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<a href="#pub-methods">Public Member Functions</a> &#124;
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<a href="../../dc/d67/classgraph_1_1is__graph__bipartite_1_1_graph-members.html">List of all members</a> </div>
<div class="headertitle">
<div class="title">graph::is_graph_bipartite::Graph Class Reference</div> </div>
<div class="headertitle"><div class="title">graph::is_graph_bipartite::Graph Class Reference</div></div>
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<p>Class for representing graph as an adjacency list.
<a href="../../de/d00/classgraph_1_1is__graph__bipartite_1_1_graph.html#details">More...</a></p>
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Collaboration diagram for graph::is_graph_bipartite::Graph:</div>
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<tr class="memdesc:a6aef65b40347c4606662cad4dd2e14d3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructor that initializes the graph on creation. <a href="../../de/d00/classgraph_1_1is__graph__bipartite_1_1_graph.html#a6aef65b40347c4606662cad4dd2e14d3">More...</a><br /></td></tr>
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<tr class="memdesc:a9b0c6400693a5cfff971f768dd5ca5ca"><td class="mdescLeft">&#160;</td><td class="mdescRight">function to add edges to our graph <a href="../../de/d00/classgraph_1_1is__graph__bipartite_1_1_graph.html#a9b0c6400693a5cfff971f768dd5ca5ca">More...</a><br /></td></tr>
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<tr class="memdesc:aefea7ee87a708298c486d5a38ac628ef"><td class="mdescLeft">&#160;</td><td class="mdescRight">size of the graph <br /></td></tr>
<tr class="separator:aefea7ee87a708298c486d5a38ac628ef"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d00/classgraph_1_1is__graph__bipartite_1_1_graph.html#ab0efcfa04fff8616aff0062522d1483f">adj</a></td></tr>
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<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>adj</b></td></tr>
<tr class="memdesc:ab0efcfa04fff8616aff0062522d1483f"><td class="mdescLeft">&#160;</td><td class="mdescRight">adj stores the graph as an adjacency list <br /></td></tr>
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<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d00/classgraph_1_1is__graph__bipartite_1_1_graph.html#a9d10768f927baa8a4d4a5ffce295b6b6">side</a></td></tr>
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<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>side</b></td></tr>
<tr class="memdesc:a9d10768f927baa8a4d4a5ffce295b6b6"><td class="mdescLeft">&#160;</td><td class="mdescRight">stores the side of the vertex <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Class for representing graph as an adjacency list. </p>
<div class="textblock"><p >Class for representing graph as an adjacency list. </p>
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<h2 class="memtitle"><span class="permalink"><a href="#a6aef65b40347c4606662cad4dd2e14d3">&#9670;&nbsp;</a></span>Graph()</h2>
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<div class="fragment"><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; {</div>
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<div class="fragment"><div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> {</div>
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<div class="ttc" id="aresize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/resize.html">std::vector::resize</a></div><div class="ttdeci">T resize(T... args)</div></div>
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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ad8c10df34357b2cd865c81e0c4f0bd8c">&#9670;&nbsp;</a></span>addEdge()</h2>
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<div class="fragment"><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; {</div>
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<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a9b0c6400693a5cfff971f768dd5ca5ca">&#9670;&nbsp;</a></span>is_bipartite()</h2>
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<p>function to add edges to our graph </p>
<p>function that checks whether the graph is bipartite or not the function returns true if the graph is a bipartite graph the function returns false if the graph is not a bipartite graph</p>
<p>Here, side refers to the two disjoint subsets of the bipartite graph. Initially, the values of side are set to -1 which is an unassigned state. A for loop is run for every vertex of the graph. If the current edge has no side assigned to it, then a Breadth First Search operation is performed. If two neighbours have the same side then the graph will not be bipartite and the value of check becomes false. If and only if each pair of neighbours have different sides, the value of check will be true and hence the graph bipartite.</p>
<p >function that checks whether the graph is bipartite or not the function returns true if the graph is a bipartite graph the function returns false if the graph is not a bipartite graph</p>
<p >Here, side refers to the two disjoint subsets of the bipartite graph. Initially, the values of side are set to -1 which is an unassigned state. A for loop is run for every vertex of the graph. If the current edge has no side assigned to it, then a Breadth First Search operation is performed. If two neighbours have the same side then the graph will not be bipartite and the value of check becomes false. If and only if each pair of neighbours have different sides, the value of check will be true and hence the graph bipartite.</p>
<dl class="section return"><dt>Returns</dt><dd><code>true</code> if th graph is bipartite </dd>
<dd>
<code>false</code> otherwise </dd></dl>
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<p>Implementation of <a href="https://en.wikipedia.org/wiki/Cycle_sort">Cycle sort</a> algorithm.
