Prerequisites

Subarray Sum Equals K

Problem Statement

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.

Problem Link

Number of Submatrices That Sum to Target - LeetCode

Code

class Solution {
public:
    int numSubmatrixSumTarget(vector<vector<int>>& matrix, int target) {
        
        int m = matrix.size();
        int n = matrix[0].size();
        int result = 0;
        for(int i=0;i<m;i++)
        {
            vector<int> row(n,0);
            for(int j=i;j<m;j++)
            {
                for(int k=0;k<n;k++)
                    row[k] += matrix[j][k];
                
                result+=find_result(row,target);
            }
        }
        
        return result;
        
    }
    
    int find_result(vector<int>& row,int target)
    {
        unordered_map<int,int> m;
        
        m[0] = 1;
        int res = 0;
        int curr_sum = 0;
        for(int ele:row)
        {
            curr_sum+=ele;
            res+=m[curr_sum-target];
            m[curr_sum]++;
        }
        return res;
    }
};

Time complexity O(mnn)

Space complexity O(m)