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 <= 1001 <= matrix[0].length <= 100-1000 <= matrix[i] <= 1000-10^8 <= target <= 10^8
Solution
/**
* @param {number[][]} matrix
* @param {number} target
* @return {number}
*/
var numSubmatrixSumTarget = function(matrix, target) {
var m = matrix.length;
var n = matrix[0].length;
for (var i = 0; i < m; i++) {
for (var j = 1; j < n; j++) {
matrix[i][j] += matrix[i][j - 1];
}
}
var res = 0;
for (var j1 = 0; j1 < n; j1++) {
for (var j2 = j1; j2 < n; j2++) {
var map = {};
var sum = 0;
map[0] = 1;
for (var i = 0; i < m; i++) {
sum += matrix[i][j2] - (matrix[i][j1 - 1] || 0);
if (map[sum - target]) res += map[sum - target];
map[sum] = (map[sum] || 0) + 1;
}
}
}
return res;
};
Explain:
Prefix sum and hash map.
Complexity:
- Time complexity : O(n * n * m).
- Space complexity : O(n * m).