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Functions</h2></td></tr>
<tr class="memitem:ad0cfe2e54b1d3f9d0ca648265d917c6a"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ad0cfe2e54b1d3f9d0ca648265d917c6a"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d07/cycle__sort_8cpp.html#ad0cfe2e54b1d3f9d0ca648265d917c6a">sorting::cycle_sort::cycleSort</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;in_arr)</td></tr>
<tr class="memdesc:ad0cfe2e54b1d3f9d0ca648265d917c6a"><td class="mdescLeft">&#160;</td><td class="mdescRight">The main function implements cycleSort. <a href="../../de/d07/cycle__sort_8cpp.html#ad0cfe2e54b1d3f9d0ca648265d917c6a">More...</a><br /></td></tr>
<tr class="separator:ad0cfe2e54b1d3f9d0ca648265d917c6a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae79a9d247691fce0d655fce75f1c04fa"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ae79a9d247691fce0d655fce75f1c04fa"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d07/cycle__sort_8cpp.html#ae79a9d247691fce0d655fce75f1c04fa">sorting::cycle_sort::cycleSort</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;in_arr)</td></tr>
<tr class="memdesc:ae79a9d247691fce0d655fce75f1c04fa"><td class="mdescLeft">&#160;</td><td class="mdescRight">The main function implements cycleSort. <a href="../../de/d07/cycle__sort_8cpp.html#ae79a9d247691fce0d655fce75f1c04fa">More...</a><br /></td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d07/cycle__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test implementations. <a href="../../de/d07/cycle__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
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@@ -134,11 +133,11 @@ Functions</h2></td></tr>
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</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation of <a href="https://en.wikipedia.org/wiki/Cycle_sort">Cycle sort</a> algorithm. </p>
<p>Cycle Sort is a sorting algorithm that works in \(O(n^2)\) time in the best case and works in \(O(n^2)\) in worst case. If a element is already at its correct position, do nothing. If a element is not at its correct position, we then need to move it to its correct position by computing the correct positions.Therefore, we should make sure the duplicate elements. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/dalaoqi">TsungHan Ho</a> </dd></dl>
<div class="textblock"><p >Implementation of <a href="https://en.wikipedia.org/wiki/Cycle_sort" target="_blank">Cycle sort</a> algorithm. </p>
<p >Cycle Sort is a sorting algorithm that works in \(O(n^2)\) time in the best case and works in \(O(n^2)\) in worst case. If a element is already at its correct position, do nothing. If a element is not at its correct position, we then need to move it to its correct position by computing the correct positions.Therefore, we should make sure the duplicate elements. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/dalaoqi" target="_blank">TsungHan Ho</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ad0cfe2e54b1d3f9d0ca648265d917c6a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad0cfe2e54b1d3f9d0ca648265d917c6a">&#9670;&nbsp;</a></span>cycleSort()</h2>
<a id="ae79a9d247691fce0d655fce75f1c04fa" name="ae79a9d247691fce0d655fce75f1c04fa"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae79a9d247691fce0d655fce75f1c04fa">&#9670;&nbsp;</a></span>cycleSort()</h2>
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@@ -146,7 +145,7 @@ Functions</h2></td></tr>
template&lt;typename T &gt; </div>
<table class="memname">
<tr>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;T&gt; sorting::cycle_sort::cycleSort </td>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; sorting::cycle_sort::cycleSort </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;&#160;</td>
<td class="paramname"><em>in_arr</em></td><td>)</td>
@@ -169,65 +168,65 @@ template&lt;typename T &gt; </div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </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/container/vector.html">std::vector&lt;T&gt;</a> arr(in_arr);</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> cycle_start = 0; cycle_start &lt;= arr.size() - 1; cycle_start++) {</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="comment">// initialize item</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; T item = arr[cycle_start];</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; <span class="comment">// Count the number of elements smaller than item, this number is the</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="comment">// correct index of item.</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordtype">int</span> pos = cycle_start;</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = cycle_start + 1; i &lt; arr.size(); i++) {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="keywordflow">if</span> (arr[i] &lt; item) {</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; pos++;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; }</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; }</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="comment">// item is already in correct position</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <span class="keywordflow">if</span> (pos == cycle_start) {</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; }</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; </div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="comment">// duplicate elements</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordflow">while</span> (item == arr[pos]) pos += 1;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordflow">if</span> (pos == cycle_start) {</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(item, arr[pos]);</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; }</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="comment">// Rest of the elements</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <span class="keywordflow">while</span> (pos != cycle_start) {</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; pos = cycle_start;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="comment">// Find position where we put the element</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = cycle_start + 1; i &lt; arr.size(); i++) {</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="keywordflow">if</span> (arr[i] &lt; item) {</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; pos += 1;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; }</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; <span class="comment">// duplicate elements</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="keywordflow">while</span> (item == arr[pos]) pos += 1;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="keywordflow">if</span> (item == arr[pos]) {</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(item, arr[pos]);</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; }</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; }</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="keywordflow">return</span> arr;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</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/container/vector.html">std::vector&lt;T&gt;</a> arr(in_arr);</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> cycle_start = 0; cycle_start &lt;= arr.size() - 1; cycle_start++) {</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// initialize item</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> T item = arr[cycle_start];</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> <span class="comment">// Count the number of elements smaller than item, this number is the</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// correct index of item.</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordtype">int</span> pos = cycle_start;</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = cycle_start + 1; i &lt; arr.size(); i++) {</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keywordflow">if</span> (arr[i] &lt; item) {</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> pos++;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> }</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// item is already in correct position</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">if</span> (pos == cycle_start) {</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> }</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// duplicate elements</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordflow">while</span> (item == arr[pos]) pos += 1;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordflow">if</span> (pos == cycle_start) {</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(item, arr[pos]);</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> }</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// Rest of the elements</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keywordflow">while</span> (pos != cycle_start) {</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> pos = cycle_start;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// Find position where we put the element</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = cycle_start + 1; i &lt; arr.size(); i++) {</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">if</span> (arr[i] &lt; item) {</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> pos += 1;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> }</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> }</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// duplicate elements</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordflow">while</span> (item == arr[pos]) pos += 1;</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordflow">if</span> (item == arr[pos]) {</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(item, arr[pos]);</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> }</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">return</span> arr;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span>}</div>
<div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; {</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; <a class="code" href="../../de/d07/cycle__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the test</span></div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> {</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <a class="code hl_function" href="../../de/d07/cycle__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the test</span></div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span>}</div>
