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Commit 4cb1ae8

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feat: add rust solution to lc problem: No.2132 (doocs#1123)
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‎solution/2100-2199/2132.Stamping the Grid/README.md‎

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**方法一:二维前缀和 + 二维差分**
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根据题给的约束,很容易推出,一个格子能贴邮票的条件为,在加上邮票的长和宽后,右下角不越界的情况下,当前子区域中所有格子的和为 0。
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那么显然我们可以维护一个二维的前缀和数组,在 `O(1)` 的时间复杂度下就可以判断每次遍历到的格子是否能贴邮票。
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而因为贴邮票的操作,可以概括为将当前子区域的所有格子的值都置为 `1`,很自然的就能想到用一个二维的差分数组来维护贴邮票后的状态。
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最后只要对该差分数组再求一次二维前缀和,只要当前格子的和为 `0`,就意味着存在没有覆盖完全的情况,直接返回 `false` 即可。
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需要注意的是二维数组的下标关系,具体参考如下。
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`s[i + 1][j + 1]` 表示第 i 行第 j 列左上部分所有元素之和,其中 i, j 下标从 0 开始。
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则 `s[i + 1][j + 1] = s[i + 1][j] + s[i][j + 1] - s[i][j] + nums[i][j]`。
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};
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```
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### **Rust**
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```rust
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impl Solution {
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pub fn possible_to_stamp(grid: Vec<Vec<i32>>, stamp_height: i32, stamp_width: i32) -> bool {
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let n: usize = grid.len();
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let m: usize = grid[0].len();
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let mut prefix_vec: Vec<Vec<i32>> = vec![vec![0; m + 1]; n + 1];
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// Initialize the prefix vector
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for i in 0..n {
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for j in 0..m {
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prefix_vec[i + 1][j + 1] = prefix_vec[i][j + 1] + prefix_vec[i + 1][j] - prefix_vec[i][j] + grid[i][j];
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}
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}
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let mut diff_vec: Vec<Vec<i32>> = vec![vec![0; m + 1]; n + 1];
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// Construct the difference vector based on prefix sum vector
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for i in 0..n {
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for j in 0..m {
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// If the value of the cell is one, just bypass this
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if grid[i][j] == 1 {
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continue;
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}
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// Otherwise, try stick the stamp
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let x: usize = i + stamp_height as usize;
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let y: usize = j + stamp_width as usize;
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// Check the bound
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if x <= n && y <= m {
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// If the region can be sticked (All cells are empty, which means the sum will be zero)
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if prefix_vec[x][y] - prefix_vec[x][j] - prefix_vec[i][y] + prefix_vec[i][j] == 0 {
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// Update the difference vector
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diff_vec[i][j] += 1;
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diff_vec[x][y] += 1;
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diff_vec[x][j] -= 1;
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diff_vec[i][y] -= 1;
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}
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}
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}
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}
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let mut check_vec: Vec<Vec<i32>> = vec![vec![0; m + 1]; n + 1];
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// Check the prefix sum of difference vector, to determine if there is any empty cell left
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for i in 0..n {
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for j in 0..m {
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// If the value of the cell is one, just bypass this
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if grid[i][j] == 1 {
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continue;
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}
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// Otherwise, check if the region is empty, by calculating the prefix sum of difference vector
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check_vec[i + 1][j + 1] = check_vec[i][j + 1] + check_vec[i + 1][j] - check_vec[i][j] + diff_vec[i][j];
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if check_vec[i + 1][j + 1] == 0 {
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return false;
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}
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}
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}
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true
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}
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}
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```
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### **Go**
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```go

