2428. Maximum Sum of an Hourglass

Problem Link

Description

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You are given an m x n integer matrix grid.

We define an hourglass as a part of the matrix with the following form:

Return the maximum sum of the elements of an hourglass.

Note that an hourglass cannot be rotated and must be entirely contained within the matrix.

 

Example 1:

Input: grid = [[6,2,1,3],[4,2,1,5],[9,2,8,7],[4,1,2,9]]
Output: 30
Explanation: The cells shown above represent the hourglass with the maximum sum: 6 + 2 + 1 + 2 + 9 + 2 + 8 = 30.

Example 2:

Input: grid = [[1,2,3],[4,5,6],[7,8,9]]
Output: 35
Explanation: There is only one hourglass in the matrix, with the sum: 1 + 2 + 3 + 5 + 7 + 8 + 9 = 35.

 

Constraints:

• m == grid.length
• n == grid[i].length
• 3 <= m, n <= 150
• 0 <= grid[i][j] <= 106

Solution

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Python3

class Solution:
    def maxSum(self, grid: List[List[int]]) -> int:
        rows, cols = len(grid), len(grid[0])
        res = 0
        
        for i in range(rows - 2):
            for j in range(1, cols - 1):
                res = max(res, grid[i][j - 1] + grid[i][j] + grid[i][j + 1] + grid[i + 1][j] + grid[i + 2][j - 1] + grid[i + 2][j] + grid[i + 2][j + 1])            
        
        return res