<div class="ttc" id="acycle__sort_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../de/d07/cycle__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Test implementations.</div><div class="ttdef"><b>Definition:</b> cycle_sort.cpp:91</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&nbsp;</a></span>test()</h2>
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@@ -284,40 +283,40 @@ Here is the call graph for this function:</div>
<p>Test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; {</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <span class="comment">// Test 1</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="comment">// [4, 3, 2, 1] return [1, 2, 3, 4]</span></div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array1 = {4, 3, 2, 1};</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</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;Test 1... &quot;</span>;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> arr1 = <a class="code" href="../../de/d07/cycle__sort_8cpp.html#ad0cfe2e54b1d3f9d0ca648265d917c6a">sorting::cycle_sort::cycleSort</a>(array1);</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr1), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr1)));</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</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;passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; </div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; <span class="comment">// [4.3, -6.5, -7.4, 0, 2.7, 1.8] return [-7.4, -6.5, 0, 1.8, 2.7, 4.3]</span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> array2 = {4.3, -6.5, -7.4, 0, 2.7, 1.8};</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</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;Test 2... &quot;</span>;</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> arr2 = <a class="code" href="../../de/d07/cycle__sort_8cpp.html#ad0cfe2e54b1d3f9d0ca648265d917c6a">sorting::cycle_sort::cycleSort</a>(array2);</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr2), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr2)));</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</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;passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; </div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; <span class="comment">// Test 3</span></div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; <span class="comment">// [3, 3, 3, 3] return [3, 3, 3, 3]</span></div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array3 = {3, 3, 3, 3};</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</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;Test 3... &quot;</span>;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> arr3 = <a class="code" href="../../de/d07/cycle__sort_8cpp.html#ad0cfe2e54b1d3f9d0ca648265d917c6a">sorting::cycle_sort::cycleSort</a>(array3);</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr3), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr3)));</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</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;passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; </div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; <span class="comment">// [9, 4, 6, 8, 14, 3] return [9, 4, 6, 8, 14, 3]</span></div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array4 = {3, 4, 6, 8, 9, 14};</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</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;Test 4... &quot;</span>;</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> arr4 = <a class="code" href="../../de/d07/cycle__sort_8cpp.html#ad0cfe2e54b1d3f9d0ca648265d917c6a">sorting::cycle_sort::cycleSort</a>(array4);</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; assert(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4)));</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/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160;}</div>
<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="comment">// Test 1</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="comment">// [4, 3, 2, 1] return [1, 2, 3, 4]</span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array1 = {4, 3, 2, 1};</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</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;Test 1... &quot;</span>;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> arr1 = <a class="code hl_function" href="../../de/d07/cycle__sort_8cpp.html#ae79a9d247691fce0d655fce75f1c04fa">sorting::cycle_sort::cycleSort</a>(array1);</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr1), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr1)));</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</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;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> </div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="comment">// [4.3, -6.5, -7.4, 0, 2.7, 1.8] return [-7.4, -6.5, 0, 1.8, 2.7, 4.3]</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> array2 = {4.3, -6.5, -7.4, 0, 2.7, 1.8};</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</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;Test 2... &quot;</span>;</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> arr2 = <a class="code hl_function" href="../../de/d07/cycle__sort_8cpp.html#ae79a9d247691fce0d655fce75f1c04fa">sorting::cycle_sort::cycleSort</a>(array2);</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr2), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr2)));</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</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;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> </div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="comment">// Test 3</span></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="comment">// [3, 3, 3, 3] return [3, 3, 3, 3]</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array3 = {3, 3, 3, 3};</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</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;Test 3... &quot;</span>;</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> arr3 = <a class="code hl_function" href="../../de/d07/cycle__sort_8cpp.html#ae79a9d247691fce0d655fce75f1c04fa">sorting::cycle_sort::cycleSort</a>(array3);</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr3), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr3)));</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</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;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// [9, 4, 6, 8, 14, 3] return [9, 4, 6, 8, 14, 3]</span></div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> array4 = {3, 4, 6, 8, 9, 14};</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</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;Test 4... &quot;</span>;</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> arr4 = <a class="code hl_function" href="../../de/d07/cycle__sort_8cpp.html#ae79a9d247691fce0d655fce75f1c04fa">sorting::cycle_sort::cycleSort</a>(array4);</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4)));</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</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;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</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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<div class="ttc" id="acycle__sort_8cpp_html_ad0cfe2e54b1d3f9d0ca648265d917c6a"><div class="ttname"><a href="../../de/d07/cycle__sort_8cpp.html#ad0cfe2e54b1d3f9d0ca648265d917c6a">sorting::cycle_sort::cycleSort</a></div><div class="ttdeci">std::vector&lt; T &gt; cycleSort(const std::vector&lt; T &gt; &amp;in_arr)</div><div class="ttdoc">The main function implements cycleSort.</div><div class="ttdef"><b>Definition:</b> cycle_sort.cpp:37</div></div>
<div class="ttc" id="acycle__sort_8cpp_html_ae79a9d247691fce0d655fce75f1c04fa"><div class="ttname"><a href="../../de/d07/cycle__sort_8cpp.html#ae79a9d247691fce0d655fce75f1c04fa">sorting::cycle_sort::cycleSort</a></div><div class="ttdeci">std::vector&lt; T &gt; cycleSort(const std::vector&lt; T &gt; &amp;in_arr)</div><div class="ttdoc">The main function implements cycleSort.</div><div class="ttdef"><b>Definition:</b> cycle_sort.cpp:37</div></div>
<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a></div><div class="ttdeci">T end(T... args)</div></div>
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<p><a href="https://en.wikipedia.org/wiki/Fibonacci_search_technique">Fibonacci search algorithm</a>
<p><a href="https://en.wikipedia.org/wiki/Fibonacci_search_technique" target="_blank">Fibonacci search algorithm</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Functions</h2></td></tr>
<tr class="memitem:a0bc61b3903d9a53061bf31e5d110fe61"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d0d/fibonacci__search_8cpp.html#a0bc61b3903d9a53061bf31e5d110fe61">fibonacci_search</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &amp;arr, int value)</td></tr>
<tr class="memdesc:a0bc61b3903d9a53061bf31e5d110fe61"><td class="mdescLeft">&#160;</td><td class="mdescRight">using fibonacci search algorithm finds an index of a given element in a sorted array <a href="../../de/d0d/fibonacci__search_8cpp.html#a0bc61b3903d9a53061bf31e5d110fe61">More...</a><br /></td></tr>
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bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d0d/fibonacci__search_8cpp.html#a5e144326104e57a3808aed7eb098db0d">no_occurence_tests</a> ()</td></tr>
<tr class="memdesc:a5e144326104e57a3808aed7eb098db0d"><td class="mdescLeft">&#160;</td><td class="mdescRight">random tests for checking performance when an array doesn't contain an element <br /></td></tr>
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<tr class="memdesc:a5e144326104e57a3808aed7eb098db0d"><td class="mdescLeft">&#160;</td><td class="mdescRight">random tests for checking performance when an array doesn't contain an element <a href="../../de/d0d/fibonacci__search_8cpp.html#a5e144326104e57a3808aed7eb098db0d">More...</a><br /></td></tr>
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<tr class="memitem:a2aa09bef74ee063c1331de0883af4f4f"><td class="memItemLeft" align="right" valign="top"><a id="a2aa09bef74ee063c1331de0883af4f4f"></a>
bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d0d/fibonacci__search_8cpp.html#a2aa09bef74ee063c1331de0883af4f4f">random_tests</a> ()</td></tr>
