1292. Maximum Side Length of a Square with Sum Less than or Equal to Threshold

Given a `m x n` matrix `mat` and an integer `threshold`. Return the maximum side-length of a square with a sum less than or equal to `threshold` or return 0 if there is no such square.

Example 1:

```Input: mat = [[1,1,3,2,4,3,2],[1,1,3,2,4,3,2],[1,1,3,2,4,3,2]], threshold = 4
Output: 2
Explanation: The maximum side length of square with sum less than 4 is 2 as shown.
```

Example 2:

```Input: mat = [[2,2,2,2,2],[2,2,2,2,2],[2,2,2,2,2],[2,2,2,2,2],[2,2,2,2,2]], threshold = 1
Output: 0
```

Example 3:

```Input: mat = [[1,1,1,1],[1,0,0,0],[1,0,0,0],[1,0,0,0]], threshold = 6
Output: 3
```

Example 4:

```Input: mat = [[18,70],[61,1],[25,85],[14,40],[11,96],[97,96],[63,45]], threshold = 40184
Output: 2
```

Constraints:

• `1 <= m, n <= 300`
• `m == mat.length`
• `n == mat[i].length`
• `0 <= mat[i][j] <= 10000`
• `0 <= threshold <= 10^5`

1292. Maximum Side Length of a Square with Sum Less than or Equal to Threshold
``````struct Solution;

impl Solution {
fn max_side_length(mat: Vec<Vec<i32>>, threshold: i32) -> i32 {
let n = mat.len();
let m = mat[0].len();
let mut prefix = vec![vec![0; m + 1]; n + 1];
let mut k = 1;
for i in 0..n {
for j in 0..m {
prefix[i][j] = mat[i][j];
if i > 0 {
prefix[i][j] += prefix[i - 1][j];
}
if j > 0 {
prefix[i][j] += prefix[i][j - 1];
}
if i > 0 && j > 0 {
prefix[i][j] -= prefix[i - 1][j - 1];
}
if i >= k - 1 && j >= k - 1 {
let mut sum = prefix[i][j];
if i >= k {
sum -= prefix[i - k][j];
}
if j >= k {
sum -= prefix[i][j - k];
}
if i >= k && j >= k {
sum += prefix[i - k][j - k];
}
if sum <= threshold {
k += 1;
}
}
}
}
(k - 1) as i32
}
}

#[test]
fn test() {
let mat = vec_vec_i32![
[1, 1, 3, 2, 4, 3, 2],
[1, 1, 3, 2, 4, 3, 2],
[1, 1, 3, 2, 4, 3, 2]
];
let threshold = 4;
let res = 2;
assert_eq!(Solution::max_side_length(mat, threshold), res);
let mat = vec_vec_i32![
[2, 2, 2, 2, 2],
[2, 2, 2, 2, 2],
[2, 2, 2, 2, 2],
[2, 2, 2, 2, 2],
[2, 2, 2, 2, 2]
];
let threshold = 1;
let res = 0;
assert_eq!(Solution::max_side_length(mat, threshold), res);
let mat = vec_vec_i32![[1, 1, 1, 1], [1, 0, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0]];
let threshold = 6;
let res = 3;
assert_eq!(Solution::max_side_length(mat, threshold), res);
let mat = vec_vec_i32![
[18, 70],
[61, 1],
[25, 85],
[14, 40],
[11, 96],
[97, 96],
[63, 45]
];
let threshold = 40184;
let res = 2;
assert_eq!(Solution::max_side_length(mat, threshold), res);
}
``````