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<div class="headertitle"><div class="title">travelling_salesman_using_bit_manipulation.cpp File Reference</div></div>
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<p>Implementation to [Travelling Salesman problem using bit-masking] (<a href="https://www.geeksforgeeks.org/travelling-salesman-problem-set-1/">https://www.geeksforgeeks.org/travelling-salesman-problem-set-1/</a>)
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;limits&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for travelling_salesman_using_bit_manipulation.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d81/namespacebit__manipulation.html">bit_manipulation</a></td></tr>
<tr class="memdesc:d7/d81/namespacebit__manipulation"><td class="mdescLeft">&#160;</td><td class="mdescRight">for IO operations <br /></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d3f/namespacetravelling_salesman__bitmanipulation.html">travellingSalesman_bitmanipulation</a></td></tr>
<tr class="memdesc:d7/d3f/namespacetravelling_salesman__bitmanipulation"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for the <a href="https://www.geeksforgeeks.org/travelling-salesman-problem-set-1/" target="_blank">Travelling Salesman Bitmask</a> implementation. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:ad08f082be02c3437c2fe89cb035fcee1" id="r_ad08f082be02c3437c2fe89cb035fcee1"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ad08f082be02c3437c2fe89cb035fcee1">bit_manipulation::travelling_salesman_using_bit_manipulation::travelling_salesman_using_bit_manipulation</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint32_t &gt; &gt; dist, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a> setOfCities, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a> city, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a> n, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint32_t &gt; &gt; &amp;dp)</td></tr>
<tr class="memdesc:ad08f082be02c3437c2fe89cb035fcee1"><td class="mdescLeft">&#160;</td><td class="mdescRight">The function implements travellingSalesman using bitmanipulation. <br /></td></tr>
<tr class="separator:ad08f082be02c3437c2fe89cb035fcee1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation to [Travelling Salesman problem using bit-masking] (<a href="https://www.geeksforgeeks.org/travelling-salesman-problem-set-1/">https://www.geeksforgeeks.org/travelling-salesman-problem-set-1/</a>) </p>
<p>Given the distance/cost(as and adjacency matrix) between each city/node to the other city/node , the problem is to find the shortest possible route that visits every city exactly once and returns to the starting point or we can say the minimum cost of whole tour.</p>
<p>Explanation: INPUT -&gt; You are given with a adjacency matrix A = {} which contains the distance between two cities/node.</p>
<p>OUTPUT -&gt; <a class="el" href="../../d4/d12/namespace_minimum.html" title="Implementation of Minimum Edit Distance algorithm.">Minimum</a> cost of whole tour from starting point</p>
<p>Worst Case Time Complexity: O(n^2 * 2^n) Space complexity: O(n) </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Rytnix" target="_blank">Utkarsh Yadav</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 138</span> {</div>
<div class="line"><span class="lineno"> 139</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 140</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 141</span>}</div>
<div class="ttc" id="atravelling__salesman__using__bit__manipulation_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> travelling_salesman_using_bit_manipulation.cpp:99</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">static void test </td>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 99</span> {</div>
<div class="line"><span class="lineno"> 100</span> <span class="comment">// 1st test-case</span></div>
<div class="line"><span class="lineno"> 101</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint32_t&gt;</a>&gt; dist = {</div>
<div class="line"><span class="lineno"> 102</span> {0, 20, 42, 35}, {20, 0, 30, 34}, {42, 30, 0, 12}, {35, 34, 12, 0}};</div>
<div class="line"><span class="lineno"> 103</span> uint32_t V = dist.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 104</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint32_t&gt;</a>&gt; <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>(1 &lt;&lt; V, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a>(V, -1));</div>
<div class="line"><span class="lineno"> 105</span> assert(bit_manipulation::travelling_salesman_using_bit_manipulation::</div>
