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<h1 id="124-hanota-problem">12.4 &nbsp; Hanota Problem<a class="headerlink" href="#124-hanota-problem" title="Permanent link">&para;</a></h1>
<p>In merge sort and building binary trees, we decompose the original problem into two subproblems, each half the size of the original problem. However, for the hanota problem, we adopt a different decomposition strategy.</p>
<div class="admonition question">
<p class="admonition-title">Question</p>
<p>Given three pillars, denoted as <code>A</code>, <code>B</code>, and <code>C</code>. Initially, pillar <code>A</code> has <span class="arithmatex">\(n\)</span> discs stacked on it, arranged from top to bottom in ascending order of size. Our task is to move these <span class="arithmatex">\(n\)</span> discs to pillar <code>C</code> while maintaining their original order (as shown in Figure 12-10). The following rules must be followed when moving the discs.</p>
<ol>
<li>A disc can only be taken from the top of one pillar and placed on top of another pillar.</li>
<li>Only one disc can be moved at a time.</li>
<li>A smaller disc must always be on top of a larger disc.</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="Example of the hanota problem" class="animation-figure" src="../hanota_problem.assets/hanota_example.png" /></a></p>
<p align="center"> Figure 12-10 &nbsp; Example of the hanota problem </p>
<p><strong>We denote the hanota problem of size <span class="arithmatex">\(i\)</span> as <span class="arithmatex">\(f(i)\)</span></strong>. For example, <span class="arithmatex">\(f(3)\)</span> represents moving <span class="arithmatex">\(3\)</span> discs from <code>A</code> to <code>C</code>.</p>
<h3 id="1-considering-the-base-cases">1. &nbsp; Considering the Base Cases<a class="headerlink" href="#1-considering-the-base-cases" title="Permanent link">&para;</a></h3>
<p>As shown in Figure 12-11, for problem <span class="arithmatex">\(f(1)\)</span>, when there is only one disc, we can move it directly from <code>A</code> to <code>C</code>.</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="Solution for a problem of size 1" 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"> Figure 12-11 &nbsp; Solution for a problem of size 1 </p>
<p>As shown in Figure 12-12, for problem <span class="arithmatex">\(f(2)\)</span>, when there are two discs, <strong>since we must always keep the smaller disc on top of the larger disc, we need to use <code>B</code> to assist in the move</strong>.</p>
<ol>
<li>First, move the smaller disc from <code>A</code> to <code>B</code>.</li>
<li>Then move the larger disc from <code>A</code> to <code>C</code>.</li>
<li>Finally, move the smaller disc from <code>B</code> to <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="Solution for a problem of size 2" 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"> Figure 12-12 &nbsp; Solution for a problem of size 2 </p>
<p>The process of solving problem <span class="arithmatex">\(f(2)\)</span> can be summarized as: <strong>moving two discs from <code>A</code> to <code>C</code> with the help of <code>B</code></strong>. Here, <code>C</code> is called the target pillar, and <code>B</code> is called the buffer pillar.</p>
<h3 id="2-subproblem-decomposition">2. &nbsp; Subproblem Decomposition<a class="headerlink" href="#2-subproblem-decomposition" title="Permanent link">&para;</a></h3>
<p>For problem <span class="arithmatex">\(f(3)\)</span>, when there are three discs, the situation becomes slightly more complex.</p>
<p>Since we already know the solutions to <span class="arithmatex">\(f(1)\)</span> and <span class="arithmatex">\(f(2)\)</span>, we can think from a divide and conquer perspective, <strong>treating the top two discs on <code>A</code> as a whole</strong>, and execute the steps shown in Figure 12-13. This successfully moves the three discs from <code>A</code> to <code>C</code>.</p>
<ol>
<li>Let <code>B</code> be the target pillar and <code>C</code> be the buffer pillar, and move two discs from <code>A</code> to <code>B</code>.</li>
<li>Move the remaining disc from <code>A</code> directly to <code>C</code>.</li>
<li>Let <code>C</code> be the target pillar and <code>A</code> be the buffer pillar, and move two discs from <code>B</code> to <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="Solution for a problem of size 3" 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"> Figure 12-13 &nbsp; Solution for a problem of size 3 </p>
<p>Essentially, <strong>we divide problem <span class="arithmatex">\(f(3)\)</span> into two subproblems <span class="arithmatex">\(f(2)\)</span> and one subproblem <span class="arithmatex">\(f(1)\)</span></strong>. By solving these three subproblems in order, the original problem is solved. This shows that the subproblems are independent and their solutions can be merged.</p>
<p>From this, we can summarize the divide and conquer strategy for solving the hanota problem shown in Figure 12-14: divide the original problem <span class="arithmatex">\(f(n)\)</span> into two subproblems <span class="arithmatex">\(f(n-1)\)</span> and one subproblem <span class="arithmatex">\(f(1)\)</span>, and solve these three subproblems in the following order.</p>
<ol>
<li>Move <span class="arithmatex">\(n-1\)</span> discs from <code>A</code> to <code>B</code> with the help of <code>C</code>.</li>
<li>Move the remaining <span class="arithmatex">\(1\)</span> disc directly from <code>A</code> to <code>C</code>.</li>
<li>Move <span class="arithmatex">\(n-1\)</span> discs from <code>B</code> to <code>C</code> with the help of <code>A</code>.</li>
</ol>
<p>For these two subproblems <span class="arithmatex">\(f(n-1)\)</span>, <strong>we can recursively divide them in the same way</strong> until reaching the smallest subproblem <span class="arithmatex">\(f(1)\)</span>. The solution to <span class="arithmatex">\(f(1)\)</span> is known and requires only one move operation.</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="Divide and conquer strategy for solving the hanota problem" class="animation-figure" src="../hanota_problem.assets/hanota_divide_and_conquer.png" /></a></p>
<p align="center"> Figure 12-14 &nbsp; Divide and conquer strategy for solving the hanota problem </p>
<h3 id="3-code-implementation">3. &nbsp; Code Implementation<a class="headerlink" href="#3-code-implementation" title="Permanent link">&para;</a></h3>
