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 <span id="projectnumber">1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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<div class="title">backtracking Namespace Reference</div> </div>
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<p>Backtracking algorithms.
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<a href="../../db/dc0/namespacebacktracking.html#details">More...</a></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a8cfb2d08840766ac4402196079308a36"><td class="memTemplParams" colspan="2">template<size_t V> </td></tr>
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<tr class="memitem:a8cfb2d08840766ac4402196079308a36"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html#a8cfb2d08840766ac4402196079308a36">printSolution</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V > &color)</td></tr>
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<tr class="separator:a8cfb2d08840766ac4402196079308a36"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a5a6c3c2b065ea1c07adf2f638f8efc43"><td class="memTemplParams" colspan="2">template<size_t V> </td></tr>
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<tr class="memitem:a5a6c3c2b065ea1c07adf2f638f8efc43"><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html#a5a6c3c2b065ea1c07adf2f638f8efc43">isSafe</a> (int v, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V >, V > &graph, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V > &color, int c)</td></tr>
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<tr class="separator:a5a6c3c2b065ea1c07adf2f638f8efc43"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a29360ddb1bad75caa61ec895b6e71986"><td class="memTemplParams" colspan="2">template<size_t V> </td></tr>
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<tr class="memitem:a29360ddb1bad75caa61ec895b6e71986"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html#a29360ddb1bad75caa61ec895b6e71986">graphColoring</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V >, V > &graph, int m, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V > color, int v)</td></tr>
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<tr class="separator:a29360ddb1bad75caa61ec895b6e71986"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a531de8cb2d4d16ca63353d9c72158257"><td class="memTemplParams" colspan="2">template<size_t V> </td></tr>
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<tr class="memitem:a531de8cb2d4d16ca63353d9c72158257"><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html#a531de8cb2d4d16ca63353d9c72158257">issafe</a> (int x, int y, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V >, V > &sol)</td></tr>
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<tr class="separator:a531de8cb2d4d16ca63353d9c72158257"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a932e38e8912742cedf7b5a837168e03a"><td class="memTemplParams" colspan="2">template<size_t V> </td></tr>
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<tr class="memitem:a932e38e8912742cedf7b5a837168e03a"><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html#a932e38e8912742cedf7b5a837168e03a">solve</a> (int x, int y, int <a class="el" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a>, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V >, V > &sol, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V > &xmov, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V > &ymov)</td></tr>
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<tr class="separator:a932e38e8912742cedf7b5a837168e03a"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a78540bcb5ef3473b2348cbc34748ec50"><td class="memTemplParams" colspan="2">template<size_t T> </td></tr>
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<tr class="memitem:a78540bcb5ef3473b2348cbc34748ec50"><td class="memTemplItemLeft" align="right" valign="top">int </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html#a78540bcb5ef3473b2348cbc34748ec50">minimax</a> (int depth, int node_index, bool is_max, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, T > &scores, double <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
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<tr class="separator:a78540bcb5ef3473b2348cbc34748ec50"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a80af16e57cfb6aaab2bf1da4c4db3308"><td class="memTemplParams" colspan="2">template<size_t V> </td></tr>
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<tr class="memitem:a80af16e57cfb6aaab2bf1da4c4db3308"><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html#a80af16e57cfb6aaab2bf1da4c4db3308">isPossible</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V >, V > &mat, int i, int j, int no, int n)</td></tr>
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<tr class="separator:a80af16e57cfb6aaab2bf1da4c4db3308"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a4664b23ed7939e3df1c0cb23013eec0c"><td class="memTemplParams" colspan="2">template<size_t V> </td></tr>
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<tr class="memitem:a4664b23ed7939e3df1c0cb23013eec0c"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html#a4664b23ed7939e3df1c0cb23013eec0c">printMat</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V >, V > &mat, int n)</td></tr>
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<tr class="separator:a4664b23ed7939e3df1c0cb23013eec0c"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:af6b62cbc209d7e13ffca0ab3ed3392b6"><td class="memTemplParams" colspan="2">template<size_t V> </td></tr>
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<tr class="memitem:af6b62cbc209d7e13ffca0ab3ed3392b6"><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html#af6b62cbc209d7e13ffca0ab3ed3392b6">solveSudoku</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V >, V > &mat, int i, int j)</td></tr>
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<tr class="separator:af6b62cbc209d7e13ffca0ab3ed3392b6"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>Backtracking algorithms. </p>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="a29360ddb1bad75caa61ec895b6e71986"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a29360ddb1bad75caa61ec895b6e71986">◆ </a></span>graphColoring()</h2>
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template<size_t V> </div>
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<td class="memname">void backtracking::graphColoring </td>
