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<p><a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;array&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for n_queens.cpp:</div>
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<p><a href="../../d4/d3e/n__queens_8cpp_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-namespaces" class="groupheader"><a id="namespaces" name="namespaces"></a>
Namespaces</h2></td></tr>
<tr class="memitem:backtracking" id="r_backtracking"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html">backtracking</a></td></tr>
<tr class="memdesc:db/dc0/namespacebacktracking"><td class="mdescLeft">&#160;</td><td class="mdescRight">for vector container <br /></td></tr>
<tr class="memitem:n_5Fqueens" id="r_n_5Fqueens"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/da1/namespacen__queens.html">n_queens</a></td></tr>
<tr class="memdesc:d3/da1/namespacen__queens"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle. <br /></td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a40ae0c7fd04eb20e7f3bff13fc6a5808" id="r_a40ae0c7fd04eb20e7f3bff13fc6a5808"><td class="memTemplParams" colspan="2">template&lt;size_t n&gt; </td></tr>
<tr class="memitem:a40ae0c7fd04eb20e7f3bff13fc6a5808 template"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a40ae0c7fd04eb20e7f3bff13fc6a5808">backtracking::n_queens::printSolution</a> (const std::array&lt; std::array&lt; int, n &gt;, n &gt; &amp;board)</td></tr>
<tr class="memitem:a5730b6683f6adcf5c5ef75cf53dc7160" id="r_a5730b6683f6adcf5c5ef75cf53dc7160"><td class="memTemplParams" colspan="2">template&lt;size_t n&gt; </td></tr>
<tr class="memitem:a5730b6683f6adcf5c5ef75cf53dc7160 template"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a5730b6683f6adcf5c5ef75cf53dc7160">backtracking::n_queens::isSafe</a> (const std::array&lt; std::array&lt; int, n &gt;, n &gt; &amp;board, const int &amp;row, const int &amp;col)</td></tr>
<tr class="memitem:a0dbd7af47d87f0b956609fe9e3288ecb" id="r_a0dbd7af47d87f0b956609fe9e3288ecb"><td class="memTemplParams" colspan="2">template&lt;size_t n&gt; </td></tr>
<tr class="memitem:a0dbd7af47d87f0b956609fe9e3288ecb template"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a0dbd7af47d87f0b956609fe9e3288ecb">backtracking::n_queens::solveNQ</a> (std::array&lt; std::array&lt; int, n &gt;, n &gt; board, const int &amp;col)</td></tr>
<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>
</table>
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">Eight Queens</a> puzzle </p>
<p>The <b>eight queens puzzle</b> is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. The eight queens puzzle is an example of the more general <b>n queens problem</b> of placing n non-attacking queens on an n×n chessboard, for which solutions exist for all natural numbers n with the exception of n = 2 and n = 3.</p>
<dl class="section author"><dt>Author</dt><dd>Unknown author </dd>
<dd>
<a href="https://github.com/Panquesito7" target="_blank">David Leal</a> </dd></dl>
<p class="definition">Definition in file <a class="el" href="../../d4/d3e/n__queens_8cpp_source.html">n_queens.cpp</a>.</p>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
<a id="a5730b6683f6adcf5c5ef75cf53dc7160" name="a5730b6683f6adcf5c5ef75cf53dc7160"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a5730b6683f6adcf5c5ef75cf53dc7160">&#9670;&#160;</a></span>isSafe()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;size_t n&gt; </div>
<table class="memname">
<tr>
<td class="memname">bool backtracking::n_queens::isSafe </td>
<td>(</td>
<td class="paramtype">const std::array&lt; std::array&lt; int, n &gt;, n &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>board</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int &amp;</td> <td class="paramname"><span class="paramname"><em>row</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int &amp;</td> <td class="paramname"><span class="paramname"><em>col</em></span>&#160;)</td>
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<p>Check if a queen can be placed on matrix </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">n</td><td>number of matrix size </td></tr>
</table>
</dd>
</dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">board</td><td>matrix where numbers are saved </td></tr>
<tr><td class="paramname">row</td><td>current index in rows </td></tr>
<tr><td class="paramname">col</td><td>current index in columns </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><span class="tt">true</span> if queen can be placed on matrix </dd>
<dd>
