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<div class="headertitle"><div class="title">hamiltons_cycle.cpp File Reference</div></div>
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<div class="contents">
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<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.
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <cassert></code><br />
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<code>#include <iostream></code><br />
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<code>#include <vector></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for hamiltons_cycle.cpp:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" loading="lazy" frameborder="0" src="../../dd/d59/hamiltons__cycle_8cpp__incl.svg" width="252" height="111"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></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>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:abcf824e347eecfeeb69ea0280f34f3e4" id="r_abcf824e347eecfeeb69ea0280f34f3e4"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> (const std::vector< std::vector< bool > > &routes)</td></tr>
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<tr class="memitem:ae7880ce913f3058a35ff106d5be9e243" id="r_ae7880ce913f3058a35ff106d5be9e243"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae7880ce913f3058a35ff106d5be9e243">test1</a> ()</td></tr>
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<tr class="memitem:a45d94ead4cf4e1ff9f87c38bc99f59ae" id="r_a45d94ead4cf4e1ff9f87c38bc99f59ae"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a> ()</td></tr>
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<tr class="memitem:a0cc94918b6831f308d4fe4fa27f08299" id="r_a0cc94918b6831f308d4fe4fa27f08299"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="#a0cc94918b6831f308d4fe4fa27f08299">test3</a> ()</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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</table>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
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<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>
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<p>I use \(2^n\times n\) matrix and for every \([i, j]\) ( \(i < 2^n\) and \(j < n\)) 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>
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<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>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/vakhokoto" target="_blank">vakhokoto</a> </dd>
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<dd>
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<a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
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<p class="definition">Definition in file <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp_source.html">hamiltons_cycle.cpp</a>.</p>
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</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
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<a id="abcf824e347eecfeeb69ea0280f34f3e4" name="abcf824e347eecfeeb69ea0280f34f3e4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#abcf824e347eecfeeb69ea0280f34f3e4">◆ </a></span>hamilton_cycle()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">bool hamilton_cycle </td>
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<td>(</td>
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<td class="paramtype">const std::vector< std::vector< bool > > &</td> <td class="paramname"><span class="paramname"><em>routes</em></span></td><td>)</td>
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<td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>The function determines if there is a hamilton's cycle in the graph</p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<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>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd><span class="tt">true</span> if there is Hamiltonian cycle in the graph </dd>
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<dd>
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<span class="tt">false</span> if there is no Hamiltonian cycle in the graph </dd></dl>
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<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>
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<div class="fragment"><div class="line"><span class="lineno"> 30</span> {</div>
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<div class="line"><span class="lineno"> 31</span> <span class="keyword">const</span> <span class="keywordtype">size_t</span> n = routes.size();</div>
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<div class="line"><span class="lineno"> 32</span> <span class="comment">// height of dp array which is 2^n</span></div>
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<div class="line"><span class="lineno"> 33</span> <span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a> = 1 << n;</div>
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<div class="line"><span class="lineno"> 34</span> std::vector<std::vector<bool>> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>(<a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>, std::vector<bool>(n, <span class="keyword">false</span>));</div>
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<div class="line"><span class="lineno"> 35</span> </div>
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<div class="line"><span class="lineno"> 36</span> <span class="comment">// to fill in the [2^i, i] cells with true</span></div>
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<div class="line"><span class="lineno"> 37</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i < n; ++i) {</div>
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<div class="line"><span class="lineno"> 38</span> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[1 << i][i] = <span class="keyword">true</span>;</div>
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<div class="line"><span class="lineno"> 39</span> }</div>
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<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 1; i < <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>; i++) {</div>
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<div class="line"><span class="lineno"> 41</span> std::vector<size_t> zeros, ones;</div>
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<div class="line"><span class="lineno"> 42</span> <span class="comment">// finding positions with 1s and 0s and separate them</span></div>
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<div class="line"><span class="lineno"> 43</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> pos = 0; pos < n; ++pos) {</div>
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<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">if</span> ((1 << pos) & i) {</div>
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<div class="line"><span class="lineno"> 45</span> ones.push_back(pos);</div>
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<div class="line"><span class="lineno"> 46</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><span class="lineno"> 47</span> zeros.push_back(pos);</div>
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<div class="line"><span class="lineno"> 48</span> }</div>
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<div class="line"><span class="lineno"> 49</span> }</div>