<tr class="memdesc:a2aa09bef74ee063c1331de0883af4f4f"><td class="mdescLeft">&#160;</td><td class="mdescRight">random tests which cover cases when we have one, multiple or zero occurences of the value we're looking for <br /></td></tr>
<tr class="memitem:a2aa09bef74ee063c1331de0883af4f4f"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d0d/fibonacci__search_8cpp.html#a2aa09bef74ee063c1331de0883af4f4f">random_tests</a> ()</td></tr>
<tr class="memdesc:a2aa09bef74ee063c1331de0883af4f4f"><td class="mdescLeft">&#160;</td><td class="mdescRight">random tests which cover cases when we have one, multiple or zero occurences of the value we're looking for <a href="../../de/d0d/fibonacci__search_8cpp.html#a2aa09bef74ee063c1331de0883af4f4f">More...</a><br /></td></tr>
<tr class="separator:a2aa09bef74ee063c1331de0883af4f4f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d0d/fibonacci__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</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/Fibonacci_search_technique">Fibonacci search algorithm</a> </p>
<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Fibonacci_search_technique" target="_blank">Fibonacci search algorithm</a> </p>
<dl class="section author"><dt>Author</dt><dd>sprintyaf </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a0bc61b3903d9a53061bf31e5d110fe61"></a>
<a id="a0bc61b3903d9a53061bf31e5d110fe61" name="a0bc61b3903d9a53061bf31e5d110fe61"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0bc61b3903d9a53061bf31e5d110fe61">&#9670;&nbsp;</a></span>fibonacci_search()</h2>
<div class="memitem">
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>if the array contains the value, returns an index of the element. otherwise -1. </dd></dl>
<div class="fragment"><div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; {</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; <span class="comment">// initialize last and current members of Fibonacci sequence </span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; <span class="keywordtype">int</span> last = 0, current = 1;</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; <span class="keywordtype">int</span> length = arr.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); <span class="comment">// array size</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; <span class="comment">// next member of Fibonacci sequence which is &quot;last&quot; + &quot;current&quot;</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; <span class="keywordtype">int</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = last + current; </div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; </div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="comment">// &quot;next&quot; will store the smallest Fibonacci number greater or equal to &quot;length&quot;</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordflow">while</span>(next &lt; length){</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; last = current;</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; current = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a>;</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = last + current;</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; }</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="comment">// &quot;offset&quot; is the end of eliminated range from front</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; <span class="keywordtype">int</span> offset = -1, index;</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="comment">// while loop until there are elements left to consider.</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="comment">// when &quot;next&quot; becomes 1, last is equal to 0, so search is done,</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="comment">// because arr[offset] will already be eliminated</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordflow">while</span>(next &gt; 1){</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="comment">// check if &quot;last&quot; is valid location</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; index = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(offset + last, length-1);</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="comment">// if value is greater than the value at &quot;index&quot;, eliminate the subarray from offset to index</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="keywordflow">if</span>(arr[index] &lt; value){</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = current;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; current = last;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; last = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> - current;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; offset = index;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="comment">// if value is less than the value at &quot;index&quot;, eliminate the subarray after index+1</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; } <span class="keywordflow">else</span> <span class="keywordflow">if</span>(arr[index] &gt; value){</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = last;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; current = current - last;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; last = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> - current;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="comment">// element is found</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordflow">return</span> index;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; }</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">// comparing the last element</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <span class="keywordflow">if</span>(current &amp;&amp; !arr.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/empty.html">empty</a>() &amp;&amp; arr[offset+1] == value){</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keywordflow">return</span> offset+1;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; }</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <span class="comment">// value was not found, return -1</span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="keywordflow">return</span> -1;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> {</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// initialize last and current members of Fibonacci sequence </span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> <span class="keywordtype">int</span> last = 0, current = 1;</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <span class="keywordtype">int</span> length = arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); <span class="comment">// array size</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// next member of Fibonacci sequence which is &quot;last&quot; + &quot;current&quot;</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keywordtype">int</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = last + current; </div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> </div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="comment">// &quot;next&quot; will store the smallest Fibonacci number greater or equal to &quot;length&quot;</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keywordflow">while</span>(next &lt; length){</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> last = current;</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> current = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a>;</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = last + current;</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> }</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// &quot;offset&quot; is the end of eliminated range from front</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordtype">int</span> offset = -1, index;</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// while loop until there are elements left to consider.</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// when &quot;next&quot; becomes 1, last is equal to 0, so search is done,</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// because arr[offset] will already be eliminated</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">while</span>(next &gt; 1){</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// check if &quot;last&quot; is valid location</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> index = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(offset + last, length-1);</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="comment">// if value is greater than the value at &quot;index&quot;, eliminate the subarray from offset to index</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordflow">if</span>(arr[index] &lt; value){</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = current;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> current = last;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> last = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> - current;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> offset = index;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// if value is less than the value at &quot;index&quot;, eliminate the subarray after index+1</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span>(arr[index] &gt; value){</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> = last;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> current = current - last;</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> last = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/next.html">next</a> - current;</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// element is found</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordflow">return</span> index;</div>
<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> }</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// comparing the last element</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">if</span>(current &amp;&amp; !arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/empty.html">empty</a>() &amp;&amp; arr[offset+1] == value){</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">return</span> offset+1;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> }</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// value was not found, return -1</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span>}</div>
<div class="ttc" id="aempty_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/empty.html">std::vector::empty</a></div><div class="ttdeci">T empty(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<p>Main Function testing the algorithm </p>