<p>In the code, we declare a recursive function <code>dfs(i, src, buf, tar)</code>, whose purpose is to move the top <span class="arithmatex">\(i\)</span> discs from pillar <code>src</code> to target pillar <code>tar</code> with the help of buffer pillar <code>buf</code>:</p>
<div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
<div class="tabbed-content">
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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="w"> </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;Move a disk&quot;&quot;&quot;</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="c1"># Take out a disk from the top of src</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"># Place the disk on top of tar</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="w"> </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;Solve the Tower of Hanoi problem f(i)&quot;&quot;&quot;</span>
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="c1"># If there is only one disk left in src, move it directly to 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"># Subproblem f(i-1): move the top i-1 disks from src to buf using tar</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"># Subproblem f(1): move the remaining disk from src to 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"># Subproblem f(i-1): move the top i-1 disks from buf to tar using src</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="w"> </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;Solve the Tower of Hanoi problem&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"># Move the top n disks from A to C using B</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">/* Move a disk */</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">// Take out a disk from the top of src</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">// Place the disk on top of tar</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">/* Solve the Tower of Hanoi problem 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">// If there is only one disk left in src, move it directly to 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">// Subproblem f(i-1): move the top i-1 disks from src to buf using tar</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">// Subproblem f(1): move the remaining disk from src to 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">// Subproblem f(i-1): move the top i-1 disks from buf to tar using src</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">/* Solve the Tower of Hanoi problem */</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">// Move the top n disks from A to C using B</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">/* Move a disk */</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">// Take out a disk from the top of src</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">// Place the disk on top of tar</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">/* Solve the Tower of Hanoi problem 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">// If there is only one disk left in src, move it directly to 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">// Subproblem f(i-1): move the top i-1 disks from src to buf using tar</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">// Subproblem f(1): move the remaining disk from src to 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">// Subproblem f(i-1): move the top i-1 disks from buf to tar using src</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">/* Solve the Tower of Hanoi problem */</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">// Move the top n disks from A to C using B</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">/* Move a disk */</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">// Take out a disk from the top of src</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="mi">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="mi">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">// Place the disk on top of tar</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">/* Solve the Tower of Hanoi problem 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">// If there is only one disk left in src, move it directly to 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="mi">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">// Subproblem f(i-1): move the top i-1 disks from src to buf using tar</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="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-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="c1">// Subproblem f(1): move the remaining disk from src to 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">// Subproblem f(i-1): move the top i-1 disks from buf to tar using src</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="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-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">/* Solve the Tower of Hanoi problem */</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">// Move the top n disks from A to C using B</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">/* Move a disk */</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">// Take out a disk from the top of src</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">// Place the disk on top of tar</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">// Remove top disk from src</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">/* Solve the Tower of Hanoi problem 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">// If there is only one disk left in src, move it directly to 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">// Subproblem f(i-1): move the top i-1 disks from src to buf using tar</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">// Subproblem f(1): move the remaining disk from src to 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">// Subproblem f(i-1): move the top i-1 disks from buf to tar using src</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">/* Solve the Tower of Hanoi problem */</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">// Move the top n disks from A to C using B</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">/* Move a disk */</span>
