 0;
+            for mask in 0..1 << n {
+                if (seat | mask) != seat || (mask & (mask << 1)) != 0 {
+                    continue;
+                }
+                let cnt = mask.count_ones();
+                if i == m - 1 {
+                    ans = std::cmp::max(ans, cnt as i32);
+                } else {
+                    let mut nxt = ss[i + 1];
+                    nxt &= !(mask >> 1);
+                    nxt &= !(mask << 1);
+                    ans = std::cmp::max(ans, cnt as i32 + dfs(nxt, i + 1, f, ss, m, n));
+                }
+            }
+            f[seat][i] = ans;
+            ans
+        }
+
+        let m = seats.len();
+        let n = seats[0].len();
+        let mut ss = vec![0; m];
+        let mut f = vec![vec![-1; m]; 1 << n];
+
+        for i in 0..m {
+            for j in 0..n {
+                if seats[i][j] == '.' {
+                    ss[i] |= 1 << j;
+                }
+            }
+        }
+
+        dfs(ss[0], 0, &mut f, &ss, m, n)
+    }
+}

src/math/mod.rs

@@ -17,3 +17,4 @@ pub mod circle_and_rectangle_overlapping;
 pub mod find_the_pivot_integer;
 pub mod next_greater_numerically_balanced_number;
 pub mod number_of_burgers_with_no_waste_of_ingredients;
+pub mod maximum_students_taking_exam;

tests/math/maximum_students_taking_exam_test.rs

@@ -0,0 +1,51 @@
+use rust_practice::math::maximum_students_taking_exam::Solution;
+
+#[test]
+fn max_students() {
+    // 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。
+    let seats = vec![
+        vec!['#', '.', '#', '#', '.', '#'],
+        vec!['.', '#', '#', '#', '#', '.'],
+        vec!['#', '.', '#', '#', '.', '#'],
+    ];
+    assert_eq!(Solution::max_students(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。
+    let seats = vec![
+        vec!['.', '#'],
+        vec!['#', '#'],
+        vec!['#', '.'],
+        vec!['#', '#'],
+        vec!['.', '#'],
+    ];
+    assert_eq!(Solution::max_students(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。
+    let seats = vec![
+        vec!['#', '.', '.', '.', '#'],
+        vec!['.', '#', '.', '#', '.'],
+        vec!['.', '.', '#', '.', '.'],
+        vec!['.', '#', '.', '#', '.'],
+        vec!['#', '.', '.', '.', '#'],
+    ];
+    assert_eq!(Solution::max_students(seats), 10);
+}

tests/math/mod.rs

@@ -17,3 +17,4 @@ pub mod circle_and_rectangle_overlapping_test;
 pub mod find_the_pivot_integer_test;
 pub mod next_greater_numerically_balanced_number_test;
 pub mod number_of_burgers_with_no_waste_of_ingredients_test;
+pub mod maximum_students_taking_exam_test;