0028_P1074_Number_of_Submatrices_That_Sum_to_Target.cpp

/* 
Day: 28
Problem Number: 1074 (https://leetcode.com/problems/number-of-submatrices-that-sum-to-target)
Date: 28-01-2024 
Description:
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

Code:  */
class Solution {
public:
    int numSubmatrixSumTarget(vector<vector<int>>& matrix, int target) {
        int m = matrix.size(), n = matrix[0].size();
        int ans = 0;
        for (int i = 0; i < m; ++i) {
            vector<int> col(n);
            for (int j = i; j < m; ++j) {
                for (int k = 0; k < n; ++k) {
                    col[k] += matrix[j][k];
                }
                ans += f(col, target);
            }
        }
        return ans;
    }

    int f(vector<int>& nums, int target) {
        unordered_map<int, int> d{{0, 1}};
        int cnt = 0, s = 0;
        for (int& x : nums) {
            s += x;
            if (d.count(s - target)) {
                cnt += d[s - target];
            }
            ++d[s];
        }
        return cnt;
    }
};