magic-squares-in-grid

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Algorithms

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

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

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

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/11/magic_main.jpg" style="width: 322px; height: 242px;" />
<pre>
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:
<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>

Example 2:

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

&nbsp;
Constraints:

<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>

numMagicSquaresInside

Magic Squares In Grid

Largest Magic Square

largest-magic-square

最大的幻方

Array

Hash Table

Math

Matrix

<code>3 x 3</code> 的幻方是一个填充有&nbsp;从 <code>1</code> 到 <code>9</code>&nbsp; 的不同数字的 <code>3 x 3</code> 矩阵，其中每行，每列以及两条对角线上的各数之和都相等。

给定一个由整数组成的<code>row x col</code>&nbsp;的 <code>grid</code>，其中有多少个&nbsp;<code>3 × 3</code> 的 “幻方” 子矩阵？

注意：虽然幻方只能包含 1 到 9 的数字，但&nbsp;<code>grid</code> 可以包含最多15的数字。

&nbsp;

示例 1：

<img src="https://assets.leetcode.com/uploads/2020/09/11/magic_main.jpg" />

<pre>
输入: grid = [[4,3,8,4],[9,5,1,9],[2,7,6,2]
输出: 1
解释: 
下面的子矩阵是一个 3 x 3 的幻方：
<img src="https://assets.leetcode.com/uploads/2020/09/11/magic_valid.jpg" />
而这一个不是：
<img src="https://assets.leetcode.com/uploads/2020/09/11/magic_invalid.jpg" />
总的来说，在本示例所给定的矩阵中只有一个 3 x 3 的幻方子矩阵。
</pre>

示例 2:

<pre>
输入: grid = [[8]]
输出: 0
</pre>

&nbsp;

提示:

<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>