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<div class="line"><span class="lineno"> 50</span> </div>
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<div class="line"><span class="lineno"> 51</span> <span class="keywordflow">for</span> (<span class="keyword">auto</span> &o : ones) {</div>
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<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">if</span> (!<a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][o]) {</div>
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<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">continue</span>;</div>
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<div class="line"><span class="lineno"> 54</span> }</div>
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<div class="line"><span class="lineno"> 55</span> </div>
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<div class="line"><span class="lineno"> 56</span> <span class="keywordflow">for</span> (<span class="keyword">auto</span> &z : zeros) {</div>
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<div class="line"><span class="lineno"> 57</span> <span class="keywordflow">if</span> (!routes[o][z]) {</div>
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<div class="line"><span class="lineno"> 58</span> <span class="keywordflow">continue</span>;</div>
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<div class="line"><span class="lineno"> 59</span> }</div>
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<div class="line"><span class="lineno"> 60</span> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i + (1 << z)][z] = <span class="keyword">true</span>;</div>
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<div class="line"><span class="lineno"> 61</span> }</div>
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<div class="line"><span class="lineno"> 62</span> }</div>
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<div class="line"><span class="lineno"> 63</span> }</div>
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<div class="line"><span class="lineno"> 64</span> </div>
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<div class="line"><span class="lineno"> 65</span> <span class="keywordtype">bool</span> is_cycle = <span class="keyword">false</span>;</div>
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<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i < n; i++) {</div>
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<div class="line"><span class="lineno"> 67</span> is_cycle |= <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[<a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a> - 1][i];</div>
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<div class="line"><span class="lineno"> 68</span> <span class="keywordflow">if</span> (is_cycle) { <span class="comment">// if true, all subsequent loop will be true. hence</span></div>
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<div class="line"><span class="lineno"> 69</span> <span class="comment">// break</span></div>
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<div class="line"><span class="lineno"> 70</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><span class="lineno"> 71</span> }</div>
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<div class="line"><span class="lineno"> 72</span> }</div>
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<div class="line"><span class="lineno"> 73</span> <span class="keywordflow">return</span> is_cycle;</div>
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<div class="line"><span class="lineno"> 74</span>}</div>
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<div class="ttc" id="aavltree_8cpp_html_ae4a66d8b0c2b0d626aea45977e358c83"><div class="ttname"><a href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a></div><div class="ttdeci">int height(node *root)</div><div class="ttdef"><b>Definition</b> <a href="../../d8/dee/avltree_8cpp_source.html#l00038">avltree.cpp:38</a></div></div>
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<div class="ttc" id="anamespacedp_html"><div class="ttname"><a href="../../df/d88/namespacedp.html">dp</a></div><div class="ttdoc">for std::vector</div><div class="ttdef"><b>Definition</b> <a href="../../de/d8c/partition__problem_8cpp_source.html#l00039">partition_problem.cpp:39</a></div></div>
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</div><!-- fragment -->
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</div>
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</div>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Main function </p>
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<p class="definition">Definition at line <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp_source.html#l00140">140</a> of file <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp_source.html">hamiltons_cycle.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 140</span> {</div>
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<div class="line"><span class="lineno"> 141</span> <a class="code hl_function" href="#ae7880ce913f3058a35ff106d5be9e243">test1</a>();</div>
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<div class="line"><span class="lineno"> 142</span> <a class="code hl_function" href="#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a>();</div>
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<div class="line"><span class="lineno"> 143</span> <a class="code hl_function" href="#a0cc94918b6831f308d4fe4fa27f08299">test3</a>();</div>
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<div class="line"><span class="lineno"> 144</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 145</span>}</div>
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<div class="ttc" id="ahamiltons__cycle_8cpp_html_a0cc94918b6831f308d4fe4fa27f08299"><div class="ttname"><a href="#a0cc94918b6831f308d4fe4fa27f08299">test3</a></div><div class="ttdeci">static void test3()</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d0c/hamiltons__cycle_8cpp_source.html#l00122">hamiltons_cycle.cpp:122</a></div></div>
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<div class="ttc" id="ahamiltons__cycle_8cpp_html_a45d94ead4cf4e1ff9f87c38bc99f59ae"><div class="ttname"><a href="#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a></div><div class="ttdeci">static void test2()</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d0c/hamiltons__cycle_8cpp_source.html#l00103">hamiltons_cycle.cpp:103</a></div></div>
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<div class="ttc" id="ahamiltons__cycle_8cpp_html_ae7880ce913f3058a35ff106d5be9e243"><div class="ttname"><a href="#ae7880ce913f3058a35ff106d5be9e243">test1</a></div><div class="ttdeci">static void test1()</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d0c/hamiltons__cycle_8cpp_source.html#l00081">hamiltons_cycle.cpp:81</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae7880ce913f3058a35ff106d5be9e243">◆ </a></span>test1()</h2>
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<td class="memname">void test1 </td>
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<span class="mlabels"><span class="mlabel static">static</span></span> </td>
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<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 -> 2 -> 3 -> 4</span> </p><dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
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<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>