‎solution/2100-2199/2132.Stamping the Grid/README_EN.md‎

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## Solutions
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Based on the constraints provided by the question, it's easy to infer that a cell can accommodate a stamp if, after adding the length and width of the stamp, the bottom-right corner does not exceed the boundary, and the sum of all cells in the current sub-area is zero.
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Apparently, we can maintain a two-dimensional prefix sum array, and in `O(1)` time complexity, we can judge whether each cell traversed can accommodate a stamp.
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Since the action of affixing a stamp can be generalized to setting the values of all cells in the current sub-area to `1`, it's natural to think of maintaining the state after stamp affixing using a two-dimensional difference array.
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Finally, just calculate the two-dimensional prefix sum for this difference array again.
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If the sum of the current cell is `0`, it means there are cases that have not been completely covered, and you can directly return `false`.
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It's worth noting the subscript relationship of the two-dimensional array, which is as follows.
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`s[i + 1][j + 1]` represents the sum of all elements in the upper left part of the i-th row and j-th column, where the subscript i, j starts from 0.
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So `s[i + 1][j + 1] = s[i + 1][j] + s[i][j + 1] - s[i][j] + nums[i][j]`.
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For a sub-matrix with (x1, y1) as the upper left corner and (x2, y2) as the bottom right corner, the sum `sub = s[x2 + 1][y2 + 1] - s[x2 + 1][y1] - s[x1][y2 + 1] + s[x1][y1]`.
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<!-- tabs:start -->
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### **Python3**
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};
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```
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### **Rust**
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```rust
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impl Solution {
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pub fn possible_to_stamp(grid: Vec<Vec<i32>>, stamp_height: i32, stamp_width: i32) -> bool {
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let n: usize = grid.len();
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let m: usize = grid[0].len();
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let mut prefix_vec: Vec<Vec<i32>> = vec![vec![0; m + 1]; n + 1];
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// Initialize the prefix vector
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for i in 0..n {
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for j in 0..m {
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prefix_vec[i + 1][j + 1] = prefix_vec[i][j + 1] + prefix_vec[i + 1][j] - prefix_vec[i][j] + grid[i][j];
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}
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}
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let mut diff_vec: Vec<Vec<i32>> = vec![vec![0; m + 1]; n + 1];
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// Construct the difference vector based on prefix sum vector
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for i in 0..n {
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for j in 0..m {
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// If the value of the cell is one, just bypass this
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if grid[i][j] == 1 {
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continue;
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}
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// Otherwise, try stick the stamp
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let x: usize = i + stamp_height as usize;
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let y: usize = j + stamp_width as usize;
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// Check the bound
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if x <= n && y <= m {
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// If the region can be sticked (All cells are empty, which means the sum will be zero)
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if prefix_vec[x][y] - prefix_vec[x][j] - prefix_vec[i][y] + prefix_vec[i][j] == 0 {
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// Update the difference vector
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diff_vec[i][j] += 1;
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diff_vec[x][y] += 1;
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diff_vec[x][j] -= 1;
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diff_vec[i][y] -= 1;
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}
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}
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}
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}
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let mut check_vec: Vec<Vec<i32>> = vec![vec![0; m + 1]; n + 1];
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// Check the prefix sum of difference vector, to determine if there is any empty cell left
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for i in 0..n {
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for j in 0..m {
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// If the value of the cell is one, just bypass this
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if grid[i][j] == 1 {
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continue;
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}
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// Otherwise, check if the region is empty, by calculating the prefix sum of difference vector
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check_vec[i + 1][j + 1] = check_vec[i][j + 1] + check_vec[i + 1][j] - check_vec[i][j] + diff_vec[i][j];
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if check_vec[i + 1][j + 1] == 0 {
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return false;
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}
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}
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}
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true
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}
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}
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```
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### **Go**
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```go
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impl Solution {
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pub fn possible_to_stamp(grid: Vec<Vec<i32>>, stamp_height: i32, stamp_width: i32) -> bool {
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let n: usize = grid.len();
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let m: usize = grid[0].len();
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let mut prefix_vec: Vec<Vec<i32>> = vec![vec![0; m + 1]; n + 1];
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// Initialize the prefix vector
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for i in 0..n {
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for j in 0..m {
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prefix_vec[i + 1][j + 1] = prefix_vec[i][j + 1] + prefix_vec[i + 1][j] - prefix_vec[i][j] + grid[i][j];
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}
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}
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let mut diff_vec: Vec<Vec<i32>> = vec![vec![0; m + 1]; n + 1];
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// Construct the difference vector based on prefix sum vector
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for i in 0..n {
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for j in 0..m {
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// If the value of the cell is one, just bypass this
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if grid[i][j] == 1 {
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continue;
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}
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// Otherwise, try stick the stamp
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let x: usize = i + stamp_height as usize;
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let y: usize = j + stamp_width as usize;
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// Check the bound
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if x <= n && y <= m {
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// If the region can be sticked (All cells are empty, which means the sum will be zero)
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if prefix_vec[x][y] - prefix_vec[x][j] - prefix_vec[i][y] + prefix_vec[i][j] == 0 {
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// Update the difference vector
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diff_vec[i][j] += 1;
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diff_vec[x][y] += 1;
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diff_vec[x][j] -= 1;
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diff_vec[i][y] -= 1;
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}
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}
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}
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}
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let mut check_vec: Vec<Vec<i32>> = vec![vec![0; m + 1]; n + 1];
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// Check the prefix sum of difference vector, to determine if there is any empty cell left
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for i in 0..n {
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for j in 0..m {
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// If the value of the cell is one, just bypass this
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if grid[i][j] == 1 {
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continue;
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}
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// Otherwise, check if the region is empty, by calculating the prefix sum of difference vector
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check_vec[i + 1][j + 1] = check_vec[i][j + 1] + check_vec[i + 1][j] - check_vec[i][j] + diff_vec[i][j];
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if check_vec[i + 1][j + 1] == 0 {
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return false;
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}
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}
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}
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true
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}
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}

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