<div class="fragment"><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160; {</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160; assert(<a class="code" href="../../de/d0d/fibonacci__search_8cpp.html#a5e144326104e57a3808aed7eb098db0d">no_occurence_tests</a>());</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; assert(<a class="code" href="../../de/d0d/fibonacci__search_8cpp.html#a2aa09bef74ee063c1331de0883af4f4f">random_tests</a>());</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160;}</div>
<p >Main Function testing the algorithm </p>
<div class="fragment"><div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> {</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> assert(<a class="code hl_function" href="../../de/d0d/fibonacci__search_8cpp.html#a5e144326104e57a3808aed7eb098db0d">no_occurence_tests</a>());</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> assert(<a class="code hl_function" href="../../de/d0d/fibonacci__search_8cpp.html#a2aa09bef74ee063c1331de0883af4f4f">random_tests</a>());</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span>}</div>
<div class="ttc" id="afibonacci__search_8cpp_html_a2aa09bef74ee063c1331de0883af4f4f"><div class="ttname"><a href="../../de/d0d/fibonacci__search_8cpp.html#a2aa09bef74ee063c1331de0883af4f4f">random_tests</a></div><div class="ttdeci">bool random_tests()</div><div class="ttdoc">random tests which cover cases when we have one, multiple or zero occurences of the value we're looki...</div><div class="ttdef"><b>Definition:</b> fibonacci_search.cpp:96</div></div>
<div class="ttc" id="afibonacci__search_8cpp_html_a5e144326104e57a3808aed7eb098db0d"><div class="ttname"><a href="../../de/d0d/fibonacci__search_8cpp.html#a5e144326104e57a3808aed7eb098db0d">no_occurence_tests</a></div><div class="ttdeci">bool no_occurence_tests()</div><div class="ttdoc">random tests for checking performance when an array doesn't contain an element</div><div class="ttdef"><b>Definition:</b> fibonacci_search.cpp:72</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a5e144326104e57a3808aed7eb098db0d">&#9670;&nbsp;</a></span>no_occurence_tests()</h2>
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<p>random tests for checking performance when an array doesn't contain an element </p>
<div class="fragment"><div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> {</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordtype">bool</span> passed = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordtype">int</span> rand_num, rand_value, index, num_tests = 1000;</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> arr;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordflow">while</span>(num_tests--){</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/clear.html">clear</a>();</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt; 100; i++){</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> rand_num = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 1000;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(rand_num);</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> }</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> rand_value = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 1000;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordflow">while</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/find.html">std::find</a>(arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>(), rand_value) != arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>()){</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/remove.html">std::remove</a>(arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>(), rand_value);</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> }</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/sort.html">sort</a>(arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>());</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> index = <a class="code hl_function" href="../../de/d0d/fibonacci__search_8cpp.html#a0bc61b3903d9a53061bf31e5d110fe61">fibonacci_search</a>(arr, rand_value);</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> passed = passed &amp;&amp; (index == -1);</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> }</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordflow">return</span> passed;</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span>}</div>
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<div class="ttc" id="afibonacci__search_8cpp_html_a0bc61b3903d9a53061bf31e5d110fe61"><div class="ttname"><a href="../../de/d0d/fibonacci__search_8cpp.html#a0bc61b3903d9a53061bf31e5d110fe61">fibonacci_search</a></div><div class="ttdeci">int fibonacci_search(const std::vector&lt; int &gt; &amp;arr, int value)</div><div class="ttdoc">using fibonacci search algorithm finds an index of a given element in a sorted array</div><div class="ttdef"><b>Definition:</b> fibonacci_search.cpp:23</div></div>
<div class="ttc" id="afind_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/find.html">std::find</a></div><div class="ttdeci">T find(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a2aa09bef74ee063c1331de0883af4f4f">&#9670;&nbsp;</a></span>random_tests()</h2>
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<td class="memname">bool random_tests </td>
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<p>random tests which cover cases when we have one, multiple or zero occurences of the value we're looking for </p>
<div class="fragment"><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="keywordtype">bool</span> passed = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordtype">int</span> rand_num, rand_value, index, real_value, num_tests = 10000;</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> arr;</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keywordflow">while</span>(num_tests--){</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/clear.html">clear</a>();</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt; 100; i++){</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> rand_num = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 1000;</div>
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<a href="#func-members">Functions</a> &#124;
<a href="#var-members">Variables</a> </div>
<div class="headertitle">
<div class="title">disjoint_set.cpp File Reference</div> </div>
<div class="headertitle"><div class="title">disjoint_set.cpp File Reference</div></div>
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<div class="contents">
<p><a href="https://en.wikipedia.org/wiki/Disjoint-set_data_structure">Disjoint Sets Data Structure (Disjoint Sets)</a>
<p><a href="https://en.wikipedia.org/wiki/Disjoint-set_data_structure" target="_blank">Disjoint Sets Data Structure (Disjoint Sets)</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
@@ -109,7 +108,7 @@ Include dependency graph for disjoint_set.cpp:</div>
</div>
</div>
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Functions</h2></td></tr>
<tr class="memitem:a010965fc5f16cca5a62506afab24e4ec"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d23/disjoint__set_8cpp.html#a010965fc5f16cca5a62506afab24e4ec">CreateSet</a> (int n)</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="../../de/d23/disjoint__set_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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Variables</h2></td></tr>
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<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>root</b></td></tr>
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<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>rank</b></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/Disjoint-set_data_structure">Disjoint Sets Data Structure (Disjoint Sets)</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/leoyang429">leoyang429</a></dd></dl>
<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Disjoint-set_data_structure" target="_blank">Disjoint Sets Data Structure (Disjoint Sets)</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/leoyang429" target="_blank">leoyang429</a></dd></dl>
<p>A disjoint set data structure (also called union find or merge find set) is a data structure that tracks a set of elements partitioned into a number of disjoint (non-overlapping) subsets. Some situations where disjoint sets can be used are- to find connected components of a graph, kruskal's algorithm for finding <a class="el" href="../../d4/d12/namespace_minimum.html" title="Implementation of Minimum Edit Distance algorithm.">Minimum</a> Spanning Tree etc. There are two operation which we perform on disjoint sets - 1) Union 2) Find </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a010965fc5f16cca5a62506afab24e4ec"></a>
<a id="a010965fc5f16cca5a62506afab24e4ec" name="a010965fc5f16cca5a62506afab24e4ec"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a010965fc5f16cca5a62506afab24e4ec">&#9670;&nbsp;</a></span>CreateSet()</h2>
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<p>Function to create a set </p><dl class="params"><dt>Parameters</dt><dd>
<p >Function to create a set </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>number of element </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; root = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;int&gt;</a>(n + 1);</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; rank = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;int&gt;</a>(n + 1, 1);</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= n; ++i) {</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> rank = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;int&gt;</a>(n + 1, 1);</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a34b9ead0608e676d9ae5188672427cc8">&#9670;&nbsp;</a></span>Find()</h2>
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<p>Find operation takes a number x and returns the set to which this number belongs to. </p><dl class="params"><dt>Parameters</dt><dd>
<p >Find operation takes a number x and returns the set to which this number belongs to. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>element of some set </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>set to which x belongs to </dd></dl>