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<td>(</td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V >, V > & </td>
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<td class="paramname"><em>graph</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>m</em>, </td>
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<td></td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V > </td>
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<td class="paramname"><em>color</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>v</em> </td>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</div><div class="memdoc">
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<p>A recursive utility function to solve m coloring problem </p><dl class="tparams"><dt>Template Parameters</dt><dd>
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<table class="tparams">
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<tr><td class="paramname">V</td><td>number of vertices in the graph </td></tr>
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</table>
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</dd>
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</dl>
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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="paramdir"></td><td class="paramname">graph</td><td>matrix of graph nonnectivity </td></tr>
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<tr><td class="paramdir"></td><td class="paramname">m</td><td>number of colors </td></tr>
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<tr><td class="paramdir">[in,out]</td><td class="paramname">color</td><td>description // used in,out to notify in documentation that this parameter gets modified by the function </td></tr>
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<tr><td class="paramdir"></td><td class="paramname">v</td><td>index of graph vertex to check </td></tr>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  {</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="comment">// base case:</span></div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="comment">// If all vertices are assigned a color then return true</span></div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keywordflow">if</span> (v == V) {</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  backtracking::printSolution<V>(color);</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keywordflow">return</span>;</div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  }</div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  </div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="comment">// Consider this vertex v and try different colors</span></div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> c = 1; c <= m; c++) {</div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="comment">// Check if assignment of color c to v is fine</span></div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordflow">if</span> (backtracking::isSafe<V>(v, <a class="code" href="../../df/dce/namespacegraph.html">graph</a>, color, c)) {</div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  color[v] = c;</div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  </div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="comment">// recur to assign colors to rest of the vertices</span></div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  backtracking::graphColoring<V>(<a class="code" href="../../df/dce/namespacegraph.html">graph</a>, m, color, v + 1);</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  </div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="comment">// If assigning color c doesn't lead to a solution then remove it</span></div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  color[v] = 0;</div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  }</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  }</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  }</div>
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<a id="a80af16e57cfb6aaab2bf1da4c4db3308"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a80af16e57cfb6aaab2bf1da4c4db3308">◆ </a></span>isPossible()</h2>
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template<size_t V> </div>
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<td class="memname">bool backtracking::isPossible </td>
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<td>(</td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V >, V > & </td>
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<td class="paramname"><em>mat</em>, </td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>no</em>, </td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>n</em> </td>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</div><div class="memdoc">
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<p>Checks if it's possible to place a number 'no' </p><dl class="tparams"><dt>Template Parameters</dt><dd>
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<table class="tparams">
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<tr><td class="paramname">V</td><td>number of vertices in the array </td></tr>
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</table>
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</dd>
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</dl>
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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">mat</td><td>matrix where numbers are saved </td></tr>
|
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<tr><td class="paramname">i</td><td>current index in rows </td></tr>
|
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<tr><td class="paramname">j</td><td>current index in columns </td></tr>
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<tr><td class="paramname">no</td><td>number to be added in matrix </td></tr>
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<tr><td class="paramname">n</td><td>number of times loop will run </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><code>true</code> if 'mat' is different from 'no' </dd>
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<dd>
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<code>false</code> if 'mat' equals to 'no' </dd></dl>
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<p>'no' shouldn't be present in either row i or column j</p>
