largest-plus-sign

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Algorithms

You are given an integer <code>n</code>. You have an <code>n x n</code> binary grid <code>grid</code> with all values initially <code>1</code>&#39;s except for some indices given in the array <code>mines</code>. The <code>ith</code> element of the array <code>mines</code> is defined as <code>mines[i] = [xi, yi]</code> where <code>grid[xi][yi] == 0</code>.

Return the order of the largest axis-aligned plus sign of 1&#39;s contained in <code>grid</code>. If there is none, return <code>0</code>.

An axis-aligned plus sign of <code>1</code>&#39;s of order <code>k</code> has some center <code>grid[r][c] == 1</code> along with four arms of length <code>k - 1</code> going up, down, left, and right, and made of <code>1</code>&#39;s. Note that there could be <code>0</code>&#39;s or <code>1</code>&#39;s beyond the arms of the plus sign, only the relevant area of the plus sign is checked for <code>1</code>&#39;s.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/13/plus1-grid.jpg" style="width: 404px; height: 405px;" />
<pre>
Input: n = 5, mines = [[4,2]]
Output: 2
Explanation: In the above grid, the largest plus sign can only be of order 2. One of them is shown.
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/13/plus2-grid.jpg" style="width: 84px; height: 85px;" />
<pre>
Input: n = 1, mines = [[0,0]]
Output: 0
Explanation: There is no plus sign, so return 0.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 500</code></li>
	<li><code>1 &lt;= mines.length &lt;= 5000</code></li>
	<li><code>0 &lt;= xi, yi &lt; n</code></li>
	<li>All the pairs <code>(xi, yi)</code> are unique.</li>
</ul>

orderOfLargestPlusSign

Largest Plus Sign

Maximal Square

maximal-square

最大正方形

Array

Dynamic Programming

在一个 <code>n x n</code> 的矩阵&nbsp;<code>grid</code>&nbsp;中，除了在数组&nbsp;<code>mines</code>&nbsp;中给出的元素为&nbsp;<code>0</code>，其他每个元素都为&nbsp;<code>1</code>。<code>mines[i] = [xi, yi]</code>表示&nbsp;<code>grid[xi][yi] == 0</code>

返回 &nbsp;<code>grid</code> 中包含&nbsp;<code>1</code>&nbsp;的最大的 轴对齐 加号标志的阶数 。如果未找到加号标志，则返回 <code>0</code> 。

一个&nbsp;<code>k</code>&nbsp;阶由&nbsp;<code>1</code>&nbsp;组成的 “轴对称”加号标志 具有中心网格&nbsp;<code>grid[r][c] == 1</code>&nbsp;，以及4个从中心向上、向下、向左、向右延伸，长度为&nbsp;<code>k-1</code>，由&nbsp;<code>1</code>&nbsp;组成的臂。注意，只有加号标志的所有网格要求为 <code>1</code> ，别的网格可能为 <code>0</code> 也可能为 <code>1</code> 。

&nbsp;

示例 1：

<img src="https://assets.leetcode.com/uploads/2021/06/13/plus1-grid.jpg" />

<pre>
输入: n = 5, mines = [[4, 2]]
输出: 2
解释: 在上面的网格中，最大加号标志的阶只能是2。一个标志已在图中标出。
</pre>

示例 2：

<img src="https://assets.leetcode.com/uploads/2021/06/13/plus2-grid.jpg" />

<pre>
输入: n = 1, mines = [[0, 0]]
输出: 0
解释: 没有加号标志，返回 0 。
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= n &lt;= 500</code></li>
	<li><code>1 &lt;= mines.length &lt;= 5000</code></li>
	<li><code>0 &lt;= xi, yi&nbsp;&lt; n</code></li>
	<li>每一对&nbsp;<code>(xi, yi)</code>&nbsp;都 不重复​​​​​​​</li>
</ul>