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<div class="headertitle"><div class="title">n_queens.cpp</div></div>
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<a href="../../d4/d3e/n__queens_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include &lt;array&gt;</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> </div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../db/dc0/namespacebacktracking.html">backtracking</a> {</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d3/da1/namespacen__queens.html">n_queens</a> {</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="keyword">template</span> &lt;<span class="keywordtype">size_t</span> n&gt;</div>
<div class="foldopen" id="foldopen00038" data-start="{" data-end="}">
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"><a class="line" href="../../d4/d3e/n__queens_8cpp.html#a40ae0c7fd04eb20e7f3bff13fc6a5808"> 38</a></span><span class="keywordtype">void</span> printSolution(<span class="keyword">const</span> std::array&lt;std::array&lt;int, n&gt;, n&gt; &amp;board) {</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</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> i = 0; i &lt; n; i++) {</div>
<div class="line"><a id="l00041" name="l00041"></a><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"><a id="l00042" name="l00042"></a><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"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> }</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> }</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span>}</div>
</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="keyword">template</span> &lt;<span class="keywordtype">size_t</span> n&gt;</div>
<div class="foldopen" id="foldopen00058" data-start="{" data-end="}">
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"><a class="line" href="../../d4/d3e/n__queens_8cpp.html#a5730b6683f6adcf5c5ef75cf53dc7160"> 58</a></span><span class="keywordtype">bool</span> isSafe(<span class="keyword">const</span> std::array&lt;std::array&lt;int, n&gt;, n&gt; &amp;board, <span class="keyword">const</span> <span class="keywordtype">int</span> &amp;row,</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keyword">const</span> <span class="keywordtype">int</span> &amp;col) {</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordtype">int</span> i = 0, j = 0;</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> </div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// Check this row on left side</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">for</span> (i = 0; i &lt; col; i++) {</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">if</span> (board[row][i]) {</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keywordflow">return</span> <span class="keyword">false</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> </div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// Check upper diagonal on left side</span></div>
<div class="line"><a id="l00070" name="l00070"></a><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"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">if</span> (board[i][j]) {</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> }</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> }</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// Check lower diagonal on left side</span></div>
<div class="line"><a id="l00076" name="l00076"></a><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"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">if</span> (board[i][j]) {</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> }</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> }</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span>}</div>
</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> </div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span><span class="keyword">template</span> &lt;<span class="keywordtype">size_t</span> n&gt;</div>
<div class="foldopen" id="foldopen00091" data-start="{" data-end="}">
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"><a class="line" href="../../d4/d3e/n__queens_8cpp.html#a0dbd7af47d87f0b956609fe9e3288ecb"> 91</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d4/d3e/n__queens_8cpp.html#a0dbd7af47d87f0b956609fe9e3288ecb">solveNQ</a>(std::array&lt;std::array&lt;int, n&gt;, n&gt; board, <span class="keyword">const</span> <span class="keywordtype">int</span> &amp;col) {</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keywordflow">if</span> (col &gt;= n) {</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> printSolution&lt;n&gt;(board);</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">return</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> </div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// Consider this column and try placing</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// this queen in all rows one by one</span></div>
<div class="line"><a id="l00099" name="l00099"></a><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"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="comment">// Check if queen can be placed</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="comment">// on board[i][col]</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keywordflow">if</span> (isSafe&lt;n&gt;(board, i, col)) {</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// Place this queen in matrix</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> board[i][col] = 1;</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> </div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="comment">// Recursive to place rest of the queens</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> solveNQ&lt;n&gt;(board, col + 1);</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> </div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> board[i][col] = 0; <span class="comment">// backtrack</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>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span>}</div>
</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span>} <span class="comment">// namespace n_queens</span></div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span>} <span class="comment">// namespace backtracking</span></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> </div>
<div class="foldopen" id="foldopen00120" data-start="{" data-end="}">
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"><a class="line" href="../../d4/d3e/n__queens_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 120</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d3e/n__queens_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keyword">const</span> <span class="keywordtype">int</span> n = 4;</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> std::array&lt;std::array&lt;int, n&gt;, n&gt; board = {</div>
<div class="line"><a id="l00123" name="l00123"></a><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"><a id="l00124" name="l00124"></a><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"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> </div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> backtracking::n_queens::solveNQ&lt;n&gt;(board, 0);</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span>}</div>
</div>
<div class="ttc" id="an__queens_8cpp_html_a0dbd7af47d87f0b956609fe9e3288ecb"><div class="ttname"><a href="../../d4/d3e/n__queens_8cpp.html#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="#l00091">n_queens.cpp:91</a></div></div>
<div class="ttc" id="an__queens_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d4/d3e/n__queens_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="#l00120">n_queens.cpp:120</a></div></div>
<div class="ttc" id="anamespacebacktracking_html"><div class="ttname"><a href="../../db/dc0/namespacebacktracking.html">backtracking</a></div><div class="ttdoc">for vector container</div></div>
<div class="ttc" id="anamespacen__queens_html"><div class="ttname"><a href="../../d3/da1/namespacen__queens.html">n_queens</a></div><div class="ttdoc">Functions for Eight Queens puzzle.</div></div>
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