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第 8 章 &nbsp;
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第 10 章 &nbsp; 搜索
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第 11 章 &nbsp; 排序
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第 12 章 &nbsp; 分治
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第 13 章 &nbsp; 回溯
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<h1 id="124">12.4 &nbsp; 汉诺塔问题<a class="headerlink" href="#124" title="Permanent link">&para;</a></h1>
<p>在归并排序和构建二叉树中,我们都是将原问题分解为两个规模为原问题一半的子问题。然而对于汉诺塔问题,我们采用不同的分解策略。</p>
<div class="admonition question">
<p class="admonition-title">Question</p>
<p>给定三根柱子,记为 <code>A</code><code>B</code><code>C</code> 。起始状态下,柱子 <code>A</code> 上套着 <span class="arithmatex">\(n\)</span> 个圆盘,它们从上到下按照从小到大的顺序排列。我们的任务是要把这 <span class="arithmatex">\(n\)</span> 个圆盘移到柱子 <code>C</code> 上,并保持它们的原有顺序不变(如图 12-10 所示)。在移动圆盘的过程中,需要遵守以下规则。</p>
<ol>
<li>圆盘只能从一根柱子顶部拿出,从另一根柱子顶部放入。</li>
<li>每次只能移动一个圆盘。</li>
<li>小圆盘必须时刻位于大圆盘之上。</li>
</ol>
</div>
<p><a class="glightbox" href="../hanota_problem.assets/hanota_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="汉诺塔问题示例" class="animation-figure" src="../hanota_problem.assets/hanota_example.png" /></a></p>
<p align="center"> 图 12-10 &nbsp; 汉诺塔问题示例 </p>
<p><strong>我们将规模为 <span class="arithmatex">\(i\)</span> 的汉诺塔问题记作 <span class="arithmatex">\(f(i)\)</span></strong> 。例如 <span class="arithmatex">\(f(3)\)</span> 代表将 <span class="arithmatex">\(3\)</span> 个圆盘从 <code>A</code> 移动至 <code>C</code> 的汉诺塔问题。</p>
<h3 id="1">1. &nbsp; 考虑基本情况<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
<p>如图 12-11 所示,对于问题 <span class="arithmatex">\(f(1)\)</span> ,即当只有一个圆盘时,我们将它直接从 <code>A</code> 移动至 <code>C</code> 即可。</p>
<div class="tabbed-set tabbed-alternate" data-tabs="1:2"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f1_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="规模为 1 的问题的解" class="animation-figure" src="../hanota_problem.assets/hanota_f1_step1.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f1_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f1_step2" class="animation-figure" src="../hanota_problem.assets/hanota_f1_step2.png" /></a></p>
</div>
</div>
</div>
<p align="center"> 图 12-11 &nbsp; 规模为 1 的问题的解 </p>
<p>如图 12-12 所示,对于问题 <span class="arithmatex">\(f(2)\)</span> ,即当有两个圆盘时,<strong>由于要时刻满足小圆盘在大圆盘之上,因此需要借助 <code>B</code> 来完成移动</strong></p>
<ol>
<li>先将上面的小圆盘从 <code>A</code> 移至 <code>B</code></li>
<li>再将大圆盘从 <code>A</code> 移至 <code>C</code></li>
<li>最后将小圆盘从 <code>B</code> 移至 <code>C</code></li>
</ol>
<div class="tabbed-set tabbed-alternate" data-tabs="2:4"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f2_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="规模为 2 的问题的解" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step1.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f2_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f2_step2" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step2.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f2_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f2_step3" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step3.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f2_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f2_step4" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step4.png" /></a></p>
</div>
</div>
</div>
<p align="center"> 图 12-12 &nbsp; 规模为 2 的问题的解 </p>
<p>解决问题 <span class="arithmatex">\(f(2)\)</span> 的过程可总结为:<strong>将两个圆盘借助 <code>B</code><code>A</code> 移至 <code>C</code></strong> 。其中,<code>C</code> 称为目标柱、<code>B</code> 称为缓冲柱。</p>
<h3 id="2">2. &nbsp; 子问题分解<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
<p>对于问题 <span class="arithmatex">\(f(3)\)</span> ,即当有三个圆盘时,情况变得稍微复杂了一些。</p>
<p>因为已知 <span class="arithmatex">\(f(1)\)</span><span class="arithmatex">\(f(2)\)</span> 的解,所以我们可从分治角度思考,<strong><code>A</code> 顶部的两个圆盘看作一个整体</strong>,执行图 12-13 所示的步骤。这样三个圆盘就被顺利地从 <code>A</code> 移至 <code>C</code> 了。</p>
<ol>
<li><code>B</code> 为目标柱、<code>C</code> 为缓冲柱,将两个圆盘从 <code>A</code> 移至 <code>B</code></li>
<li><code>A</code> 中剩余的一个圆盘从 <code>A</code> 直接移动至 <code>C</code></li>
<li><code>C</code> 为目标柱、<code>A</code> 为缓冲柱,将两个圆盘从 <code>B</code> 移至 <code>C</code></li>
</ol>
<div class="tabbed-set tabbed-alternate" data-tabs="3:4"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">&lt;1&gt;</label><label for="__tabbed_3_2">&lt;2&gt;</label><label for="__tabbed_3_3">&lt;3&gt;</label><label for="__tabbed_3_4">&lt;4&gt;</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f3_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="规模为 3 的问题的解" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step1.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f3_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f3_step2" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step2.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f3_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f3_step3" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step3.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f3_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f3_step4" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step4.png" /></a></p>
</div>
</div>
</div>
<p align="center"> 图 12-13 &nbsp; 规模为 3 的问题的解 </p>
<p>从本质上看,<strong>我们将问题 <span class="arithmatex">\(f(3)\)</span> 划分为两个子问题 <span class="arithmatex">\(f(2)\)</span> 和一个子问题 <span class="arithmatex">\(f(1)\)</span></strong> 。按顺序解决这三个子问题之后,原问题随之得到解决。这说明子问题是独立的,而且解可以合并。</p>
<p>至此,我们可总结出图 12-14 所示的解决汉诺塔问题的分治策略:将原问题 <span class="arithmatex">\(f(n)\)</span> 划分为两个子问题 <span class="arithmatex">\(f(n-1)\)</span> 和一个子问题 <span class="arithmatex">\(f(1)\)</span> ,并按照以下顺序解决这三个子问题。</p>
<ol>
<li><span class="arithmatex">\(n-1\)</span> 个圆盘借助 <code>C</code><code>A</code> 移至 <code>B</code></li>
<li>将剩余 <span class="arithmatex">\(1\)</span> 个圆盘从 <code>A</code> 直接移至 <code>C</code></li>
<li><span class="arithmatex">\(n-1\)</span> 个圆盘借助 <code>A</code><code>B</code> 移至 <code>C</code></li>
