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

Problem Link

Description

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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.

 

Example 1:

Input: grid = [[7,6,3],[6,6,1]], k = 18
Output: 4
Explanation: There are only 4 submatrices, shown in the image above, that contain the top-left element of grid, and have a sum less than or equal to 18.

Example 2:

Input: grid = [[7,2,9],[1,5,0],[2,6,6]], k = 20
Output: 6
Explanation: There are only 6 submatrices, shown in the image above, that contain the top-left element of grid, and have a sum less than or equal to 20.

 

Constraints:

• m == grid.length
• n == grid[i].length
• 1 <= n, m <= 1000
• 0 <= grid[i][j] <= 1000
• 1 <= k <= 109

Solution

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Python3

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