<span class="tt">false</span> if queen can't be placed on matrix </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d4/d3e/n__queens_8cpp_source.html#l00058">58</a> of file <a class="el" href="../../d4/d3e/n__queens_8cpp_source.html">n_queens.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 59</span> {</div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordtype">int</span> i = 0, j = 0;</div>
<div class="line"><span class="lineno"> 61</span> </div>
<div class="line"><span class="lineno"> 62</span> <span class="comment">// Check this row on left side</span></div>
<div class="line"><span class="lineno"> 63</span> <span class="keywordflow">for</span> (i = 0; i &lt; col; i++) {</div>
<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">if</span> (board[row][i]) {</div>
<div class="line"><span class="lineno"> 65</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 66</span> }</div>
<div class="line"><span class="lineno"> 67</span> }</div>
<div class="line"><span class="lineno"> 68</span> </div>
<div class="line"><span class="lineno"> 69</span> <span class="comment">// Check upper diagonal on left side</span></div>
<div class="line"><span class="lineno"> 70</span> <span class="keywordflow">for</span> (i = row, j = col; i &gt;= 0 &amp;&amp; j &gt;= 0; i--, j--) {</div>
<div class="line"><span class="lineno"> 71</span> <span class="keywordflow">if</span> (board[i][j]) {</div>
<div class="line"><span class="lineno"> 72</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 73</span> }</div>
<div class="line"><span class="lineno"> 74</span> }</div>
<div class="line"><span class="lineno"> 75</span> <span class="comment">// Check lower diagonal on left side</span></div>
<div class="line"><span class="lineno"> 76</span> <span class="keywordflow">for</span> (i = row, j = col; j &gt;= 0 &amp;&amp; i &lt; n; i++, j--) {</div>
<div class="line"><span class="lineno"> 77</span> <span class="keywordflow">if</span> (board[i][j]) {</div>
<div class="line"><span class="lineno"> 78</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 79</span> }</div>
<div class="line"><span class="lineno"> 80</span> }</div>
<div class="line"><span class="lineno"> 81</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><span class="lineno"> 82</span>}</div>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d4/d3e/n__queens_8cpp_source.html#l00120">120</a> of file <a class="el" href="../../d4/d3e/n__queens_8cpp_source.html">n_queens.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 120</span> {</div>
<div class="line"><span class="lineno"> 121</span> <span class="keyword">const</span> <span class="keywordtype">int</span> n = 4;</div>
<div class="line"><span class="lineno"> 122</span> std::array&lt;std::array&lt;int, n&gt;, n&gt; board = {</div>
<div class="line"><span class="lineno"> 123</span> std::array&lt;int, n&gt;({0, 0, 0, 0}), std::array&lt;int, n&gt;({0, 0, 0, 0}),</div>
<div class="line"><span class="lineno"> 124</span> std::array&lt;int, n&gt;({0, 0, 0, 0}), std::array&lt;int, n&gt;({0, 0, 0, 0})};</div>
<div class="line"><span class="lineno"> 125</span> </div>
<div class="line"><span class="lineno"> 126</span> <a class="code hl_function" href="#a0dbd7af47d87f0b956609fe9e3288ecb">backtracking::n_queens::solveNQ&lt;n&gt;</a>(board, 0);</div>
<div class="line"><span class="lineno"> 127</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 128</span>}</div>
<div class="ttc" id="an__queens_8cpp_html_a0dbd7af47d87f0b956609fe9e3288ecb"><div class="ttname"><a href="#a0dbd7af47d87f0b956609fe9e3288ecb">backtracking::n_queens::solveNQ</a></div><div class="ttdeci">void solveNQ(std::array&lt; std::array&lt; int, n &gt;, n &gt; board, const int &amp;col)</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d3e/n__queens_8cpp_source.html#l00091">n_queens.cpp:91</a></div></div>
</div><!-- fragment -->
</div>
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<a id="a40ae0c7fd04eb20e7f3bff13fc6a5808" name="a40ae0c7fd04eb20e7f3bff13fc6a5808"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a40ae0c7fd04eb20e7f3bff13fc6a5808">&#9670;&#160;</a></span>printSolution()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;size_t n&gt; </div>
<table class="memname">
<tr>
<td class="memname">void backtracking::n_queens::printSolution </td>
<td>(</td>
<td class="paramtype">const std::array&lt; std::array&lt; int, n &gt;, n &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>board</em></span></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Utility function to print matrix </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">n</td><td>number of matrix size </td></tr>
</table>
</dd>
</dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">board</td><td>matrix where numbers are saved </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="../../d4/d3e/n__queens_8cpp_source.html#l00038">38</a> of file <a class="el" href="../../d4/d3e/n__queens_8cpp_source.html">n_queens.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 38</span> {</div>
<div class="line"><span class="lineno"> 39</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><span class="lineno"> 41</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><span class="lineno"> 42</span> std::cout &lt;&lt; <span class="stringliteral">&quot;&quot;</span> &lt;&lt; board[i][j] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><span class="lineno"> 43</span> }</div>
<div class="line"><span class="lineno"> 44</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 45</span> }</div>
<div class="line"><span class="lineno"> 46</span>}</div>
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<a id="a0dbd7af47d87f0b956609fe9e3288ecb" name="a0dbd7af47d87f0b956609fe9e3288ecb"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0dbd7af47d87f0b956609fe9e3288ecb">&#9670;&#160;</a></span>solveNQ()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;size_t n&gt; </div>
<table class="memname">
<tr>
<td class="memname">void backtracking::n_queens::solveNQ </td>
<td>(</td>
<td class="paramtype">std::array&lt; std::array&lt; int, n &gt;, n &gt;</td> <td class="paramname"><span class="paramname"><em>board</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int &amp;</td> <td class="paramname"><span class="paramname"><em>col</em></span>&#160;)</td>
</tr>
</table>
</div><div class="memdoc">
<p>Solve n queens problem </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">n</td><td>number of matrix size </td></tr>
</table>
</dd>
</dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">board</td><td>matrix where numbers are saved </td></tr>
<tr><td class="paramname">col</td><td>current index in columns </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="../../d4/d3e/n__queens_8cpp_source.html#l00091">91</a> of file <a class="el" href="../../d4/d3e/n__queens_8cpp_source.html">n_queens.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 91</span> {</div>
<div class="line"><span class="lineno"> 92</span> <span class="keywordflow">if</span> (col &gt;= n) {</div>
<div class="line"><span class="lineno"> 93</span> <a class="code hl_function" href="#a40ae0c7fd04eb20e7f3bff13fc6a5808">printSolution&lt;n&gt;</a>(board);</div>
<div class="line"><span class="lineno"> 94</span> <span class="keywordflow">return</span>;</div>
<div class="line"><span class="lineno"> 95</span> }</div>
<div class="line"><span class="lineno"> 96</span> </div>
<div class="line"><span class="lineno"> 97</span> <span class="comment">// Consider this column and try placing</span></div>
<div class="line"><span class="lineno"> 98</span> <span class="comment">// this queen in all rows one by one</span></div>
<div class="line"><span class="lineno"> 99</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><span class="lineno"> 100</span> <span class="comment">// Check if queen can be placed</span></div>
<div class="line"><span class="lineno"> 101</span> <span class="comment">// on board[i][col]</span></div>
<div class="line"><span class="lineno"> 102</span> <span class="keywordflow">if</span> (isSafe&lt;n&gt;(board, i, col)) {</div>
<div class="line"><span class="lineno"> 103</span> <span class="comment">// Place this queen in matrix</span></div>
<div class="line"><span class="lineno"> 104</span> board[i][col] = 1;</div>
<div class="line"><span class="lineno"> 105</span> </div>
<div class="line"><span class="lineno"> 106</span> <span class="comment">// Recursive to place rest of the queens</span></div>
<div class="line"><span class="lineno"> 107</span> solveNQ&lt;n&gt;(board, col + 1);</div>
<div class="line"><span class="lineno"> 108</span> </div>
<div class="line"><span class="lineno"> 109</span> board[i][col] = 0; <span class="comment">// backtrack</span></div>
<div class="line"><span class="lineno"> 110</span> }</div>
<div class="line"><span class="lineno"> 111</span> }</div>
<div class="line"><span class="lineno"> 112</span>}</div>
<div class="ttc" id="an__queens_8cpp_html_a40ae0c7fd04eb20e7f3bff13fc6a5808"><div class="ttname"><a href="#a40ae0c7fd04eb20e7f3bff13fc6a5808">backtracking::n_queens::printSolution</a></div><div class="ttdeci">void printSolution(const std::array&lt; std::array&lt; int, n &gt;, n &gt; &amp;board)</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d3e/n__queens_8cpp_source.html#l00038">n_queens.cpp:38</a></div></div>
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