</ol>
<p>对于这两个子问题 <span class="arithmatex">\(f(n-1)\)</span> <strong>可以通过相同的方式进行递归划分</strong>,直至达到最小子问题 <span class="arithmatex">\(f(1)\)</span> 。而 <span class="arithmatex">\(f(1)\)</span> 的解是已知的,只需一次移动操作即可。</p>
<p><a class="glightbox" href="../hanota_problem.assets/hanota_divide_and_conquer.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="解决汉诺塔问题的分治策略" class="animation-figure" src="../hanota_problem.assets/hanota_divide_and_conquer.png" /></a></p>
<p align="center"> 图 12-14 &nbsp; 解决汉诺塔问题的分治策略 </p>
<h3 id="3">3. &nbsp; 代码实现<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
<p>在代码中,我们声明一个递归函数 <code>dfs(i, src, buf, tar)</code> ,它的作用是将柱 <code>src</code> 顶部的 <span class="arithmatex">\(i\)</span> 个圆盘借助缓冲柱 <code>buf</code> 移动至目标柱 <code>tar</code> </p>
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<div class="highlight"><span class="filename">hanota.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span> <span class="nf">move</span><span class="p">(</span><span class="n">src</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">tar</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;移动一个圆盘&quot;&quot;&quot;</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="c1"># 从 src 顶部拿出一个圆盘</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">pan</span> <span class="o">=</span> <span class="n">src</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="c1"># 将圆盘放入 tar 顶部</span>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">tar</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pan</span><span class="p">)</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="k">def</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">src</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">buf</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">tar</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;求解汉诺塔问题 f(i)&quot;&quot;&quot;</span>
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="c1"># 若 src 只剩下一个圆盘,则直接将其移到 tar</span>
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">)</span>
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="k">return</span>
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="c1"># 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf</span>
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">,</span> <span class="n">buf</span><span class="p">)</span>
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a> <span class="c1"># 子问题 f(1) :将 src 剩余一个圆盘移到 tar</span>
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a> <span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">)</span>
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a> <span class="c1"># 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar</span>
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">buf</span><span class="p">,</span> <span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">)</span>
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="k">def</span> <span class="nf">solve_hanota</span><span class="p">(</span><span class="n">A</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">B</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">C</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;求解汉诺塔问题&quot;&quot;&quot;</span>
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a> <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a> <span class="c1"># 将 A 顶部 n 个圆盘借助 B 移到 C</span>
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="p">)</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hanota.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 移动一个圆盘 */</span>
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w"> </span><span class="c1">// 从 src 顶部拿出一个圆盘</span>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="n">back</span><span class="p">();</span>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="c1">// 将圆盘放入 tar 顶部</span>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="n">tar</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pan</span><span class="p">);</span>
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="p">}</span>
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a>
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="cm">/* 求解汉诺塔问题 f(i) */</span>
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w"> </span><span class="c1">// 若 src 只剩下一个圆盘,则直接将其移到 tar</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf</span>
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">);</span>
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w"> </span><span class="c1">// 子问题 f(1) :将 src 剩余一个圆盘移到 tar</span>
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar</span>
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="p">}</span>
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a>
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="cm">/* 求解汉诺塔问题 */</span>
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="kt">void</span><span class="w"> </span><span class="nf">solveHanota</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">C</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w"> </span><span class="c1">// 将 A 顶部 n 个圆盘借助 B 移到 C</span>
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hanota.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 移动一个圆盘 */</span>
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w"> </span><span class="c1">// 从 src 顶部拿出一个圆盘</span>
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">src</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="c1">// 将圆盘放入 tar 顶部</span>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="n">tar</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pan</span><span class="p">);</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="p">}</span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="cm">/* 求解汉诺塔问题 f(i) */</span>
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w"> </span><span class="c1">// 若 src 只剩下一个圆盘,则直接将其移到 tar</span>
