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@@ -3,7 +3,7 @@
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<title>Algorithms_in_C++: backtracking/n_queens.cpp File Reference</title>
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<div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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@@ -189,30 +189,30 @@ 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 id="l00059" name="l00059"></a><span class="lineno"> 59</span> {</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 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>
</div><!-- fragment -->
</div>
</div>
@@ -234,15 +234,15 @@ template&lt;size_t n&gt; </div>
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> {</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> <a class="code hl_classRef" 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 id="l00123" name="l00123"></a><span class="lineno"> 123</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a>({0, 0, 0, 0}), <a class="code hl_classRef" 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 id="l00124" name="l00124"></a><span class="lineno"> 124</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a>({0, 0, 0, 0}), <a class="code hl_classRef" 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 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 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> <a class="code hl_classRef" 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"><span class="lineno"> 123</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a>({0, 0, 0, 0}), <a class="code hl_classRef" 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"><span class="lineno"> 124</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, n&gt;</a>({0, 0, 0, 0}), <a class="code hl_classRef" 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"><span class="lineno"> 125</span> </div>
<div class="line"><span class="lineno"> 126</span> backtracking::n_queens::solveNQ&lt;n&gt;(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="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
</div><!-- fragment -->
</div>
@@ -276,15 +276,15 @@ template&lt;size_t n&gt; </div>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> {</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</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="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> <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="l00043" name="l00043"></a><span class="lineno"> 43</span> }</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</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="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 class="fragment"><div class="line"><span class="lineno"> 38</span> {</div>
<div class="line"><span class="lineno"> 39</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"><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> <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"><span class="lineno"> 43</span> }</div>
<div class="line"><span class="lineno"> 44</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"><span class="lineno"> 45</span> }</div>
<div class="line"><span class="lineno"> 46</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>
</div><!-- fragment -->
</div>
@@ -329,28 +329,28 @@ template&lt;size_t n&gt; </div>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> {</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 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> printSolution&lt;n&gt;(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><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
<div class="dyncontent">
@@ -366,7 +366,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
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<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
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