<p>A <code>3 x 3</code> <strong>magic square</strong> is a <code>3 x 3</code> grid filled with distinct numbers <strong>from </strong>1<strong> to </strong>9 such that each row, column, and both diagonals all have the same sum.</p>

<p>Given a <code>row x col</code> <code>grid</code> of integers, how many <code>3 x 3</code> magic square subgrids are there?</p>

<p>Note: while a magic square can only contain numbers from 1 to 9, <code>grid</code> may contain numbers up to 15.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/11/magic_main.jpg" style="width: 322px; height: 242px;" />
<pre>
<strong>Input:</strong> grid = [[4,3,8,4],[9,5,1,9],[2,7,6,2]]
<strong>Output:</strong> 1
<strong>Explanation: </strong>
The following subgrid is a 3 x 3 magic square:
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/11/magic_valid.jpg" style="width: 242px; height: 242px;" />
while this one is not:
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/11/magic_invalid.jpg" style="width: 242px; height: 242px;" />
In total, there is only one magic square inside the given grid.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[8]]
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>row == grid.length</code></li>
	<li><code>col == grid[i].length</code></li>
	<li><code>1 &lt;= row, col &lt;= 10</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 15</code></li>
</ul>

#include <vector>
#include <algorithm>

using namespace std;

class Solution {
public:
    int numMagicSquaresInside(vector<vector<int>>& grid) {
        int count = 0;
        int rows = grid.size();
        int cols = grid[0].size();

        for (int i = 0; i <= rows - 3; i++) {
            for (int j = 0; j <= cols - 3; j++) {
                if (isMagicSquare(grid, i, j)) {
                    count++;
                }
            }
        }
        return count;
    }

private:
    bool isMagicSquare(vector<vector<int>>& grid, int rowStart, int colStart) {
        vector<int> nums;

        for (int i = rowStart; i < rowStart + 3; i++) {
            for (int j = colStart; j < colStart + 3; j++) {
                nums.push_back(grid[i][j]);
            }
        }
        sort(nums.begin(), nums.end());

        for (int k = 0; k < 9; k++) {
            if (nums[k] != k + 1) return false;
        }

        int sum = grid[rowStart][colStart] + grid[rowStart][colStart + 1] + grid[rowStart][colStart + 2];

        for (int i = rowStart; i < rowStart + 3; i++) {
            if (grid[i][colStart] + grid[i][colStart + 1] + grid[i][colStart + 2] != sum) {
                return false;
            }
        }

        for (int j = colStart; j < colStart + 3; j++) {
            if (grid[rowStart][j] + grid[rowStart + 1][j] + grid[rowStart + 2][j] != sum) {
                return false;
            }
        }

        if (grid[rowStart][colStart] + grid[rowStart + 1][colStart + 1] + grid[rowStart + 2][colStart + 2] != sum) {
            return false;
        }
        if (grid[rowStart][colStart + 2] + grid[rowStart + 1][colStart + 1] + grid[rowStart + 2][colStart] != sum) {
            return false;
        }

        return true;
    }
};
11600