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<p>'no' shouldn't be present in the 3*3 subgrid</p>
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<div class="fragment"><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  {<span class="comment"></span></div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"> /// 'no' shouldn't be present in either row i or column j</span></div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"></span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> x = 0; x < n; x++) {</div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keywordflow">if</span> (mat[x][j] == no || mat[i][x] == no) {</div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  }</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  }</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment"></span> </div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment"> /// 'no' shouldn't be present in the 3*3 subgrid</span></div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment"></span> <span class="keywordtype">int</span> sx = (i / 3) * 3;</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keywordtype">int</span> sy = (j / 3) * 3;</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  </div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> x = sx; x < sx + 3; x++) {</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> y = sy; y < sy + 3; y++) {</div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keywordflow">if</span> (mat[x][y] == no) {</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  }</div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  }</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  }</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  </div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  }</div>
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</div><!-- fragment -->
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<h2 class="memtitle"><span class="permalink"><a href="#a5a6c3c2b065ea1c07adf2f638f8efc43">◆ </a></span>isSafe()</h2>
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template<size_t V> </div>
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<td class="memname">bool backtracking::isSafe </td>
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<td>(</td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>v</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V >, V > & </td>
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<td class="paramname"><em>graph</em>, </td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V > & </td>
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<td class="paramname"><em>color</em>, </td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>c</em> </td>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</div><div class="memdoc">
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<p>A utility function to check if the current color assignment is safe for vertex v </p><dl class="tparams"><dt>Template Parameters</dt><dd>
|
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<table class="tparams">
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<tr><td class="paramname">V</td><td>number of vertices in the graph </td></tr>
|
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</table>
|
|
</dd>
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</dl>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
|
|
<tr><td class="paramname">v</td><td>index of graph vertex to check </td></tr>
|
|
<tr><td class="paramname">graph</td><td>matrix of graph nonnectivity </td></tr>
|
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<tr><td class="paramname">color</td><td>vector of colors assigned to the graph nodes/vertices </td></tr>
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<tr><td class="paramname">c</td><td>color value to check for the node <code>v</code> </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><code>true</code> if the color is safe to be assigned to the node </dd>
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<dd>
|
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<code>false</code> if the color is not safe to be assigned to the node </dd></dl>
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<div class="fragment"><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  {</div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < V; i++) {</div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordflow">if</span> (<a class="code" href="../../df/dce/namespacegraph.html">graph</a>[v][i] && c == color[i]) {</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  }</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  }</div>
|
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  }</div>
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</div><!-- fragment -->
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<a id="a531de8cb2d4d16ca63353d9c72158257"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a531de8cb2d4d16ca63353d9c72158257">◆ </a></span>issafe()</h2>
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template<size_t V> </div>
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<td class="memname">bool backtracking::issafe </td>
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<td>(</td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>y</em>, </td>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V >, V > & </td>
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<td class="paramname"><em>sol</em> </td>
|
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</div><div class="memdoc">
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<p>A utility function to check if i,j are valid indexes for N*N chessboard </p><dl class="tparams"><dt>Template Parameters</dt><dd>
|
|
<table class="tparams">
|
|
<tr><td class="paramname">V</td><td>number of vertices in array </td></tr>
|
|
</table>
|
|
</dd>
|
|
</dl>
|
|
<dl class="params"><dt>Parameters</dt><dd>
|
|
<table class="params">
|
|
<tr><td class="paramname">x</td><td>current index in rows </td></tr>
|
|
<tr><td class="paramname">y</td><td>current index in columns </td></tr>
|
|
<tr><td class="paramname">sol</td><td>matrix where numbers are saved </td></tr>
|
|
</table>
|
|
</dd>
|
|
</dl>
|
|
<dl class="section return"><dt>Returns</dt><dd><code>true</code> if .... </dd>
|
|
<dd>
|
|
<code>false</code> if .... </dd></dl>
|
|
<div class="fragment"><div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  {</div>
