Magic Squares In Grid
<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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0800-0899/0840.Magic%20Squares%20In%20Grid/images/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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0800-0899/0840.Magic%20Squares%20In%20Grid/images/magic_valid.jpg" style="width: 242px; height: 242px;" />
while this one is not:
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0800-0899/0840.Magic%20Squares%20In%20Grid/images/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>
Array; Hash Table; Math; Matrix
func numMagicSquaresInside(grid [][]int) (ans int) {
	m, n := len(grid), len(grid[0])
	check := func(i, j int) int {
		if i+3 > m || j+3 > n {
			return 0
		}
		cnt := [16]int{}
		row := [3]int{}
		col := [3]int{}
		a, b := 0, 0
		for x := i; x < i+3; x++ {
			for y := j; y < j+3; y++ {
				v := grid[x][y]
				if v < 1 || v > 9 || cnt[v] > 0 {
					return 0
				}
				cnt[v]++
				row[x-i] += v
				col[y-j] += v
				if x-i == y-j {
					a += v
				}
				if x-i == 2-(y-j) {
					b += v
				}
			}
		}
		if a != b {
			return 0
		}
		for k := 0; k < 3; k++ {
			if row[k] != a || col[k] != a {
				return 0
			}
		}
		return 1
	}
	for i := 0; i < m; i++ {
		for j := 0; j < n; j++ {
			ans += check(i, j)
		}
	}
	return
}