<div class="line"><span class="lineno"> 106</span> <a class="code hl_function" href="#ad08f082be02c3437c2fe89cb035fcee1">travelling_salesman_using_bit_manipulation</a>(dist, 1, 0, V, <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>) ==</div>
<div class="line"><span class="lineno"> 107</span> 97);</div>
<div class="line"><span class="lineno"> 108</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test-case: passed!&quot;</span></div>
<div class="line"><span class="lineno"> 109</span> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 110</span> </div>
<div class="line"><span class="lineno"> 111</span> <span class="comment">// 2nd test-case</span></div>
<div class="line"><span class="lineno"> 112</span> dist = {{0, 5, 10, 15}, {5, 0, 20, 30}, {10, 20, 0, 35}, {15, 30, 35, 0}};</div>
<div class="line"><span class="lineno"> 113</span> V = dist.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 114</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint32_t&gt;</a>&gt; dp1(1 &lt;&lt; V,</div>
<div class="line"><span class="lineno"> 115</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a>(V, -1));</div>
<div class="line"><span class="lineno"> 116</span> assert(bit_manipulation::travelling_salesman_using_bit_manipulation::</div>
<div class="line"><span class="lineno"> 117</span> <a class="code hl_function" href="#ad08f082be02c3437c2fe89cb035fcee1">travelling_salesman_using_bit_manipulation</a>(dist, 1, 0, V, dp1) ==</div>
<div class="line"><span class="lineno"> 118</span> 75);</div>
<div class="line"><span class="lineno"> 119</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test-case: passed!&quot;</span></div>
<div class="line"><span class="lineno"> 120</span> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 121</span> <span class="comment">// 3rd test-case</span></div>
<div class="line"><span class="lineno"> 122</span> dist = {{0, 10, 15, 20}, {10, 0, 35, 25}, {15, 35, 0, 30}, {20, 25, 30, 0}};</div>
<div class="line"><span class="lineno"> 123</span> V = dist.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 124</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint32_t&gt;</a>&gt; dp2(1 &lt;&lt; V,</div>
<div class="line"><span class="lineno"> 125</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a>(V, -1));</div>
<div class="line"><span class="lineno"> 126</span> assert(bit_manipulation::travelling_salesman_using_bit_manipulation::</div>
<div class="line"><span class="lineno"> 127</span> <a class="code hl_function" href="#ad08f082be02c3437c2fe89cb035fcee1">travelling_salesman_using_bit_manipulation</a>(dist, 1, 0, V, dp2) ==</div>
<div class="line"><span class="lineno"> 128</span> 80);</div>
<div class="line"><span class="lineno"> 129</span> </div>
<div class="line"><span class="lineno"> 130</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test-case: passed!&quot;</span></div>
<div class="line"><span class="lineno"> 131</span> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 132</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<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> partition_problem.cpp:39</div></div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
<div class="ttc" id="atravelling__salesman__using__bit__manipulation_8cpp_html_ad08f082be02c3437c2fe89cb035fcee1"><div class="ttname"><a href="#ad08f082be02c3437c2fe89cb035fcee1">bit_manipulation::travelling_salesman_using_bit_manipulation::travelling_salesman_using_bit_manipulation</a></div><div class="ttdeci">std::uint64_t travelling_salesman_using_bit_manipulation(std::vector&lt; std::vector&lt; uint32_t &gt; &gt; dist, std::uint64_t setOfCities, std::uint64_t city, std::uint64_t n, std::vector&lt; std::vector&lt; uint32_t &gt; &gt; &amp;dp)</div><div class="ttdoc">The function implements travellingSalesman using bitmanipulation.</div><div class="ttdef"><b>Definition</b> travelling_salesman_using_bit_manipulation.cpp:52</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a> bit_manipulation::travelling_salesman_using_bit_manipulation::travelling_salesman_using_bit_manipulation </td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint32_t &gt; &gt;</td> <td class="paramname"><span class="paramname"><em>dist</em></span>, </td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a></td> <td class="paramname"><span class="paramname"><em>setOfCities</em></span>, </td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a></td> <td class="paramname"><span class="paramname"><em>city</em></span>, </td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a></td> <td class="paramname"><span class="paramname"><em>n</em></span>, </td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint32_t &gt; &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>dp</em></span>&#160;)</td>