<div class="fragment"><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; {</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <span class="keywordflow">if</span> (root[x] == x) {</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="keywordflow">return</span> root[x] = <a class="code" href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a>(root[x]);</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> {</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordflow">return</span> root[x] = <a class="code hl_function" href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a>(root[x]);</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a2fb0a7cd26a477e2d48ba7e0118bc985">&#9670;&nbsp;</a></span>InSameUnion()</h2>
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<p>A utility function to check if x and y are from same set or not </p><dl class="params"><dt>Parameters</dt><dd>
<p >A utility function to check if x and y are from same set or not </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>element of some set </td></tr>
<tr><td class="paramname">y</td><td>element of some set </td></tr>
</table>
</dd>
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<div class="fragment"><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160;{ <span class="keywordflow">return</span> <a class="code" href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a>(x) == <a class="code" href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a>(y); }</div>
<div class="fragment"><div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span>{ <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a>(x) == <a class="code hl_function" href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a>(y); }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<p>Main function </p>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; <span class="keywordflow">break</span>;</div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; <span class="comment">// tests InSameUnion &amp; Union</span></div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; <a class="code" href="../../de/d23/disjoint__set_8cpp.html#a44481bb75386fbb0f958a388d4b9f757">Union</a>(1, 2);</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;1 and 2 are now in the same subset&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; <span class="keywordflow">if</span> (!<a class="code" href="../../de/d23/disjoint__set_8cpp.html#a2fb0a7cd26a477e2d48ba7e0118bc985">InSameUnion</a>(1, 2)) {</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;Fail&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; }</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160;}</div>
<p >Main function </p>
<div class="fragment"><div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> {</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// tests CreateSet &amp; Find</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordtype">int</span> n = 100;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <a class="code hl_function" href="../../de/d23/disjoint__set_8cpp.html#a010965fc5f16cca5a62506afab24e4ec">CreateSet</a>(n);</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= 100; ++i) {</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordflow">if</span> (root[i] != i) {</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;Fail&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// tests InSameUnion &amp; Union</span></div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../de/d23/disjoint__set_8cpp.html#a2fb0a7cd26a477e2d48ba7e0118bc985">InSameUnion</a>(1, 2)) {</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;Fail&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</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> <a class="code hl_function" href="../../de/d23/disjoint__set_8cpp.html#a44481bb75386fbb0f958a388d4b9f757">Union</a>(1, 2);</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;1 and 2 are now in the same subset&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;Fail&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</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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<div class="ttc" id="adisjoint__set_8cpp_html_a2fb0a7cd26a477e2d48ba7e0118bc985"><div class="ttname"><a href="../../de/d23/disjoint__set_8cpp.html#a2fb0a7cd26a477e2d48ba7e0118bc985">InSameUnion</a></div><div class="ttdeci">bool InSameUnion(int x, int y)</div><div class="ttdef"><b>Definition:</b> disjoint_set.cpp:67</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a44481bb75386fbb0f958a388d4b9f757">&#9670;&nbsp;</a></span>Union()</h2>
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<p>Union operation combines two disjoint sets to make a single set in this union function we pass two elements and check if they are from different sets then combine those sets </p><dl class="params"><dt>Parameters</dt><dd>
<p >Union operation combines two disjoint sets to make a single set in this union function we pass two elements and check if they are from different sets then combine those sets </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>element of some set </td></tr>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <span class="keywordflow">if</span> (rank[a] &lt; rank[b]) {</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; root[a] = b;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (rank[a] &gt; rank[b]) {</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; root[b] = a;</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; root[a] = b;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; ++rank[b];</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; }</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; }</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160;}</div>
<div class="fragment"><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> <span class="keywordtype">int</span> a = <a class="code hl_function" href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a>(x), b = <a class="code hl_function" href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a>(y);</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> root[a] = b;</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> root[b] = a;</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> root[a] = b;</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> ++rank[b];</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> }</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> }</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span>}</div>
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@@ -92,8 +92,7 @@ $(document).ready(function(){initNavTree('de/d47/string__fibonacci_8cpp.html','.
<div class="header">
<div class="summary">
<a href="#func-members">Functions</a> </div>
<div class="headertitle">
<div class="title">string_fibonacci.cpp File Reference</div> </div>
<div class="headertitle"><div class="title">string_fibonacci.cpp File Reference</div></div>
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@@ -108,7 +107,7 @@ Include dependency graph for string_fibonacci.cpp:</div>
</div>
</div>
</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a28052eee05d43c2ebc5147c52bd50c35"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d47/string__fibonacci_8cpp.html#a28052eee05d43c2ebc5147c52bd50c35">add</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> a, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> b)</td></tr>
<tr class="separator:a28052eee05d43c2ebc5147c52bd50c35"><td class="memSeparator" colspan="2">&#160;</td></tr>
@@ -118,11 +117,11 @@ Functions</h2></td></tr>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>This Programme returns the Nth fibonacci as a string. </p>
<p>The method used is manual addition with carry and placing it in a string which is called string addition This makes it have no bounds or limits</p>
<div class="textblock"><p >This Programme returns the Nth fibonacci as a string. </p>
<p >The method used is manual addition with carry and placing it in a string which is called string addition This makes it have no bounds or limits</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/de4/fibonacci__large_8cpp.html" title="Computes N^th Fibonacci number given as input argument. Uses custom build arbitrary integers library ...">fibonacci_large.cpp</a>, <a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html" title="Faster computation of Fibonacci series.">fibonacci_fast.cpp</a>, <a class="el" href="../../d9/d89/fibonacci_8cpp.html" title="Generate fibonacci sequence.">fibonacci.cpp</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a28052eee05d43c2ebc5147c52bd50c35"></a>
<a id="a28052eee05d43c2ebc5147c52bd50c35" name="a28052eee05d43c2ebc5147c52bd50c35"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a28052eee05d43c2ebc5147c52bd50c35">&#9670;&nbsp;</a></span>add()</h2>
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@@ -147,7 +146,7 @@ Functions</h2></td></tr>
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<p>function to add two string numbers </p><dl class="params"><dt>Parameters</dt><dd>
<p >function to add two string numbers </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">a</td><td>first number in string to add </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">b</td><td>second number in string to add </td></tr>
@@ -155,46 +154,46 @@ Functions</h2></td></tr>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>sum as a <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> </dd></dl>