|
|
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keywordflow">return</span> (x < V && x >= 0 && y < V && y >= 0 && sol[x][y] == -1);</div>
|
|
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  }</div>
|
|
</div><!-- fragment -->
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</div>
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</div>
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<a id="a78540bcb5ef3473b2348cbc34748ec50"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a78540bcb5ef3473b2348cbc34748ec50">◆ </a></span>minimax()</h2>
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template<size_t T> </div>
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<td class="memname">int backtracking::minimax </td>
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|
<td>(</td>
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|
<td class="paramtype">int </td>
|
|
<td class="paramname"><em>depth</em>, </td>
|
|
</tr>
|
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<tr>
|
|
<td class="paramkey"></td>
|
|
<td></td>
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<td class="paramtype">int </td>
|
|
<td class="paramname"><em>node_index</em>, </td>
|
|
</tr>
|
|
<tr>
|
|
<td class="paramkey"></td>
|
|
<td></td>
|
|
<td class="paramtype">bool </td>
|
|
<td class="paramname"><em>is_max</em>, </td>
|
|
</tr>
|
|
<tr>
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|
<td class="paramkey"></td>
|
|
<td></td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, T > & </td>
|
|
<td class="paramname"><em>scores</em>, </td>
|
|
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|
|
<tr>
|
|
<td class="paramkey"></td>
|
|
<td></td>
|
|
<td class="paramtype">double </td>
|
|
<td class="paramname"><em>height</em> </td>
|
|
</tr>
|
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<tr>
|
|
<td></td>
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<td>)</td>
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<td></td><td></td>
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</div><div class="memdoc">
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<p>Check which number is the maximum/minimum in the array </p><dl class="params"><dt>Parameters</dt><dd>
|
|
<table class="params">
|
|
<tr><td class="paramname">depth</td><td>current depth in game tree </td></tr>
|
|
<tr><td class="paramname">node_index</td><td>current index in array </td></tr>
|
|
<tr><td class="paramname">is_max</td><td>if current index is the longest number </td></tr>
|
|
<tr><td class="paramname">scores</td><td>saved numbers in array </td></tr>
|
|
<tr><td class="paramname">height</td><td>maximum height for game tree </td></tr>
|
|
</table>
|
|
</dd>
|
|
</dl>
|
|
<dl class="section return"><dt>Returns</dt><dd>maximum or minimum number </dd></dl>
|
|
<div class="fragment"><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  {</div>
|
|
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordflow">if</span> (depth == <a class="code" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>) {</div>
|
|
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordflow">return</span> scores[node_index];</div>
|
|
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  }</div>
|
|
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  </div>
|
|
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordtype">int</span> v1 = <a class="code" href="../../db/dc0/namespacebacktracking.html#a78540bcb5ef3473b2348cbc34748ec50">minimax</a>(depth + 1, node_index * 2, !is_max, scores, <a class="code" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>);</div>
|
|
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordtype">int</span> v2 = <a class="code" href="../../db/dc0/namespacebacktracking.html#a78540bcb5ef3473b2348cbc34748ec50">minimax</a>(depth + 1, node_index * 2 + 1, !is_max, scores, <a class="code" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>);</div>
|
|
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  </div>
|
|
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keywordflow">return</span> is_max ? <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(v1, v2) : <a class="code" href="../../d8/dcc/namespacestd.html">std</a>::<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a>(v1, v2);</div>
|
|
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> }</div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/dc0/namespacebacktracking_a78540bcb5ef3473b2348cbc34748ec50_cgraph.svg" width="286" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<a id="a4664b23ed7939e3df1c0cb23013eec0c"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a4664b23ed7939e3df1c0cb23013eec0c">◆ </a></span>printMat()</h2>
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<td class="memname">void backtracking::printMat </td>
|
|
<td>(</td>
|
|
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V >, V > & </td>
|
|
<td class="paramname"><em>mat</em>, </td>
|
|
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|
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<td class="paramkey"></td>
|
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|
|
<td class="paramtype">int </td>
|
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<td class="paramname"><em>n</em> </td>
|
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|
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<tr>
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<p>Utility function to print matrix </p><dl class="tparams"><dt>Template Parameters</dt><dd>
|
|
<table class="tparams">
|
|
<tr><td class="paramname">V</td><td>number of vertices in array </td></tr>
|
|
</table>
|
|
</dd>
|
|
</dl>
|
|
<dl class="params"><dt>Parameters</dt><dd>
|
|
<table class="params">
|
|
<tr><td class="paramname">mat</td><td>matrix where numbers are saved </td></tr>
|
|
<tr><td class="paramname">n</td><td>number of times loop will run </td></tr>
|
|
</table>
|
|
</dd>
|
|
</dl>
|
|
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
|
|
<div class="fragment"><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  {</div>
|
|
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < n; i++) {</div>
|
|
