1074. Number of Submatrices That Sum to Target

Given a `matrix` and a `target`, return the number of non-empty submatrices that sum to target.

A submatrix `x1, y1, x2, y2` is the set of all cells `matrix[x][y]` with `x1 <= x <= x2` and `y1 <= y <= y2`.

Two submatrices `(x1, y1, x2, y2)` and `(x1', y1', x2', y2')` are different if they have some coordinate that is different: for example, if `x1 != x1'`.

Example 1:

```Input: matrix = [[0,1,0],[1,1,1],[0,1,0]], target = 0
Output: 4
Explanation: The four 1x1 submatrices that only contain 0.
```

Example 2:

```Input: matrix = [[1,-1],[-1,1]], target = 0
Output: 5
Explanation: The two 1x2 submatrices, plus the two 2x1 submatrices, plus the 2x2 submatrix.
```

Example 3:

```Input: matrix = [[904]], target = 0
Output: 0
```

Constraints:

• `1 <= matrix.length <= 100`
• `1 <= matrix[0].length <= 100`
• `-1000 <= matrix[i] <= 1000`
• `-10^8 <= target <= 10^8`

1074. Number of Submatrices That Sum to Target
``````struct Solution;
use std::collections::HashMap;

impl Solution {
fn num_submatrix_sum_target(matrix: Vec<Vec<i32>>, target: i32) -> i32 {
let n = matrix.len();
let m = matrix[0].len();
let mut prefix = vec![vec![]; n];
for i in 0..n {
let mut prev = 0;
for j in 0..m {
prev += matrix[i][j];
prefix[i].push(prev);
}
}
let mut res = 0;
for j1 in 0..m {
for j2 in j1..m {
let mut hm: HashMap<i32, usize> = HashMap::new();
hm.insert(0, 1);
let mut sum = 0;
for i in 0..n {
let cur = if j1 == 0 {
prefix[i][j2]
} else {
prefix[i][j2] - prefix[i][j1 - 1]
};
sum += cur;
res += *hm.entry(sum - target).or_default();
*hm.entry(sum).or_default() += 1;
}
}
}
res as i32
}
}

#[test]
fn test() {
let matrix = vec_vec_i32![[0, 1, 0], [1, 1, 1], [0, 1, 0]];
let target = 0;
let res = 4;
assert_eq!(Solution::num_submatrix_sum_target(matrix, target), res);
let matrix = vec_vec_i32![[1, -1], [-1, 1]];
let target = 0;
let res = 5;
assert_eq!(Solution::num_submatrix_sum_target(matrix, target), res);

let matrix = vec_vec_i32![
[0, 1, 1, 1, 0, 1],
[0, 0, 0, 0, 0, 1],
[0, 0, 1, 0, 0, 1],
[1, 1, 0, 1, 1, 0],
[1, 0, 0, 1, 0, 0]
];
let target = 0;

let res = 43;
assert_eq!(Solution::num_submatrix_sum_target(matrix, target), res);
}
``````