leetcode-problemset/leetcode-cn/problem (Chinese)/最少翻转次数使二进制矩阵回文 II [minimum-number-of-flips-to-make-binary-grid-palindromic-ii].html

<p>给你一个&nbsp;<code>m x n</code>&nbsp;的二进制矩阵&nbsp;<code>grid</code>&nbsp;。</p>

<p>如果矩阵中一行或者一列从前往后与从后往前读是一样的，那么我们称这一行或者这一列是 <strong>回文</strong>&nbsp;的。</p>

<p>你可以将 <code>grid</code>&nbsp;中任意格子的值 <strong>翻转</strong>&nbsp;，也就是将格子里的值从 <code>0</code>&nbsp;变成 <code>1</code>&nbsp;，或者从 <code>1</code>&nbsp;变成 <code>0</code>&nbsp;。</p>

<p>请你返回 <strong>最少</strong>&nbsp;翻转次数，使得矩阵中 <strong>所有</strong>&nbsp;行和列都是 <strong>回文的</strong>&nbsp;，且矩阵中 <code>1</code>&nbsp;的数目可以被 <code>4</code>&nbsp;<strong>整除</strong>&nbsp;。</p>

<p>&nbsp;</p>

<p><strong class="example">示例 1：</strong></p>

<div class="example-block">
<p><span class="example-io"><b>输入：</b>grid = [[1,0,0],[0,1,0],[0,0,1]]</span></p>

<p><span class="example-io"><b>输出：</b>3</span></p>

<p><strong>解释：</strong></p>

<p><img src="https://assets.leetcode.com/uploads/2024/08/01/image.png" style="width: 400px; height: 105px;" /></p>
</div>

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

<div class="example-block">
<p><span class="example-io"><b>输入：</b>grid = [[0,1],[0,1],[0,0]]</span></p>

<p><span class="example-io"><b>输出：</b>2</span></p>

<p><strong>解释：</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/07/08/screenshot-from-2024-07-09-01-37-48.png" style="width: 300px; height: 104px;" /></p>
</div>

<p><strong class="example">示例 3：</strong></p>

<div class="example-block">
<p><span class="example-io"><b>输入：</b>grid = [[1],[1]]</span></p>

<p><span class="example-io"><b>输出：</b>2</span></p>

<p><strong>解释：</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/08/01/screenshot-from-2024-08-01-23-05-26.png" style="width: 200px; height: 70px;" /></p>
</div>

<p>&nbsp;</p>

<p><strong>提示：</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;= 2 * 10<sup>5</sup></code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 1</code></li>
</ul>