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@ -3789,7 +3789,7 @@ dp[i-1] , dp[i-2] , \dots , dp[2] , dp[1]
<div class="arithmatex">\[
dp[i] = dp[i-1] + dp[i-2]
\]</div>
<p>这意味着在爬楼梯问题中，各个子问题之间存在递推关系，<strong>原问题的解可以由子问题的解构建得来</strong>。</p>
<p>这意味着在爬楼梯问题中，各个子问题之间存在递推关系，<strong>原问题的解可以由子问题的解构建得来</strong>。下图展示了该递推关系。</p>
<p><img alt="方案数量递推关系" src="../intro_to_dynamic_programming.assets/climbing_stairs_state_transfer.png" /></p>
<p align="center"> 图：方案数量递推关系 </p>
@ -4492,6 +4492,10 @@ dp[i] = dp[i-1] + dp[i-2]
</div>
</div>
</div>
<p>下图模拟了以上代码的执行过程。</p>
<p><img alt="爬楼梯的动态规划过程" src="../intro_to_dynamic_programming.assets/climbing_stairs_dp.png" /></p>
<p align="center"> 图：爬楼梯的动态规划过程 </p>
<p>与回溯算法一样，动态规划也使用“状态”概念来表示问题求解的某个特定阶段，每个状态都对应一个子问题以及相应的局部最优解。例如，爬楼梯问题的状态定义为当前所在楼梯阶数 <span class="arithmatex">\(i\)</span> 。</p>
<p>总结以上，动态规划的常用术语包括：</p>
<ul>
@ -4499,9 +4503,6 @@ dp[i] = dp[i-1] + dp[i-2]
<li>将最小子问题对应的状态（即第 <span class="arithmatex">\(1\)</span> , <span class="arithmatex">\(2\)</span> 阶楼梯）称为「初始状态」。</li>
<li>将递推公式 <span class="arithmatex">\(dp[i] = dp[i-1] + dp[i-2]\)</span> 称为「状态转移方程」。</li>
</ul>
<p><img alt="爬楼梯的动态规划过程" src="../intro_to_dynamic_programming.assets/climbing_stairs_dp.png" /></p>
<p align="center"> 图：爬楼梯的动态规划过程 </p>
<h2 id="1414">14.1.4 &nbsp; 状态压缩<a class="headerlink" href="#1414" title="Permanent link">&para;</a></h2>
<p>细心的你可能发现，<strong>由于 <span class="arithmatex">\(dp[i]\)</span> 只与 <span class="arithmatex">\(dp[i-1]\)</span> 和 <span class="arithmatex">\(dp[i-2]\)</span> 有关，因此我们无须使用一个数组 <code>dp</code> 来存储所有子问题的解</strong>，而只需两个变量滚动前进即可。</p>
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