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# Number of Submatrices That Sum to Target

Updated: Apr 20, 2021

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 m = matrix.length,n=matrix[0].length;

for(int row =0;row<m;row++){
for(int col=1;col<n;col++){
matrix[row][col]+=matrix[row][col-1];
}
}
int count=0;

for(int i=0;i<n;i++){
for(int j=i;j<n;j++){
Map<Integer,Integer> map = new HashMap<>();
map.put(0,1);
int sum=0;

for(int row=0;row<m;row++){
sum += matrix[row][j] - (i>0 ? matrix[row][i-1] : 0);
count += map.getOrDefault(sum-target,0);
map.put(sum,map.getOrDefault(sum,0)+1);
}

}
}

return count;
}
}```