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf</span>
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">);</span>
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w"> </span><span class="c1">// 子问题 f(1) :将 src 剩余一个圆盘移到 tar</span>
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar</span>
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="p">}</span>
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a>
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="cm">/* 求解汉诺塔问题 */</span>
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="kt">void</span><span class="w"> </span><span class="nf">solveHanota</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">C</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w"> </span><span class="c1">// 将 A 顶部 n 个圆盘借助 B 移到 C</span>
<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hanota.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 移动一个圆盘 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Move</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="c1">// 从 src 顶部拿出一个圆盘</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">[</span><span class="o">^</span><span class="m">1</span><span class="p">];</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">src</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="c1">// 将圆盘放入 tar 顶部</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="n">tar</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">pan</span><span class="p">);</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="p">}</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="cm">/* 求解汉诺塔问题 f(i) */</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="k">void</span><span class="w"> </span><span class="nf">DFS</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="c1">// 若 src 只剩下一个圆盘,则直接将其移到 tar</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="n">Move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">);</span>
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="c1">// 子问题 f(1) :将 src 剩余一个圆盘移到 tar</span>
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w"> </span><span class="n">Move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar</span>
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="p">}</span>
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a>
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="cm">/* 求解汉诺塔问题 */</span>
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="k">void</span><span class="w"> </span><span class="nf">SolveHanota</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">C</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w"> </span><span class="c1">// 将 A 顶部 n 个圆盘借助 B 移到 C</span>
<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hanota.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 移动一个圆盘 */</span>
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="w"> </span><span class="o">*</span><span class="nx">list</span><span class="p">.</span><span class="nx">List</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="c1">// 从 src 顶部拿出一个圆盘</span>
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="nx">pan</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">src</span><span class="p">.</span><span class="nx">Back</span><span class="p">()</span>
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="c1">// 将圆盘放入 tar 顶部</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="nx">tar</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="nx">pan</span><span class="p">.</span><span class="nx">Value</span><span class="p">)</span>
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="c1">// 移除 src 顶部圆盘</span>
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="nx">src</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">pan</span><span class="p">)</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="p">}</span>
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="cm">/* 求解汉诺塔问题 f(i) */</span>
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="kd">func</span><span class="w"> </span><span class="nx">dfsHanota</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="w"> </span><span class="o">*</span><span class="nx">list</span><span class="p">.</span><span class="nx">List</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="c1">// 若 src 只剩下一个圆盘,则直接将其移到 tar</span>
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">)</span>
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w"> </span><span class="k">return</span>
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf</span>
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w"> </span><span class="nx">dfsHanota</span><span class="p">(</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">)</span>
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w"> </span><span class="c1">// 子问题 f(1) :将 src 剩余一个圆盘移到 tar</span>
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w"> </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">)</span>
<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar</span>
<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w"> </span><span class="nx">dfsHanota</span><span class="p">(</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">)</span>
<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="p">}</span>
<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a>
<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="cm">/* 求解汉诺塔问题 */</span>
<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="kd">func</span><span class="w"> </span><span class="nx">solveHanota</span><span class="p">(</span><span class="nx">A</span><span class="p">,</span><span class="w"> </span><span class="nx">B</span><span class="p">,</span><span class="w"> </span><span class="nx">C</span><span class="w"> </span><span class="o">*</span><span class="nx">list</span><span class="p">.</span><span class="nx">List</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">A</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span>
