1074. Number of Submatrices That Sum to Target

Problem

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

Solution

class Solution {
    public int numSubmatrixSumTarget(int[][] matrix, int target) {
        int rows = matrix.length;
        int columns = matrix[0].length;
        for (int i = 0; i < rows; i++) {
            for (int j = 1; j < columns; j++) {
                matrix[i][j] += matrix[i][j - 1];
            }
        }
        HashMap<Integer, Integer> sumMap = new HashMap<>();
        int cur;
        int res = 0;
        for (int i = 0; i < columns; i++) {
            for (int j = i; j < columns; j++) {
                sumMap.clear();
                sumMap.put(0, 1);
                cur = 0;
                for (int[] ints : matrix) {
                    cur += ints[j] - (i > 0 ? ints[i - 1] : 0);
                    res += sumMap.getOrDefault(cur - target, 0);
                    sumMap.put(cur, sumMap.getOrDefault(cur, 0) + 1);
                }
            }
        }
        return res;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).