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2023-07-26 08:59:03 +08:00
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chapter_greedy/max_capacity_problem/index.html
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@@ -3418,8 +3418,8 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
<p>我们发现，<strong>如果此时将长板 <span class="arithmatex">\(j\)</span> 向短板 <span class="arithmatex">\(i\)</span> 靠近，则容量一定变小</strong>。这是因为在移动长板 <span class="arithmatex">\(j\)</span> 后：</p>
<ul>
<li>宽度 <span class="arithmatex">\(j-i\)</span> 肯定变小；</li>
<li>高度由短板决定，因此高度只可能不变（ <span class="arithmatex">\(i\)</span> 仍为短板）或变小（移动后的 <span class="arithmatex">\(j\)</span> 成为短板）；</li>
<li>宽度 <span class="arithmatex">\(j-i\)</span> 肯定变小。</li>
<li>高度由短板决定，因此高度只可能不变（ <span class="arithmatex">\(i\)</span> 仍为短板）或变小（移动后的 <span class="arithmatex">\(j\)</span> 成为短板）。</li>
</ul>
<p><img alt="向内移动长板后的状态" src="../max_capacity_problem.assets/max_capacity_moving_long_board.png" /></p>
<p align="center"> Fig. 向内移动长板后的状态 </p>