leetcode-problemset/leetcode-cn/problem (Chinese)/放三个车的价值之和最大 II [maximum-value-sum-by-placing-three-rooks-ii].html

<p>给你一个&nbsp;<code>m x n</code>&nbsp;的二维整数数组&nbsp;<code>board</code>&nbsp;，它表示一个国际象棋棋盘，其中&nbsp;<code>board[i][j]</code>&nbsp;表示格子 <code>(i, j)</code>&nbsp;的 <strong>价值</strong>&nbsp;。</p>

<p>处于 <strong>同一行</strong>&nbsp;或者 <strong>同一列</strong>&nbsp;车会互相 <strong>攻击</strong>&nbsp;。你需要在棋盘上放三个车，确保它们两两之间都&nbsp;<b>无法互相攻击</b>&nbsp;。</p>

<p>请你返回满足上述条件下，三个车所在格子 <strong>值</strong>&nbsp;之和 <strong>最大</strong>&nbsp;为多少。</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>board = </span>[[-3,1,1,1],[-3,1,-3,1],[-3,2,1,1]]</p>

<p><b>输出：</b>4</p>

<p><strong>解释：</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/08/08/rooks2.png" style="width: 294px; height: 450px;" /></p>

<p>我们可以将车分别放在格子&nbsp;<code>(0, 2)</code>&nbsp;，<code>(1, 3)</code>&nbsp;和&nbsp;<code>(2, 1)</code>&nbsp;处，价值之和为&nbsp;<code>1 + 1 + 2 = 4</code>&nbsp;。</p>
</div>

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

<div class="example-block">
<p><span class="example-io"><b>输入：</b>board = [[1,2,3],[4,5,6],[7,8,9]]</span></p>

<p><span class="example-io"><b>输出：</b>15</span></p>

<p><strong>解释：</strong></p>

<p>我们可以将车分别放在格子&nbsp;<code>(0, 0)</code>&nbsp;，<code>(1, 1)</code>&nbsp;和&nbsp;<code>(2, 2)</code>&nbsp;处，价值之和为&nbsp;<code>1 + 5 + 9 = 15</code>&nbsp;。</p>
</div>

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

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

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

<p><strong>解释：</strong></p>

<p>我们可以将车分别放在格子&nbsp;<code>(0, 2)</code>&nbsp;，<code>(1, 1)</code>&nbsp;和&nbsp;<code>(2, 0)</code>&nbsp;处，价值之和为&nbsp;<code>1 + 1 + 1 = 3</code>&nbsp;。</p>
</div>

<p>&nbsp;</p>

<p><strong>提示：</strong></p>

<ul>
	<li><code>3 &lt;= m == board.length &lt;= 500</code></li>
	<li><code>3 &lt;= n == board[i].length &lt;= 500</code></li>
	<li><code>-10<sup>9</sup> &lt;= board[i][j] &lt;= 10<sup>9</sup></code></li>
</ul>