leetcode 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.

 

Note:

1. 1 <= matrix.length <= 300
2. 1 <= matrix[0].length <= 300
3. -1000 <= matrix[i] <= 1000
4. -10^8 <= target <= 10^8

解題思路:

class Solution {
public:
    int numSubmatrixSumTarget(vector<vector<int>>& matrix, int target) 
    {
        int rows = matrix.size() , cols = matrix[0].size() ;
        vector<vector<int>> prev_sum(rows , vector<int>(cols , 0)) ;
        int res = 0 ;
        
        for(int row = 0 ; row < rows ; row++)
            for(int col = 0 ; col < cols ; col++)
            {
                if(col == 0) prev_sum[row][col] = matrix[row][col] ;
                else prev_sum[row][col] = prev_sum[row][col - 1] + matrix[row][col] ;
            }
        
        for(int begin_row = 0 ; begin_row < rows ; begin_row++)
        {           
            vector<int> row_sum(cols , 0) ;
            for(int end_row = begin_row ; end_row < rows ; end_row++)
            {
                unordered_map<int , int> prev_col_sum ;
                for(int col = 0 ; col < cols ; col++)
                {
                    row_sum[col] += prev_sum[end_row][col] ;
                    if(row_sum[col] == target) res++ ;
                    if( !prev_col_sum.empty() && prev_col_sum.count(row_sum[col] - target)) res += prev_col_sum[row_sum[col] - target] ;
                    prev_col_sum[row_sum[col]]++ ;
                }
            }
        }
        
        return res ;
    }
};