<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="w"> </span><span class="c1">// 将 A 顶部 n 个圆盘借助 B 移到 C</span>
<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="w"> </span><span class="nx">dfsHanota</span><span class="p">(</span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">A</span><span class="p">,</span><span class="w"> </span><span class="nx">B</span><span class="p">,</span><span class="w"> </span><span class="nx">C</span><span class="p">)</span>
<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hanota.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 移动一个圆盘 */</span>
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span> <span class="nf">move</span><span class="p">(</span><span class="n">src</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">tar</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">{</span>
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a> <span class="c1">// 从 src 顶部拿出一个圆盘</span>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a> <span class="kd">let</span> <span class="nv">pan</span> <span class="p">=</span> <span class="n">src</span><span class="p">.</span><span class="n">popLast</span><span class="p">()</span><span class="o">!</span>
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a> <span class="c1">// 将圆盘放入 tar 顶部</span>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a> <span class="n">tar</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">pan</span><span class="p">)</span>
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="p">}</span>
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a>
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="cm">/* 求解汉诺塔问题 f(i) */</span>
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="kd">func</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">src</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">buf</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">tar</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">{</span>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a> <span class="c1">// 若 src 只剩下一个圆盘,则直接将其移到 tar</span>
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a> <span class="k">if</span> <span class="n">i</span> <span class="p">==</span> <span class="mi">1</span> <span class="p">{</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a> <span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">tar</span><span class="p">)</span>
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a> <span class="k">return</span>
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a> <span class="p">}</span>
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a> <span class="c1">// 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf</span>
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">src</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">src</span><span class="p">,</span> <span class="n">buf</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">tar</span><span class="p">,</span> <span class="n">tar</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">buf</span><span class="p">)</span>
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a> <span class="c1">// 子问题 f(1) :将 src 剩余一个圆盘移到 tar</span>
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a> <span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">tar</span><span class="p">)</span>
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a> <span class="c1">// 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar</span>
<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">src</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">buf</span><span class="p">,</span> <span class="n">buf</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">tar</span><span class="p">)</span>
<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="p">}</span>
<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a>
<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="cm">/* 求解汉诺塔问题 */</span>
<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="kd">func</span> <span class="nf">solveHanota</span><span class="p">(</span><span class="n">A</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">B</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">C</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">{</span>
<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">A</span><span class="p">.</span><span class="bp">count</span>
<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a> <span class="c1">// 列表尾部是柱子顶部</span>
<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a> <span class="c1">// 将 src 顶部 n 个圆盘借助 B 移到 C</span>
<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">src</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">A</span><span class="p">,</span> <span class="n">buf</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">B</span><span class="p">,</span> <span class="n">tar</span><span class="p">:</span> <span class="p">&amp;</span><span class="n">C</span><span class="p">)</span>
<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hanota.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 移动一个圆盘 */</span>
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w"> </span><span class="c1">// 从 src 顶部拿出一个圆盘</span>
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">src</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="c1">// 将圆盘放入 tar 顶部</span>
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="nx">tar</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">pan</span><span class="p">);</span>
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="p">}</span>
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a>
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="cm">/* 求解汉诺塔问题 f(i) */</span>
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w"> </span><span class="c1">// 若 src 只剩下一个圆盘,则直接将其移到 tar</span>
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w"> </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">);</span>
