840. Magic Squares In Grid

A 3 x 3 magic square is a 3 x 3 grid filled with distinct numbers from1 to9 such that each row, column, and both diagonals all have the same sum.

Given a row x col grid of integers, how many 3 x 3 "magic square" subgrids are there? (Each subgrid is contiguous).

Example 1:

Input: grid = [[4,3,8,4],[9,5,1,9],[2,7,6,2]]
Output: 1
Explanation:
The following subgrid is a 3 x 3 magic square:
![](https://assets.leetcode.com/uploads/2020/09/11/magic_valid.jpg)
while this one is not:
![](https://assets.leetcode.com/uploads/2020/09/11/magic_invalid.jpg)
In total, there is only one magic square inside the given grid.

Example 2:

Input: grid = [[8]]
Output: 0

Example 3:

Input: grid = [[4,4],[3,3]]
Output: 0

Example 4:

Input: grid = [[4,7,8],[9,5,1],[2,3,6]]
Output: 0

Constraints:

• row == grid.length
• col == grid[i].length
• 1 <= row, col <= 10
• 0 <= grid[i][j] <= 15

# @lc code=start
using LeetCode

function num_magic_squares_inside(grid::Matrix{Int})::Int
    r = [15, 15, 15]
    function is_magic_square(grid::AbstractMatrix{Int})
        sum(grid; dims=1) != reshape(r, 1, 3) && return false
        sum(grid; dims=2) != reshape(r, 3, 1) && return false
        sum(grid[i, i] for i in 1:3) == sum(grid[i, 4 - i] for i in 1:3) == 15 && return true
        return false
    end
    res = 0
    for j in 1:size(grid,2)-2, i in 1:size(grid,1)-2
        sub_mat = @view(grid[CartesianIndex(i, j):CartesianIndex(i+2, j+2)])
        all(x -> x in sub_mat, 1:9) && is_magic_square(sub_mat) && (res += 1)
    end
    return res
end
# @lc code=end

num_magic_squares_inside (generic function with 1 method)

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