Leetcode 3070. Count Submatrices with Top-Left Element and Sum Less Than k

Problem

You are given a 0-indexed integer matrix grid and an integer k.

Return the number of submatrices that contain the top-left element of the grid, and have a sum less than or equal to k.

Algorithm

Dynamic programming (DP): let f[i][j] be the sum of the submatrix from (0,0) to (i,j), and count all positions where f[i][j] ≤ k.

Code

class Solution:
    def countSubmatrices(self, grid: List[List[int]], k: int) -> int:
        m, n, ans = len(grid), len(grid[0]), 0
        for i in range(m):
            for j in range(n):
                if i > 0:
                    grid[i][j] += grid[i-1][j]
                if j > 0:
                    grid[i][j] += grid[i][j-1]
                if i > 0 and j > 0:
                    grid[i][j] -= grid[i-1][j-1]
                if grid[i][j] <= k:
                    ans += 1
        
        return ans