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<p>The function implements travellingSalesman using bitmanipulation. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">dist</td><td>is the cost to reach between two cities/nodes </td></tr>
<tr><td class="paramname">setOfCitites</td><td>represents the city in bit form.\ </td></tr>
<tr><td class="paramname">city</td><td>is taken to track the current city movement. </td></tr>
<tr><td class="paramname">n</td><td>is the no of citys . </td></tr>
<tr><td class="paramname">dp</td><td>vector is used to keep a record of state to avoid the recomputation. </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>minimum cost of traversing whole nodes/cities from starting point back to starting point </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 64</span>{</div>
<div class="line"><span class="lineno"> 65</span> <span class="comment">// base case;</span></div>
<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">if</span> (setOfCities == (1 &lt;&lt; n) - 1) { <span class="comment">// we have covered all the cities</span></div>
<div class="line"><span class="lineno"> 67</span> <span class="keywordflow">return</span> dist[city][0]; <span class="comment">// return the cost from the current city to the</span></div>
<div class="line"><span class="lineno"> 68</span> <span class="comment">// original city.</span></div>
<div class="line"><span class="lineno"> 69</span> }</div>
<div class="line"><span class="lineno"> 70</span> </div>
<div class="line"><span class="lineno"> 71</span> <span class="keywordflow">if</span> (<a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[setOfCities][city] != -1) {</div>
<div class="line"><span class="lineno"> 72</span> <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[setOfCities][city];</div>
<div class="line"><span class="lineno"> 73</span> }</div>
<div class="line"><span class="lineno"> 74</span> <span class="comment">// otherwise try all possible options</span></div>
<div class="line"><span class="lineno"> 75</span> uint64_t ans = 2147483647;</div>
<div class="line"><span class="lineno"> 76</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> choice = 0; choice &lt; n; choice++) {</div>
<div class="line"><span class="lineno"> 77</span> <span class="comment">// check if the city is visited or not.</span></div>
<div class="line"><span class="lineno"> 78</span> <span class="keywordflow">if</span> ((setOfCities &amp; (1 &lt;&lt; choice)) ==</div>
<div class="line"><span class="lineno"> 79</span> 0) { <span class="comment">// this means that this perticular city is not visited.</span></div>
<div class="line"><span class="lineno"> 80</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a> subProb =</div>
<div class="line"><span class="lineno"> 81</span> dist[city][choice] +</div>
<div class="line"><span class="lineno"> 82</span> <a class="code hl_function" href="#ad08f082be02c3437c2fe89cb035fcee1">travelling_salesman_using_bit_manipulation</a>(</div>
<div class="line"><span class="lineno"> 83</span> dist, setOfCities | (1 &lt;&lt; choice), choice, n, <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>);</div>
<div class="line"><span class="lineno"> 84</span> <span class="comment">// Here we are doing a recursive call to tsp with the updated set of</span></div>
<div class="line"><span class="lineno"> 85</span> <span class="comment">// city/node and choice which tells that where we are currently.</span></div>
<div class="line"><span class="lineno"> 86</span> ans = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(ans, subProb);</div>
<div class="line"><span class="lineno"> 87</span> }</div>
<div class="line"><span class="lineno"> 88</span> }</div>
<div class="line"><span class="lineno"> 89</span> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[setOfCities][city] = ans;</div>
<div class="line"><span class="lineno"> 90</span> <span class="keywordflow">return</span> ans;</div>
<div class="line"><span class="lineno"> 91</span>}</div>
<div class="ttc" id="ainteger_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a></div></div>
<div class="ttc" id="amin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a></div><div class="ttdeci">T min(T... args)</div></div>
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