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < n; j++) {</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << mat[i][j] << <span class="stringliteral">" "</span>;</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordflow">if</span> ((j + 1) % 3 == 0) {</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="charliteral">'\t'</span>;</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  }</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  }</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keywordflow">if</span> ((i + 1) % 3 == 0) {</div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  }</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  }</div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  }</div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/dc0/namespacebacktracking_a4664b23ed7939e3df1c0cb23013eec0c_cgraph.svg" width="282" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<h2 class="memtitle"><span class="permalink"><a href="#a8cfb2d08840766ac4402196079308a36">◆ </a></span>printSolution()</h2>
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template<size_t V> </div>
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<td class="memname">void backtracking::printSolution </td>
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<td>(</td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V > & </td>
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<td class="paramname"><em>color</em></td><td>)</td>
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<p>A utility function to print solution </p><dl class="tparams"><dt>Template Parameters</dt><dd>
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<table class="tparams">
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<tr><td class="paramname">V</td><td>number of vertices in the graph </td></tr>
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</dl>
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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">color</td><td>array of colors assigned to the nodes </td></tr>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  {</div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Following are the assigned colors\n"</span>;</div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keywordflow">for</span> (<span class="keyword">auto</span> &col : color) {</div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << col;</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  }</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a932e38e8912742cedf7b5a837168e03a">◆ </a></span>solve()</h2>
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template<size_t V> </div>
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<td class="memname">bool backtracking::solve </td>
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<td>(</td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>x</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>y</em>, </td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>mov</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V >, V > & </td>
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<td class="paramname"><em>sol</em>, </td>
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<td></td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V > & </td>
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<td class="paramname"><em>xmov</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V > & </td>
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<td class="paramname"><em>ymov</em> </td>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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<p>Knight's tour algorithm </p><dl class="tparams"><dt>Template Parameters</dt><dd>
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<table class="tparams">
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<tr><td class="paramname">V</td><td>number of vertices in array </td></tr>
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</table>
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</dl>
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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">x</td><td>current index in rows </td></tr>
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<tr><td class="paramname">y</td><td>current index in columns </td></tr>
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<tr><td class="paramname">mov</td><td>movement to be done </td></tr>
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<tr><td class="paramname">sol</td><td>matrix where numbers are saved </td></tr>
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<tr><td class="paramname">xmov</td><td>next move of knight (x coordinate) </td></tr>
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<tr><td class="paramname">ymov</td><td>next move of knight (y coordinate) </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><code>true</code> if solution exists </dd>
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<dd>
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<code>false</code> if solution does not exist </dd></dl>
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<div class="fragment"><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  {</div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keywordtype">int</span> k, xnext, ynext;</div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  </div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordflow">if</span> (<a class="code" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a> == V * V) {</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  }</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  </div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keywordflow">for</span> (k = 0; k < V; k++) {</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  xnext = x + xmov[k];</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  ynext = y + ymov[k];</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  </div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordflow">if</span> (backtracking::issafe<V>(xnext, ynext, sol)) {</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  sol[xnext][ynext] = <a class="code" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a>;</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  </div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordflow">if</span> (backtracking::solve<V>(xnext, ynext, <a class="code" href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a> + 1, sol, xmov, ymov) == <span class="keyword">true</span>) {</div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  }</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  sol[xnext][ynext] = -1;</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  }</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  }</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  }</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  }</div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/dc0/namespacebacktracking_a932e38e8912742cedf7b5a837168e03a_cgraph.svg" width="240" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<h2 class="memtitle"><span class="permalink"><a href="#af6b62cbc209d7e13ffca0ab3ed3392b6">◆ </a></span>solveSudoku()</h2>
