Largest Magic Square
<p>A <code>k x k</code> <strong>magic square</strong> is a <code>k x k</code> grid filled with integers such that every row sum, every column sum, and both diagonal sums are <strong>all equal</strong>. The integers in the magic square <strong>do not have to be distinct</strong>. Every <code>1 x 1</code> grid is trivially a <strong>magic square</strong>.</p>

<p>Given an <code>m x n</code> integer <code>grid</code>, return <em>the <strong>size</strong> (i.e., the side length </em><code>k</code><em>) of the <strong>largest magic square</strong> that can be found within this grid</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1800-1899/1895.Largest%20Magic%20Square/images/magicsquare-grid.jpg" style="width: 413px; height: 335px;" />
<pre>
<strong>Input:</strong> grid = [[7,1,4,5,6],[2,5,1,6,4],[1,5,4,3,2],[1,2,7,3,4]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The largest magic square has a size of 3.
Every row sum, column sum, and diagonal sum of this magic square is equal to 12.
- Row sums: 5+1+6 = 5+4+3 = 2+7+3 = 12
- Column sums: 5+5+2 = 1+4+7 = 6+3+3 = 12
- Diagonal sums: 5+4+3 = 6+4+2 = 12
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1800-1899/1895.Largest%20Magic%20Square/images/magicsquare2-grid.jpg" style="width: 333px; height: 255px;" />
<pre>
<strong>Input:</strong> grid = [[5,1,3,1],[9,3,3,1],[1,3,3,8]]
<strong>Output:</strong> 2
</pre>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 10<sup>6</sup></code></li>
</ul>
Array; Matrix; Prefix Sum
func largestMagicSquare(grid [][]int) int {
	m, n := len(grid), len(grid[0])
	rowsum := make([][]int, m+1)
	colsum := make([][]int, m+1)
	for i := 0; i <= m; i++ {
		rowsum[i] = make([]int, n+1)
		colsum[i] = make([]int, n+1)
	}
	for i := 1; i < m+1; i++ {
		for j := 1; j < n+1; j++ {
			rowsum[i][j] = rowsum[i][j-1] + grid[i-1][j-1]
			colsum[i][j] = colsum[i-1][j] + grid[i-1][j-1]
		}
	}
	for k := min(m, n); k > 1; k-- {
		for i := 0; i+k-1 < m; i++ {
			for j := 0; j+k-1 < n; j++ {
				i2, j2 := i+k-1, j+k-1
				if check(grid, rowsum, colsum, i, j, i2, j2) {
					return k
				}
			}
		}
	}
	return 1
}

func check(grid, rowsum, colsum [][]int, x1, y1, x2, y2 int) bool {
	val := rowsum[x1+1][y2+1] - rowsum[x1+1][y1]
	for i := x1 + 1; i < x2+1; i++ {
		if rowsum[i+1][y2+1]-rowsum[i+1][y1] != val {
			return false
		}
	}
	for j := y1; j < y2+1; j++ {
		if colsum[x2+1][j+1]-colsum[x1][j+1] != val {
			return false
		}
	}
	s := 0
	for i, j := x1, y1; i <= x2; i, j = i+1, j+1 {
		s += grid[i][j]
	}
	if s != val {
		return false
	}
	s = 0
	for i, j := x1, y2; i <= x2; i, j = i+1, j-1 {
		s += grid[i][j]
	}
	if s != val {
		return false
	}
	return true
}