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<div class="header">
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<a href="#func-members">Functions</a> </div>
<div class="headertitle"><div class="title">hamiltons_cycle.cpp File Reference</div></div>
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@@ -135,34 +125,29 @@ $(function(){initNavTree('dd/d0c/hamiltons__cycle_8cpp.html','../../'); initResi
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Include dependency graph for hamiltons_cycle.cpp:</div>
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<p><a href="../../dd/d0c/hamiltons__cycle_8cpp_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:abcf824e347eecfeeb69ea0280f34f3e4" id="r_abcf824e347eecfeeb69ea0280f34f3e4"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> (const std::vector&lt; std::vector&lt; bool &gt; &gt; &amp;routes)</td></tr>
<tr class="separator:abcf824e347eecfeeb69ea0280f34f3e4"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae7880ce913f3058a35ff106d5be9e243" id="r_ae7880ce913f3058a35ff106d5be9e243"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae7880ce913f3058a35ff106d5be9e243">test1</a> ()</td></tr>
<tr class="separator:ae7880ce913f3058a35ff106d5be9e243"><td class="memSeparator" colspan="2">&#160;</td></tr>
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</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p>The implementation of <a href="https://en.wikipedia.org/wiki/Hamiltonian_path" target="_blank">Hamilton's cycle</a> dynamic solution for vertices number less than 20. </p>
<p>I use \(2^n\times n\) matrix and for every \([i, j]\) ( \(i &lt; 2^n\) and \(j &lt; n\)) in the matrix I store <code>true</code> if it is possible to get to all vertices on which position in <code>i</code>'s binary representation is <code>1</code> so as \(j\) would be the last one.</p>
<p>In the the end if any cell in \((2^n - 1)^{\mbox{th}}\) row is <code>true</code> there exists hamiltonian cycle.</p>
<p>I use \(2^n\times n\) matrix and for every \([i, j]\) ( \(i &lt; 2^n\) and \(j &lt; n\)) in the matrix I store <span class="tt">true</span> if it is possible to get to all vertices on which position in <span class="tt">i</span>'s binary representation is <span class="tt">1</span> so as \(j\) would be the last one.</p>
<p>In the the end if any cell in \((2^n - 1)^{\mbox{th}}\) row is <span class="tt">true</span> there exists hamiltonian cycle.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/vakhokoto" target="_blank">vakhokoto</a> </dd>
<dd>
<a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
<p class="definition">Definition in file <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp_source.html">hamiltons_cycle.cpp</a>.</p>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#abcf824e347eecfeeb69ea0280f34f3e4">&#9670;&#160;</a></span>hamilton_cycle()</h2>
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<p>The function determines if there is a hamilton's cycle in the graph</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">routes</td><td>nxn boolean matrix of \([i, j]\) where \([i, j]\) is <code>true</code> if there is a road from \(i\) to \(j\) </td></tr>
<tr><td class="paramname">routes</td><td>nxn boolean matrix of \([i, j]\) where \([i, j]\) is <span class="tt">true</span> if there is a road from \(i\) to \(j\) </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><code>true</code> if there is Hamiltonian cycle in the graph </dd>
<dl class="section return"><dt>Returns</dt><dd><span class="tt">true</span> if there is Hamiltonian cycle in the graph </dd>
<dd>
<code>false</code> if there is no Hamiltonian cycle in the graph </dd></dl>
<span class="tt">false</span> if there is no Hamiltonian cycle in the graph </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp_source.html#l00030">30</a> of file <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp_source.html">hamiltons_cycle.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 30</span> {</div>
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<p>this test is testing if <a class="el" href="#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <code>true</code> for graph: <code>1 -&gt; 2 -&gt; 3 -&gt; 4</code> </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
<p>this test is testing if <a class="el" href="#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <span class="tt">true</span> for graph: <span class="tt">1 -&gt; 2 -&gt; 3 -&gt; 4</span> </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp_source.html#l00081">81</a> of file <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp_source.html">hamiltons_cycle.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 81</span> {</div>
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<p>this test is testing if <a class="el" href="#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <code>false</code> for <br />
<p>this test is testing if <a class="el" href="#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <span class="tt">false</span> for <br />
graph:</p><pre>
1 -&gt; 2 -&gt; 3
|
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<p>this test is testing if <a class="el" href="#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <code>true</code> for clique with 4 vertices </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
<p>this test is testing if <a class="el" href="#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <span class="tt">true</span> for clique with 4 vertices </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp_source.html#l00122">122</a> of file <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp_source.html">hamiltons_cycle.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 122</span> {</div>
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