[Solved] Maximum Sum of an Hourglass LeetCode Contest Problem

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

class Solution {
    public int maxSum(int[][] grid) {
          int max = Integer.MIN_VALUE;
        for (int i = 0; i < grid.length - 2; i++) {
            for (int j = 0; j < grid[i].length - 2; j++) {
                int sum = grid[i][j] + grid[i][j + 1] + grid[i][j + 2] + grid[i + 1][j + 1] + grid[i + 2][j] + grid[i + 2][j + 1] + grid[i + 2][j + 2];
                max = Math.max(max, sum);
            }
        }
        return max;
    }
}

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