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf</span>
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">);</span>
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w"> </span><span class="c1">// 子问题 f(1) :将 src 剩余一个圆盘移到 tar</span>
<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w"> </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">);</span>
<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar</span>
<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">);</span>
<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="p">}</span>
<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a>
<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="cm">/* 求解汉诺塔问题 */</span>
<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="kd">function</span><span class="w"> </span><span class="nx">solveHanota</span><span class="p">(</span><span class="nx">A</span><span class="p">,</span><span class="w"> </span><span class="nx">B</span><span class="p">,</span><span class="w"> </span><span class="nx">C</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">A</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
<a id="__codelineno-6-27" name="__codelineno-6-27" href="#__codelineno-6-27"></a><span class="w"> </span><span class="c1">// 将 A 顶部 n 个圆盘借助 B 移到 C</span>
<a id="__codelineno-6-28" name="__codelineno-6-28" href="#__codelineno-6-28"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">A</span><span class="p">,</span><span class="w"> </span><span class="nx">B</span><span class="p">,</span><span class="w"> </span><span class="nx">C</span><span class="p">);</span>
<a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hanota.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 移动一个圆盘 */</span>
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">tar</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w"> </span><span class="c1">// 从 src 顶部拿出一个圆盘</span>
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">src</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="c1">// 将圆盘放入 tar 顶部</span>
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="nx">tar</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">pan</span><span class="p">);</span>
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="p">}</span>
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a>
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="cm">/* 求解汉诺塔问题 f(i) */</span>
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">buf</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">tar</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w"> </span><span class="c1">// 若 src 只剩下一个圆盘,则直接将其移到 tar</span>
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w"> </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">);</span>
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf</span>
<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">);</span>
<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w"> </span><span class="c1">// 子问题 f(1) :将 src 剩余一个圆盘移到 tar</span>
<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w"> </span><span class="nx">move</span><span class="p">(</span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">);</span>
<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar</span>
<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">buf</span><span class="p">,</span><span class="w"> </span><span class="nx">src</span><span class="p">,</span><span class="w"> </span><span class="nx">tar</span><span class="p">);</span>
<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="p">}</span>
<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a>
<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="cm">/* 求解汉诺塔问题 */</span>
<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="kd">function</span><span class="w"> </span><span class="nx">solveHanota</span><span class="p">(</span><span class="nx">A</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">B</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">C</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">A</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w"> </span><span class="c1">// 将 A 顶部 n 个圆盘借助 B 移到 C</span>
<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">A</span><span class="p">,</span><span class="w"> </span><span class="nx">B</span><span class="p">,</span><span class="w"> </span><span class="nx">C</span><span class="p">);</span>
<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hanota.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 移动一个圆盘 */</span>
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w"> </span><span class="c1">// 从 src 顶部拿出一个圆盘</span>
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w"> </span><span class="c1">// 将圆盘放入 tar 顶部</span>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="n">tar</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">pan</span><span class="p">);</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="p">}</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a>
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="cm">/* 求解汉诺塔问题 f(i) */</span>
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="kt">void</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w"> </span><span class="c1">// 若 src 只剩下一个圆盘,则直接将其移到 tar</span>
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf</span>
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">);</span>
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w"> </span><span class="c1">// 子问题 f(1) :将 src 剩余一个圆盘移到 tar</span>
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar</span>
<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="p">}</span>
<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a>
<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="cm">/* 求解汉诺塔问题 */</span>