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<div class="fragment"><div class="line"><span class="lineno"> 81</span> {</div>
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<div class="line"><span class="lineno"> 82</span> std::vector<std::vector<bool>> arr{</div>
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<div class="line"><span class="lineno"> 83</span> std::vector<bool>({<span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>}),</div>
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<div class="line"><span class="lineno"> 84</span> std::vector<bool>({<span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>}),</div>
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<div class="line"><span class="lineno"> 85</span> std::vector<bool>({<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>}),</div>
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<div class="line"><span class="lineno"> 86</span> std::vector<bool>({<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>})};</div>
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<div class="line"><span class="lineno"> 87</span> </div>
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<div class="line"><span class="lineno"> 88</span> <span class="keywordtype">bool</span> ans = <a class="code hl_function" href="#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a>(arr);</div>
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<div class="line"><span class="lineno"> 89</span> std::cout << <span class="stringliteral">"Test 1... "</span>;</div>
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<div class="line"><span class="lineno"> 90</span> assert(ans);</div>
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<div class="line"><span class="lineno"> 91</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><span class="lineno"> 92</span>}</div>
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<div class="ttc" id="ahamiltons__cycle_8cpp_html_abcf824e347eecfeeb69ea0280f34f3e4"><div class="ttname"><a href="#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a></div><div class="ttdeci">bool hamilton_cycle(const std::vector< std::vector< bool > > &routes)</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d0c/hamiltons__cycle_8cpp_source.html#l00030">hamiltons_cycle.cpp:30</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a45d94ead4cf4e1ff9f87c38bc99f59ae">◆ </a></span>test2()</h2>
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<p>this test is testing if <a class="el" href="#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a> returns <span class="tt">false</span> for <br />
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graph:</p><pre>
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1 -> 2 -> 3
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V
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4</pre> <dl class="section return"><dt>Returns</dt><dd>None </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp_source.html#l00103">103</a> of file <a class="el" href="../../dd/d0c/hamiltons__cycle_8cpp_source.html">hamiltons_cycle.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 103</span> {</div>
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<div class="line"><span class="lineno"> 104</span> std::vector<std::vector<bool>> arr{</div>
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<div class="line"><span class="lineno"> 105</span> std::vector<bool>({<span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>}),</div>
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<div class="line"><span class="lineno"> 106</span> std::vector<bool>({<span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">true</span>}),</div>
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<div class="line"><span class="lineno"> 107</span> std::vector<bool>({<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>}),</div>
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<div class="line"><span class="lineno"> 108</span> std::vector<bool>({<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>})};</div>
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<div class="line"><span class="lineno"> 109</span> </div>
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<div class="line"><span class="lineno"> 110</span> <span class="keywordtype">bool</span> ans = <a class="code hl_function" href="#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a>(arr);</div>
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<div class="line"><span class="lineno"> 111</span> </div>
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<div class="line"><span class="lineno"> 112</span> std::cout << <span class="stringliteral">"Test 2... "</span>;</div>
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<div class="line"><span class="lineno"> 113</span> assert(!ans); <span class="comment">// not a cycle</span></div>
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<div class="line"><span class="lineno"> 114</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><span class="lineno"> 115</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0cc94918b6831f308d4fe4fa27f08299">◆ </a></span>test3()</h2>
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<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>
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<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>
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<div class="fragment"><div class="line"><span class="lineno"> 122</span> {</div>
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<div class="line"><span class="lineno"> 123</span> std::vector<std::vector<bool>> arr{</div>
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<div class="line"><span class="lineno"> 124</span> std::vector<bool>({<span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">true</span>}),</div>
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<div class="line"><span class="lineno"> 125</span> std::vector<bool>({<span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">true</span>}),</div>
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<div class="line"><span class="lineno"> 126</span> std::vector<bool>({<span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">true</span>}),</div>
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<div class="line"><span class="lineno"> 127</span> std::vector<bool>({<span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">true</span>})};</div>
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<div class="line"><span class="lineno"> 128</span> </div>
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<div class="line"><span class="lineno"> 129</span> <span class="keywordtype">bool</span> ans = <a class="code hl_function" href="#abcf824e347eecfeeb69ea0280f34f3e4">hamilton_cycle</a>(arr);</div>
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<div class="line"><span class="lineno"> 130</span> </div>
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<div class="line"><span class="lineno"> 131</span> std::cout << <span class="stringliteral">"Test 3... "</span>;</div>
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<div class="line"><span class="lineno"> 132</span> assert(ans);</div>
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<div class="line"><span class="lineno"> 133</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><span class="lineno"> 134</span>}</div>
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