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<p><a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle">Eight Queens</a> puzzle
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;array&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for n_queens.cpp:</div>
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Namespaces</h2></td></tr>
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<tr class="memdesc:db/dc0/namespacebacktracking"><td class="mdescLeft">&#160;</td><td class="mdescRight">Backtracking algorithms. <br /></td></tr>
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<tr class="memitem:d3/da1/namespacen__queens"><td class="memItemLeft" align="right" valign="top"> &#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">Eight Queens</a> puzzle. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a40ae0c7fd04eb20e7f3bff13fc6a5808"><td class="memTemplParams" colspan="2">template&lt;size_t n&gt; </td></tr>
<tr class="memitem:a40ae0c7fd04eb20e7f3bff13fc6a5808"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d4/d3e/n__queens_8cpp.html#a40ae0c7fd04eb20e7f3bff13fc6a5808">backtracking::n_queens::printSolution</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt;, n &gt; &amp;board)</td></tr>
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<tr class="memitem:a5730b6683f6adcf5c5ef75cf53dc7160"><td class="memTemplParams" colspan="2">template&lt;size_t n&gt; </td></tr>
<tr class="memitem:a5730b6683f6adcf5c5ef75cf53dc7160"><td class="memTemplItemLeft" align="right" valign="top">bool&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d4/d3e/n__queens_8cpp.html#a5730b6683f6adcf5c5ef75cf53dc7160">backtracking::n_queens::isSafe</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt;, n &gt; &amp;board, const int &amp;row, const int &amp;col)</td></tr>
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<tr class="memitem:a0dbd7af47d87f0b956609fe9e3288ecb"><td class="memTemplParams" colspan="2">template&lt;size_t n&gt; </td></tr>
<tr class="memitem:a0dbd7af47d87f0b956609fe9e3288ecb"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d4/d3e/n__queens_8cpp.html#a0dbd7af47d87f0b956609fe9e3288ecb">backtracking::n_queens::solveNQ</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt;, n &gt; board, const int &amp;col)</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d3e/n__queens_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle">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">David Leal</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a5730b6683f6adcf5c5ef75cf53dc7160"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a5730b6683f6adcf5c5ef75cf53dc7160">&#9670;&nbsp;</a></span>isSafe()</h2>
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<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 <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt;, n &gt; &amp;&#160;</td>
<td class="paramname"><em>board</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int &amp;&#160;</td>
<td class="paramname"><em>row</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int &amp;&#160;</td>
<td class="paramname"><em>col</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></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><code>true</code> if queen can be placed on matrix </dd>
<dd>
<code>false</code> if queen can't be placed on matrix </dd></dl>
<div class="fragment"><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; {</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordtype">int</span> i = 0, j = 0;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="comment">// Check this row on left side</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <span class="keywordflow">for</span> (i = 0; i &lt; col; i++) {</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keywordflow">if</span> (board[row][i]) {</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; }</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; }</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; </div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="comment">// Check upper diagonal on left side</span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="keywordflow">for</span> (i = row, j = col; i &gt;= 0 &amp;&amp; j &gt;= 0; i--, j--) {</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <span class="keywordflow">if</span> (board[i][j]) {</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; }</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; }</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="comment">// Check lower diagonal on left side</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="keywordflow">for</span> (i = row, j = col; j &gt;= 0 &amp;&amp; i &lt; n; i++, j--) {</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="keywordflow">if</span> (board[i][j]) {</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; }</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; }</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td></td>
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<p>Main function </p>
<div class="fragment"><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; {</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> n = 4;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::array&lt;int, n&gt;</a>, n&gt; board = {</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a>({0, 0, 0, 0}),</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a>({0, 0, 0, 0}),</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a>({0, 0, 0, 0}),</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a>({0, 0, 0, 0})</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; };</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; </div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; backtracking::n_queens::solveNQ&lt;n&gt;(board, 0);</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a40ae0c7fd04eb20e7f3bff13fc6a5808">&#9670;&nbsp;</a></span>printSolution()</h2>
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template&lt;size_t n&gt; </div>
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<td class="memname">void backtracking::n_queens::printSolution </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>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt;, n &gt; &amp;&#160;</td>
<td class="paramname"><em>board</em></td><td>)</td>
<td></td>
</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">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>
<div class="fragment"><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; {</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &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"><a name="l00042"></a><span class="lineno"> 42</span>&#160; }</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; }</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0dbd7af47d87f0b956609fe9e3288ecb">&#9670;&nbsp;</a></span>solveNQ()</h2>
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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"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; int, n &gt;, n &gt;&#160;</td>
<td class="paramname"><em>board</em>, </td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int &amp;&#160;</td>
<td class="paramname"><em>col</em>&#160;</td>
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<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</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>
<div class="fragment"><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; {</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <span class="keywordflow">if</span> (col &gt;= n) {</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; printSolution&lt;n&gt;(board);</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; }</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; <span class="comment">// Consider this column and try placing</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="comment">// this queen in all rows one by one</span></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; <span class="comment">// Check if queen can be placed</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; <span class="comment">// on board[i][col]</span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="keywordflow">if</span> (isSafe&lt;n&gt;(board, i, col)) {</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; <span class="comment">// Place this queen in matrix</span></div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; board[i][col] = 1;</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; </div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; <span class="comment">// Recursive to place rest of the queens</span></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; solveNQ&lt;n&gt;(board, col + 1);</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; </div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; board[i][col] = 0; <span class="comment">// backtrack</span></div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; }</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; }</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; }</div>
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