add: 用邮票贴满网格图

README.md

@@ -157,6 +157,10 @@ Rust标准库`std::collections`提供了4种通用容器类型，包含一下8
 
 ### 数组/队列/集合/映射
 
+- [用邮票贴满网格图](src/array/stamping_the_grid.rs)  [贪心, 数组, 矩阵, 前缀和]
+
+  - LeetCode 2132. 用邮票贴满网格图 <https://leetcode.cn/problems/stamping-the-grid>
+
 - [打家劫舍](src/array/house_robber.rs)  [数组, 动态规划]
 
   - LeetCode 198. 打家劫舍 <https://leetcode.cn/problems/house-robber>

src/array/mod.rs

@@ -50,3 +50,4 @@ pub mod equal_row_and_column_pairs;
 pub mod number_of_unequal_triplets_in_array;
 pub mod number_of_times_binary_string_is_prefix_aligned;
 pub mod house_robber;
+pub mod stamping_the_grid;

src/array/stamping_the_grid.rs

@@ -0,0 +1,78 @@
+// 用邮票贴满网格图
+// https://leetcode.cn/problems/stamping-the-grid
+// INLINE  ../../images/array/stamping_the_grid.jpeg
+
+pub struct Solution;
+
+impl Solution {
+    pub fn possible_to_stamp(grid: Vec<Vec<i32>>, stamp_height: i32, stamp_width: i32) -> bool {
+        let m = grid.len();
+        let n = grid[0].len();
+        let stamp_height = stamp_height as usize;
+        let stamp_width = stamp_width as usize;
+
+        // 检查网格中是否有任何空白（0），如果没有，则直接返回 true
+        if grid.iter().all(|row| row.iter().all(|&cell| cell == 1)) {
+            return true;
+        }
+
+        // 如果邮票尺寸大于网格本身，则无法放置邮票
+        if stamp_height > m || stamp_width > n {
+            return false;
+        }
+
+        let mut prefix_sum = vec![vec![0; n + 1]; m + 1];
+        let mut diff = vec![vec![0; n + 1]; m + 1];
+
+        // 计算前缀和
+        for i in 1..=m {
+            for j in 1..=n {
+                prefix_sum[i][j] = grid[i - 1][j - 1] + prefix_sum[i - 1][j] + prefix_sum[i][j - 1]
+                    - prefix_sum[i - 1][j - 1];
+            }
+        }
+
+        // 使用差分数组记录邮票放置情况
+        for i in 1..=m - stamp_height + 1 {
+            for j in 1..=n - stamp_width + 1 {
+                let x = i + stamp_height - 1;
+                let y = j + stamp_width - 1;
+                if prefix_sum[x][y] - prefix_sum[x][j - 1] - prefix_sum[i - 1][y]
+                    + prefix_sum[i - 1][j - 1]
+                    == 0
+                {
+                    diff[i][j] += 1;
+                    if y + 1 <= n {
+                        diff[i][y + 1] -= 1;
+                    }
+                    if x + 1 <= m {
+                        diff[x + 1][j] -= 1;
+                    }
+                    if x + 1 <= m && y + 1 <= n {
+                        diff[x + 1][y + 1] += 1;
+                    }
+                }
+            }
+        }
+
+        // 更新差分数组并检查是否每个空白格都至少被一个邮票覆盖
+        for i in 1..=m {
+            for j in 1..=n {
+                if i > 1 {
+                    diff[i][j] += diff[i - 1][j];
+                }
+                if j > 1 {
+                    diff[i][j] += diff[i][j - 1];
+                }
+                if i > 1 && j > 1 {
+                    diff[i][j] -= diff[i - 1][j - 1];
+                }
+                if diff[i][j] == 0 && grid[i - 1][j - 1] == 0 {
+                    return false;
+                }
+            }
+        }
+
+        true
+    }
+}

tests/array/mod.rs

@@ -50,3 +50,4 @@ pub mod equal_row_and_column_pairs_test;
 pub mod number_of_unequal_triplets_in_array_test;
 pub mod number_of_times_binary_string_is_prefix_aligned_test;
 pub mod house_robber_test;
+pub mod stamping_the_grid_test;

tests/array/stamping_the_grid_test.rs

@@ -0,0 +1,39 @@
+use rust_practice::array::stamping_the_grid::Solution;
+
+#[test]
+fn possible_to_stamp() {
+    // 示例 1：
+    // 输入：grid = [[1,0,0,0],[1,0,0,0],[1,0,0,0],[1,0,0,0],[1,0,0,0]], stampHeight = 4, stampWidth = 3
+    // 输出：true
+    // 解释：我们放入两个有重叠部分的邮票（图中标号为 1 和 2），它们能覆盖所有与空格子。
+    let grid = vec![
+        vec![1, 0, 0, 0],
+        vec![1, 0, 0, 0],
+        vec![1, 0, 0, 0],
+        vec![1, 0, 0, 0],
+        vec![1, 0, 0, 0],
+    ];
+    let stamp_height = 4;
+    let stamp_width = 3;
+    assert_eq!(
+        Solution::possible_to_stamp(grid, stamp_height, stamp_width),
+        true
+    );
+
+    // 示例 2：
+    // 输入：grid = [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]], stampHeight = 2, stampWidth = 2
+    // 输出：false
+    // 解释：没办法放入邮票覆盖所有的空格子，且邮票不超出网格图以外。
+    let grid = vec![
+        vec![1, 0, 0, 0],
+        vec![0, 1, 0, 0],
+        vec![0, 0, 1, 0],
+        vec![0, 0, 0, 1],
+    ];
+    let stamp_height = 2;
+    let stamp_width = 2;
+    assert_eq!(
+        Solution::possible_to_stamp(grid, stamp_height, stamp_width),
+        false
+    );
+}