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</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="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w"> </span><span class="c1">// Take out a disk from the top of src</span>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">pan</span><span class="w"> </span><span class="p">=</span><span class="w"> </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="w"> </span><span class="c1">// Place the disk on top of tar</span>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w"> </span><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">/* Solve the Tower of Hanoi problem f(i) */</span>
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="kd">func</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="nb">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="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">buf</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w"> </span><span class="c1">// If there is only one disk left in src, move it directly to tar</span>
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></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="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></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="p">&amp;</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="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="w"> </span><span class="k">return</span>
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w"> </span><span class="c1">// Subproblem f(i-1): move the top i-1 disks from src to buf using tar</span>
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</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="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</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="p">&amp;</span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </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="w"> </span><span class="c1">// Subproblem f(1): move the remaining disk from src to tar</span>
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></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="p">&amp;</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="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="w"> </span><span class="c1">// Subproblem f(i-1): move the top i-1 disks from buf to tar using src</span>
<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</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="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</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="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">/* Solve the Tower of Hanoi problem */</span>
<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="kd">func</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="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">B</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">C</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </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="w"> </span><span class="c1">// The tail of the list is the top of the rod</span>
<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="w"> </span><span class="c1">// Move top n disks from src to C using B</span>
<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">:</span><span class="w"> </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">/* Move a disk */</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">// Take out a disk from the top of src</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">// Place the disk on top of tar</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">/* Solve the Tower of Hanoi problem 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">// If there is only one disk left in src, move it directly to 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">// Subproblem f(i-1): move the top i-1 disks from src to buf using tar</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">// Subproblem f(1): move the remaining disk from src to 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">// Subproblem f(i-1): move the top i-1 disks from buf to tar using src</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">/* Solve the Tower of Hanoi problem */</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">// Move the top n disks from A to C using B</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">/* Move a disk */</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">// Take out a disk from the top of src</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">// Place the disk on top of tar</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">/* Solve the Tower of Hanoi problem 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">// If there is only one disk left in src, move it directly to 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">// Subproblem f(i-1): move the top i-1 disks from src to buf using tar</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">// Subproblem f(1): move the remaining disk from src to 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">// Subproblem f(i-1): move the top i-1 disks from buf to tar using src</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">/* Solve the Tower of Hanoi problem */</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">// Move the top n disks from A to C using B</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">/* Move a disk */</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">// Take out a disk from the top of src</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">// Place the disk on top of tar</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">/* Solve the Tower of Hanoi problem 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">// If there is only one disk left in src, move it directly to 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">// Subproblem f(i-1): move the top i-1 disks from src to buf using tar</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">// Subproblem f(1): move the remaining disk from src to 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">// Subproblem f(i-1): move the top i-1 disks from buf to tar using src</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">/* Solve the Tower of Hanoi problem */</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">// Move the top n disks from A to C using B</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">/* Move a disk */</span>