<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="kt">void</span><span class="w"> </span><span class="n">solveHanota</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">C</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="w"> </span><span class="c1">// 将 A 顶部 n 个圆盘借助 B 移到 C</span>
<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hanota.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 移动一个圆盘 */</span>
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span> <span class="nf">move_pan</span><span class="p">(</span><span class="n">src</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w"> </span><span class="c1">// 从 src 顶部拿出一个圆盘</span>
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="c1">// 将圆盘放入 tar 顶部</span>
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="n">tar</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">pan</span><span class="p">);</span>
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="p">}</span>
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a>
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="cm">/* 求解汉诺塔问题 f(i) */</span>
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="k">fn</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">i</span>: <span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">src</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w"> </span><span class="c1">// 若 src 只剩下一个圆盘,则直接将其移到 tar</span>
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="n">move_pan</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf</span>
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">);</span>
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w"> </span><span class="c1">// 子问题 f(1) :将 src 剩余一个圆盘移到 tar</span>
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w"> </span><span class="n">move_pan</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar</span>
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="p">}</span>
<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a>
<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="cm">/* 求解汉诺塔问题 */</span>
<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="k">fn</span> <span class="nf">solve_hanota</span><span class="p">(</span><span class="n">A</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">B</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">C</span>: <span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w"> </span><span class="c1">// 将 A 顶部 n 个圆盘借助 B 移到 C</span>
<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hanota.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 移动一个圆盘 */</span>
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">srcSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tarSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="c1">// 从 src 顶部拿出一个圆盘</span>
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">[</span><span class="o">*</span><span class="n">srcSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w"> </span><span class="n">src</span><span class="p">[</span><span class="o">*</span><span class="n">srcSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="n">srcSize</span><span class="p">)</span><span class="o">--</span><span class="p">;</span>
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w"> </span><span class="c1">// 将圆盘放入 tar 顶部</span>
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w"> </span><span class="n">tar</span><span class="p">[</span><span class="o">*</span><span class="n">tarSize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pan</span><span class="p">;</span>
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="n">tarSize</span><span class="p">)</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="p">}</span>
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a>
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="cm">/* 求解汉诺塔问题 f(i) */</span>
<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">srcSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">bufSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tarSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w"> </span><span class="c1">// 若 src 只剩下一个圆盘,则直接将其移到 tar</span>
<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">srcSize</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">tarSize</span><span class="p">);</span>
<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf</span>
<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">srcSize</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">tarSize</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">bufSize</span><span class="p">);</span>
<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w"> </span><span class="c1">// 子问题 f(1) :将 src 剩余一个圆盘移到 tar</span>
<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">srcSize</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">tarSize</span><span class="p">);</span>
<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar</span>
<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">bufSize</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">srcSize</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">tarSize</span><span class="p">);</span>
<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="p">}</span>
<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a>
<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="cm">/* 求解汉诺塔问题 */</span>
<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="kt">void</span><span class="w"> </span><span class="nf">solveHanota</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">ASize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">BSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">C</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">CSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w"> </span><span class="c1">// 将 A 顶部 n 个圆盘借助 B 移到 C</span>
<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="o">*</span><span class="n">ASize</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">ASize</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">BSize</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">,</span><span class="w"> </span><span class="n">CSize</span><span class="p">);</span>