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<td class="memname">bool backtracking::solveSudoku </td>
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<td>(</td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, V >, V > & </td>
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<td class="paramname"><em>mat</em>, </td>
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<td class="paramname"><em>i</em>, </td>
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<td class="paramname"><em>j</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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<p>Sudoku algorithm </p><dl class="tparams"><dt>Template Parameters</dt><dd>
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|
<table class="tparams">
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|
<tr><td class="paramname">V</td><td>number of vertices in array </td></tr>
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</table>
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</dd>
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</dl>
|
|
<dl class="params"><dt>Parameters</dt><dd>
|
|
<table class="params">
|
|
<tr><td class="paramname">mat</td><td>matrix where numbers are saved </td></tr>
|
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<tr><td class="paramname">i</td><td>current index in rows </td></tr>
|
|
<tr><td class="paramname">j</td><td>current index in columns </td></tr>
|
|
</table>
|
|
</dd>
|
|
</dl>
|
|
<dl class="section return"><dt>Returns</dt><dd><code>true</code> if 'no' was placed </dd>
|
|
<dd>
|
|
<code>false</code> if 'no' was not placed </dd></dl>
|
|
<p>Base Case</p>
|
|
<p>Solved for 9 rows already</p>
|
|
<p>Crossed the last Cell in the row</p>
|
|
<p>Blue Cell - Skip</p>
|
|
<p>White Cell Try to place every possible no</p>
|
|
<p>Place the 'no' - assuming a solution will exist</p>
|
|
<p>Couldn't find a solution loop will place the next no.</p>
|
|
<p><a class="el" href="../../dd/d4f/class_solution.html">Solution</a> couldn't be found for any of the numbers provided</p>
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<div class="fragment"><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  {<span class="comment"></span></div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment"> /// Base Case</span></div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment"></span> <span class="keywordflow">if</span> (i == 9) {<span class="comment"></span></div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment"> /// Solved for 9 rows already</span></div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment"></span> backtracking::printMat<V>(mat, 9);</div>
|
|
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
|
|
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  }</div>
|
|
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment"></span> </div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment"> /// Crossed the last Cell in the row</span></div>
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|
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment"></span> <span class="keywordflow">if</span> (j == 9) {</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keywordflow">return</span> backtracking::solveSudoku<V>(mat, i + 1, 0);</div>
|
|
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  }</div>
|
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment"></span> </div>
|
|
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="comment"> /// Blue Cell - Skip</span></div>
|
|
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment"></span> <span class="keywordflow">if</span> (mat[i][j] != 0) {</div>
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|
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">return</span> backtracking::solveSudoku<V>(mat, i, j + 1);</div>
|
|
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  }<span class="comment"></span></div>
|
|
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment"> /// White Cell</span></div>
|
|
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment"> /// Try to place every possible no</span></div>
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|
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment"></span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> no = 1; no <= 9; no++) {</div>
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|
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keywordflow">if</span> (backtracking::isPossible<V>(mat, i, j, no, 9)) {<span class="comment"></span></div>
|
|
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment"> /// Place the 'no' - assuming a solution will exist</span></div>
|
|
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment"></span> mat[i][j] = no;</div>
|
|
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keywordtype">bool</span> solution_found = backtracking::solveSudoku<V>(mat, i, j + 1);</div>
|
|
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keywordflow">if</span> (solution_found) {</div>
|
|
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
|
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  }<span class="comment"></span></div>
|
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment"> /// Couldn't find a solution</span></div>
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|
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment"> /// loop will place the next no.</span></div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="comment"></span> }</div>
|
|
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  }<span class="comment"></span></div>
|
|
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment"> /// Solution couldn't be found for any of the numbers provided</span></div>
|
|
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="comment"></span> mat[i][j] = 0;</div>
|
|
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  }</div>
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