README.md

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

Solutions (Rust)

1. Solution

use std::collections::HashMap;

impl Solution {
    pub fn num_submatrix_sum_target(matrix: Vec<Vec<i32>>, target: i32) -> i32 {
        let m = matrix.len();
        let n = matrix[0].len();
        let mut matrix = matrix;
        let mut count = HashMap::new();
        let mut ret = 0;

        for x1 in 0..m {
            for x2 in x1..m {
                count.insert((x1, x2, 0), 1);
            }
        }

        for x2 in 0..m {
            for y2 in 0..n {
                if x2 > 0 {
                    matrix[x2][y2] += matrix[x2 - 1][y2];
                }
                if y2 > 0 {
                    matrix[x2][y2] += matrix[x2][y2 - 1];
                }
                if x2 > 0 && y2 > 0 {
                    matrix[x2][y2] -= matrix[x2 - 1][y2 - 1];
                }

                for x1 in 0..=x2 {
                    let mut diff = matrix[x2][y2];
                    if x1 > 0 {
                        diff -= matrix[x1 - 1][y2];
                    }
                    ret += *count.get(&(x1, x2, diff - target)).unwrap_or(&0);
                    *count.entry((x1, x2, diff)).or_insert(0) += 1;
                }
            }
        }

        ret
    }
}