<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hanota.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 移动一个圆盘 */</span>
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w"> </span><span class="c1">// 从 src 顶部拿出一个圆盘</span>
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">src</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w"> </span><span class="c1">// 将圆盘放入 tar 顶部</span>
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w"> </span><span class="n">tar</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pan</span><span class="p">)</span>
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="p">}</span>
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a>
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="cm">/* 求解汉诺塔问题 f(i) */</span>
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w"> </span><span class="c1">// 若 src 只剩下一个圆盘,则直接将其移到 tar</span>
<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w"> </span><span class="k">return</span>
<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf</span>
<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">)</span>
<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w"> </span><span class="c1">// 子问题 f(1) :将 src 剩余一个圆盘移到 tar</span>
<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w"> </span><span class="c1">// 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar</span>
<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="p">}</span>
<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a>
<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="cm">/* 求解汉诺塔问题 */</span>
<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">solveHanota</span><span class="p">(</span><span class="n">A</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">:</span><span class="w"> </span><span class="n">MutableList</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="na">size</span>
<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w"> </span><span class="c1">// 将 A 顶部 n 个圆盘借助 B 移到 C</span>
<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">)</span>
<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hanota.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 移动一个圆盘 ###</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># 从 src 顶部拿出一个圆盘</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="o">.</span><span class="n">pop</span>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 将圆盘放入 tar 顶部</span>
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="n">tar</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">pan</span>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="k">end</span>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="c1">### 求解汉诺塔问题 f(i) ###</span>
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="c1"># 若 src 只剩下一个圆盘,则直接将其移到 tar</span>
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="k">return</span>
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a>
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="c1"># 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf</span>
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">)</span>
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w"> </span><span class="c1"># 子问题 f(1) :将 src 剩余一个圆盘移到 tar</span>
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w"> </span><span class="c1"># 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar</span>
<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span>
<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="k">end</span>
<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a>
<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="c1">### 求解汉诺塔问题 ###</span>
<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="k">def</span><span class="w"> </span><span class="nf">solve_hanota</span><span class="p">(</span><span class="n">_A</span><span class="p">,</span><span class="w"> </span><span class="n">_B</span><span class="p">,</span><span class="w"> </span><span class="n">_C</span><span class="p">)</span>
<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_A</span><span class="o">.</span><span class="n">length</span>
<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w"> </span><span class="c1"># 将 A 顶部 n 个圆盘借助 B 移到 C</span>
<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">_A</span><span class="p">,</span><span class="w"> </span><span class="n">_B</span><span class="p">,</span><span class="w"> </span><span class="n">_C</span><span class="p">)</span>
<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hanota.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">move</span><span class="p">}</span>
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">solveHanota</span><span class="p">}</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>可视化运行</summary>
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</details>
<p>如图 12-15 所示,汉诺塔问题形成一棵高度为 <span class="arithmatex">\(n\)</span> 的递归树,每个节点代表一个子问题,对应一个开启的 <code>dfs()</code> 函数,<strong>因此时间复杂度为 <span class="arithmatex">\(O(2^n)\)</span> ,空间复杂度为 <span class="arithmatex">\(O(n)\)</span></strong></p>
<p><a class="glightbox" href="../hanota_problem.assets/hanota_recursive_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="汉诺塔问题的递归树" class="animation-figure" src="../hanota_problem.assets/hanota_recursive_tree.png" /></a></p>
<p align="center"> 图 12-15 &nbsp; 汉诺塔问题的递归树 </p>
<div class="admonition quote">
<p class="admonition-title">Quote</p>
<p>汉诺塔问题源自一个古老的传说。在古印度的一个寺庙里,僧侣们有三根高大的钻石柱子,以及 <span class="arithmatex">\(64\)</span> 个大小不一的金圆盘。僧侣们不断地移动圆盘,他们相信在最后一个圆盘被正确放置的那一刻,这个世界就会结束。</p>
<p>然而,即使僧侣们每秒钟移动一次,总共需要大约 <span class="arithmatex">\(2^{64} \approx 1.84×10^{19}\)</span> 秒,合约 <span class="arithmatex">\(5850\)</span> 亿年,远远超过了现在对宇宙年龄的估计。所以,倘若这个传说是真的,我们应该不需要担心世界末日的到来。</p>
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