<div class="fragment"><div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; {</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> temp = <span class="stringliteral">&quot;&quot;</span>;</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; </div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; <span class="comment">// carry flag</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; <span class="keywordtype">int</span> carry = 0;</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; </div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="comment">// fills up with zeros</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordflow">while</span> (a.length() &lt; b.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>()) {</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; a = <span class="stringliteral">&quot;0&quot;</span> + a;</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; }</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; </div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <span class="comment">// fills up with zeros</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">while</span> (b.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>() &lt; a.length()) {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; b = <span class="stringliteral">&quot;0&quot;</span> + b;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; }</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; </div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="comment">// adds the numbers a and b</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = a.length() - 1; i &gt;= 0; i--) {</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordtype">char</span> val = <span class="keyword">static_cast&lt;</span><span class="keywordtype">char</span><span class="keyword">&gt;</span>(((a[i] - 48) + (b[i] - 48)) + 48 + carry);</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="keywordflow">if</span> (val &gt; 57) {</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; carry = 1;</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; val -= 10;</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; carry = 0;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; }</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; temp = val + temp;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; }</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="comment">// processes the carry flag</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <span class="keywordflow">if</span> (carry == 1) {</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; temp = <span class="stringliteral">&quot;1&quot;</span> + temp;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; }</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; </div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="comment">// removes leading zeros.</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordflow">while</span> (temp[0] == <span class="charliteral">&#39;0&#39;</span> &amp;&amp; temp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>() &gt; 1) {</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; temp = temp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(1);</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; </div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <span class="keywordflow">return</span> temp;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> {</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> temp = <span class="stringliteral">&quot;&quot;</span>;</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> </div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// carry flag</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keywordtype">int</span> carry = 0;</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> </div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="comment">// fills up with zeros</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keywordflow">while</span> (a.length() &lt; b.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>()) {</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> a = <span class="stringliteral">&quot;0&quot;</span> + a;</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> }</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// fills up with zeros</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">while</span> (b.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>() &lt; a.length()) {</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> b = <span class="stringliteral">&quot;0&quot;</span> + b;</div>
<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> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// adds the numbers a and b</span></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> i = a.length() - 1; i &gt;= 0; i--) {</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordtype">char</span> val = <span class="keyword">static_cast&lt;</span><span class="keywordtype">char</span><span class="keyword">&gt;</span>(((a[i] - 48) + (b[i] - 48)) + 48 + carry);</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">if</span> (val &gt; 57) {</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> carry = 1;</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> val -= 10;</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> carry = 0;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> }</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> temp = val + temp;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// processes the carry flag</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">if</span> (carry == 1) {</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> temp = <span class="stringliteral">&quot;1&quot;</span> + temp;</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> }</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// removes leading zeros.</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordflow">while</span> (temp[0] == <span class="charliteral">&#39;0&#39;</span> &amp;&amp; temp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>() &gt; 1) {</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> temp = temp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(1);</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> </div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">return</span> temp;</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span>}</div>
<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::length</a></div><div class="ttdeci">T length(T... args)</div></div>
<div class="ttc" id="asubstr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">std::string::substr</a></div><div class="ttdeci">T substr(T... args)</div></div>
@@ -207,7 +206,7 @@ Here is the call graph for this function:</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ad8055ee368a5d5b24de01bdde6bf8fca">&#9670;&nbsp;</a></span>fib_Accurate()</h2>
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@@ -222,23 +221,23 @@ Here is the call graph for this function:</div>
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<p>Fibonacci iterator </p><dl class="params"><dt>Parameters</dt><dd>
<p >Fibonacci iterator </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>n^th Fibonacci number </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; {</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> tmp = <span class="stringliteral">&quot;&quot;</span>;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> fibMinus1 = <span class="stringliteral">&quot;1&quot;</span>;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> fibMinus2 = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; tmp = <a class="code" href="../../de/d47/string__fibonacci_8cpp.html#a28052eee05d43c2ebc5147c52bd50c35">add</a>(fibMinus1, fibMinus2);</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; fibMinus2 = fibMinus1;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; fibMinus1 = tmp;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; }</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; fibMinus2;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160;}</div>
<div class="fragment"><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> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> tmp = <span class="stringliteral">&quot;&quot;</span>;</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> fibMinus1 = <span class="stringliteral">&quot;1&quot;</span>;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> fibMinus2 = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n; i++) {</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> tmp = <a class="code hl_function" href="../../de/d47/string__fibonacci_8cpp.html#a28052eee05d43c2ebc5147c52bd50c35">add</a>(fibMinus1, fibMinus2);</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> fibMinus2 = fibMinus1;</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> fibMinus1 = tmp;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> }</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; fibMinus2;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</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 class="ttc" id="astring__fibonacci_8cpp_html_a28052eee05d43c2ebc5147c52bd50c35"><div class="ttname"><a href="../../de/d47/string__fibonacci_8cpp.html#a28052eee05d43c2ebc5147c52bd50c35">add</a></div><div class="ttdeci">std::string add(std::string a, std::string b)</div><div class="ttdef"><b>Definition:</b> string_fibonacci.cpp:24</div></div>
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@@ -250,7 +249,7 @@ Here is the call graph for this function:</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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@@ -265,16 +264,16 @@ Here is the call graph for this function:</div>
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<p>main function </p>
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<p >main function </p>
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<p>The <a href="https://en.wikipedia.org/wiki/Knuth–Morris–Pratt_algorithm">Knuth-Morris-Pratt Algorithm</a> for finding a pattern within a piece of text with complexity O(n + m)
<p>The <a href="https://en.wikipedia.org/wiki/Knuth–Morris–Pratt_algorithm" target="_blank">Knuth-Morris-Pratt Algorithm</a> for finding a pattern within a piece of text with complexity O(n + m)
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;cstring&gt;</code><br />
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>The <a href="https://en.wikipedia.org/wiki/Knuth–Morris–Pratt_algorithm">Knuth-Morris-Pratt Algorithm</a> for finding a pattern within a piece of text with complexity O(n + m) </p>
<div class="textblock"><p >The <a href="https://en.wikipedia.org/wiki/Knuth–Morris–Pratt_algorithm" target="_blank">Knuth-Morris-Pratt Algorithm</a> for finding a pattern within a piece of text with complexity O(n + m) </p>
<ol type="1">
<li>Preprocess pattern to identify any suffixes that are identical to prefixes. This tells us where to continue from if we get a mismatch between a character in our pattern and the text.</li>
<li>Step through the text one character at a time and compare it to a character in the pattern updating our location within the pattern if necessary </li>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<p>Main function </p>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern = <span class="stringliteral">&quot;abc1abc12l&quot;</span>;</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; text = <span class="stringliteral">&quot;abcabc&quot;</span>;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; pattern = <span class="stringliteral">&quot;bca&quot;</span>;</div>
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<p>Functions for the <a href="https://www.sanfoundry.com/cpp-program-implement-quick-sort-using-randomisation">Random Pivot Quick Sort</a> implementation.