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">move_pan</span><span class="p">(</span><span class="n">src</span><span class="p">:</span><span class="w"> </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="p">:</span><span class="w"> </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">// Take out a disk from the top of src</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">// Place the disk on top of tar</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">/* Solve the Tower of Hanoi problem f(i) */</span>
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="k">fn</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">i32</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">:</span><span class="w"> </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="p">:</span><span class="w"> </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="p">:</span><span class="w"> </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">// If there is only one disk left in src, move it directly to 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">// Subproblem f(i-1): move the top i-1 disks from src to buf using tar</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">// Subproblem f(1): move the remaining disk from src to 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">// Subproblem f(i-1): move the top i-1 disks from buf to tar using src</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">/* Solve the Tower of Hanoi problem */</span>
<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="k">fn</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="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="p">:</span><span class="w"> </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="p">:</span><span class="w"> </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">// Move the top n disks from A to C using B</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">/* Move a disk */</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">// Take out a disk from the top of src</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">// Place the disk on top of tar</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">/* Solve the Tower of Hanoi problem 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">// If there is only one disk left in src, move it directly to 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">// Subproblem f(i-1): move the top i-1 disks from src to buf using tar</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">// Subproblem f(1): move the remaining disk from src to 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">// Subproblem f(i-1): move the top i-1 disks from buf to tar using src</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">/* Solve the Tower of Hanoi problem */</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">// Move the top n disks from A to C using B</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">/* Move a disk */</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">// Take out a disk from the top of src</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">// Place the disk on top of tar</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">/* Solve the Tower of Hanoi problem 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">// If there is only one disk left in src, move it directly to 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">// Subproblem f(i-1): move the top i-1 disks from src to buf using tar</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">// Subproblem f(1): move the remaining disk from src to 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">// Subproblem f(i-1): move the top i-1 disks from buf to tar using src</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">/* Solve the Tower of Hanoi problem */</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">// Move the top n disks from A to C using B</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">### Move one disk ###</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"># Take out a disk from the top of src</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"># Place the disk on top of tar</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">### Solve Tower of Hanoi 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"># If there is only one disk left in src, move it directly to 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"># Subproblem f(i-1): move the top i-1 disks from src to buf using tar</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"># Subproblem f(1): move the remaining disk from src to 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"># Subproblem f(i-1): move the top i-1 disks from buf to tar using src</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">### Solve Tower of Hanoi ###</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"># Move the top n disks from A to C using B</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>
</div>
<p>As shown in Figure 12-15, the hanota problem forms a recursion tree of height <span class="arithmatex">\(n\)</span>, where each node represents a subproblem corresponding to an invocation of the <code>dfs()</code> function, <strong>therefore the time complexity is <span class="arithmatex">\(O(2^n)\)</span> and the space complexity is <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="Recursion tree of the hanota problem" class="animation-figure" src="../hanota_problem.assets/hanota_recursive_tree.png" /></a></p>
<p align="center"> Figure 12-15 &nbsp; Recursion tree of the hanota problem </p>
<div class="admonition quote">
<p class="admonition-title">Quote</p>
<p>The hanota problem originates from an ancient legend. In a temple in ancient India, monks had three tall diamond pillars and <span class="arithmatex">\(64\)</span> golden discs of different sizes. The monks continuously moved the discs, believing that when the last disc was correctly placed, the world would come to an end.</p>
<p>However, even if the monks moved one disc per second, it would take approximately <span class="arithmatex">\(2^{64} \approx 1.84×10^{19}\)</span> seconds, which is about <span class="arithmatex">\(5850\)</span> billion years, far exceeding current estimates of the age of the universe. Therefore, if this legend is true, we should not need to worry about the end of the world.</p>
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