Largest Magic Square
A k x k magic square is a k x k grid filled with integers such that every row sum, every column sum, and both diagonal sums are all equal. The integers in the magic square do not have to be distinct. Every 1 x 1 grid is trivially a magic square.
Given an m x n integer grid, return the size (i.e., the side length k) of the largest magic square that can be found within this grid.
Example 1
7 1 4 5 6 2 5 1 6 4 1 5 4 3 2 1 2 7 3 4
Input
grid = [[7,1,4,5,6],[2,5,1,6,4],[1,5,4,3,2],[1,2,7,3,4]]Output
3The largest magic square has size 3, and every row sum, column sum, and diagonal sum of that square is equal to 12.
Example 2
5 1 3 1 9 3 3 1 1 3 3 8
Input
grid = [[5,1,3,1],[9,3,3,1],[1,3,3,8]]Output
2The largest magic square found within the grid has side length 2.
Constraints
- m == grid.length
- n == grid[i].length
- 1 <= m, n <= 50
- 1 <= grid[i][j] <= 10^6