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<div class="summary">
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<a href="#func-members">Functions</a> </div>
<div class="headertitle">
<div class="title">n_queens.cpp File Reference</div> </div>
<div class="headertitle"><div class="title">n_queens.cpp File Reference</div></div>
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<div class="contents">
<p><a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle">Eight Queens</a> puzzle
<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;iostream&gt;</code><br />
<code>#include &lt;array&gt;</code><br />
@@ -109,16 +108,16 @@ Include dependency graph for n_queens.cpp:</div>
</div>
</div>
</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="namespaces"></a>
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="namespaces" name="namespaces"></a>
Namespaces</h2></td></tr>
<tr class="memitem:db/dc0/namespacebacktracking"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../db/dc0/namespacebacktracking.html">backtracking</a></td></tr>
<tr class="memitem:db/dc0/namespacebacktracking"><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">Backtracking algorithms. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<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="memitem:d3/da1/namespacen__queens"><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>
<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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<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>
<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">David Leal</a> </dd></dl>
<a href="https://github.com/Panquesito7" target="_blank">David Leal</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a5730b6683f6adcf5c5ef75cf53dc7160"></a>
<a id="a5730b6683f6adcf5c5ef75cf53dc7160" name="a5730b6683f6adcf5c5ef75cf53dc7160"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a5730b6683f6adcf5c5ef75cf53dc7160">&#9670;&nbsp;</a></span>isSafe()</h2>
<div class="memitem">
@@ -172,7 +171,7 @@ template&lt;size_t n&gt; </div>
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<p>Check if a queen can be placed on matrix </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<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>
@@ -189,34 +188,34 @@ template&lt;size_t n&gt; </div>
<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>
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<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>
<div class="fragment"><div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> {</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordtype">int</span> i = 0, j = 0;</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> </div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// Check this row on left side</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">for</span> (i = 0; i &lt; col; i++) {</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">if</span> (board[row][i]) {</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> }</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> }</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// Check upper diagonal on left side</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">for</span> (i = row, j = col; i &gt;= 0 &amp;&amp; j &gt;= 0; i--, j--) {</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">if</span> (board[i][j]) {</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> }</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// Check lower diagonal on left side</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> }</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
<div class="memitem">
@@ -231,24 +230,24 @@ template&lt;size_t n&gt; </div>
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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>
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<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>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; </div>
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<p >Main function </p>
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<h2 class="memtitle"><span class="permalink"><a href="#a40ae0c7fd04eb20e7f3bff13fc6a5808">&#9670;&nbsp;</a></span>printSolution()</h2>
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@@ -265,7 +264,7 @@ template&lt;size_t n&gt; </div>
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<p>Utility function to print matrix </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<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>
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@@ -277,20 +276,20 @@ template&lt;size_t n&gt; </div>
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<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>
<div class="fragment"><div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> {</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;&quot;</span> &lt;&lt; board[i][j] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> }</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> }</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> }</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0dbd7af47d87f0b956609fe9e3288ecb">&#9670;&nbsp;</a></span>solveNQ()</h2>
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@@ -317,7 +316,7 @@ template&lt;size_t n&gt; </div>
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<p>Solve n queens problem </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<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>
@@ -330,28 +329,28 @@ template&lt;size_t n&gt; </div>
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<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>
<div class="fragment"><div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> {</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordflow">if</span> (col &gt;= n) {</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> printSolution&lt;n&gt;(board);</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> }</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// Consider this column and try placing</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// this queen in all rows one by one</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="comment">// Check if queen can be placed</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="comment">// on board[i][col]</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">if</span> (isSafe&lt;n&gt;(board, i, col)) {</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// Place this queen in matrix</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> board[i][col] = 1;</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="comment">// Recursive to place rest of the queens</span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> solveNQ&lt;n&gt;(board, col + 1);</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> </div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> board[i][col] = 0; <span class="comment">// backtrack</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> }</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> }</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> }</div>
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@@ -367,7 +366,7 @@ Here is the call graph for this function:</div>
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