Day4.cpp

// Question
// 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
// Solution
class Solution {
public:
    int numSubmatrixSumTarget(vector<vector<int>>& M, int T) {
        int xlen = M[0].size(), ylen = M.size(), ans = 0;
        unordered_map<int, int> res;
        for (int i = 0; i < ylen; i++)
            for (int j = 1; j < xlen; j++)
                M[i][j] += M[i][j-1];
        for (int j = 0; j < xlen; j++)
            for (int k = j; k < xlen; k++) {
                res.clear();
                res[0] = 1;
                int csum = 0;
                for (int i = 0; i < ylen; i++) {
                    csum += M[i][k] - (j ? M[i][j-1] : 0);
                    ans += res.find(csum - T) != res.end() ? res[csum - T] : 0;
                    res[csum]++;
                }
            }
        return ans;
    }
};