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<p>Compute real eigen values and eigen vectors of a symmetric matrix using <a href="https://en.wikipedia.org/wiki/QR_decomposition">QR decomposition</a> method.
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<tr class="memdesc:d2/d3b/namespaceqr__algorithm"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions to compute <a href="https://en.wikipedia.org/wiki/QR_decomposition">QR decomposition</a> of any rectangular matrix. <br /></td></tr>
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<tr class="memdesc:d2/d3b/namespaceqr__algorithm"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions to compute <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">QR decomposition</a> of any rectangular matrix. <br /></td></tr>
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Macros</h2></td></tr>
<tr class="memitem:aee57a411f07599034f5ceb8cc7d65b40"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>&#160;&#160;&#160;9</td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a33cb0a68c36aa26fd599c7c66da86ed7"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a33cb0a68c36aa26fd599c7c66da86ed7">create_matrix</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *A)</td></tr>
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<tr class="memitem:a7558fd7779bf207157ced66f275951a0"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a7558fd7779bf207157ced66f275951a0">mat_mul</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;A, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;B, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *OUT)</td></tr>
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<tr class="memitem:a9bbf469d5525a816b0d6ca812119093d"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a9bbf469d5525a816b0d6ca812119093d">create_matrix</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &gt; *A)</td></tr>
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<tr class="memitem:abb8bf4c55e10685a5eb2ad3797fde1ae"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#abb8bf4c55e10685a5eb2ad3797fde1ae">mat_mul</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &gt; &amp;A, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &gt; &amp;B, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &gt; *OUT)</td></tr>
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<tr class="memitem:a28e2fa3e803abaea6c568dc45d69d8cc"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &gt; *A, bool print_intermediates=false)</td></tr>
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<tr class="memitem:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a> ()</td></tr>
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<tr class="memitem:a0283886819c7c140a023582b7269e2d0"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Compute real eigen values and eigen vectors of a symmetric matrix using <a href="https://en.wikipedia.org/wiki/QR_decomposition">QR decomposition</a> method. </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
<div class="textblock"><p >Compute real eigen values and eigen vectors of a symmetric matrix using <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">QR decomposition</a> method. </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
</div><h2 class="groupheader">Macro Definition Documentation</h2>
<a id="aee57a411f07599034f5ceb8cc7d65b40"></a>
<a id="aee57a411f07599034f5ceb8cc7d65b40" name="aee57a411f07599034f5ceb8cc7d65b40"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aee57a411f07599034f5ceb8cc7d65b40">&#9670;&nbsp;</a></span>LIMS</h2>
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<p>limit of range of matrix values </p>
<p >limit of range of matrix values </p>
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</div>
<h2 class="groupheader">Function Documentation</h2>
<a id="a33cb0a68c36aa26fd599c7c66da86ed7"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a33cb0a68c36aa26fd599c7c66da86ed7">&#9670;&nbsp;</a></span>create_matrix()</h2>
<a id="a9bbf469d5525a816b0d6ca812119093d" name="a9bbf469d5525a816b0d6ca812119093d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a9bbf469d5525a816b0d6ca812119093d">&#9670;&nbsp;</a></span>create_matrix()</h2>
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<td class="memname">void create_matrix </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &gt; *&#160;</td>
<td class="paramname"><em>A</em></td><td>)</td>
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<p>create a symmetric square matrix of given size with random elements. A symmetric square matrix will <em>always</em> have real eigen values.</p>
<p >create a symmetric square matrix of given size with random elements. A symmetric square matrix will <em>always</em> have real eigen values.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[out]</td><td class="paramname">A</td><td>matrix to create (must be pre-allocated in memory) </td></tr>
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<div class="fragment"><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; {</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <span class="keywordtype">int</span> i, j, tmp, lim2 = <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a> &gt;&gt; 1;</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="keywordtype">int</span> <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A-&gt;size();</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; </div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; A[0][i][i] = (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="keywordflow">for</span> (j = i + 1; j &lt; <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; j++) {</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; tmp = (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; A[0][i][j] = tmp; <span class="comment">// summetrically distribute random values</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; A[0][j][i] = tmp;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; }</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;}</div>
<div class="fragment"><div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> {</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keywordtype">int</span> i, j, tmp, lim2 = <a class="code hl_define" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a> &gt;&gt; 1;</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A-&gt;size();</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> A[0][i][i] = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % <a class="code hl_define" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordflow">for</span> (j = i + 1; j &lt; <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; j++) {</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> tmp = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % <a class="code hl_define" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> A[0][i][j] = tmp; <span class="comment">// summetrically distribute random values</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> A[0][j][i] = tmp;</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</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>}</div>
<div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:47</div></div>
<div class="ttc" id="aqr__eigen__values_8cpp_html_aee57a411f07599034f5ceb8cc7d65b40"><div class="ttname"><a href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a></div><div class="ttdeci">#define LIMS</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:20</div></div>
<div class="ttc" id="arand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a></div><div class="ttdeci">T rand(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&nbsp;</a></span>main()</h2>
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<p>main function </p>
<div class="fragment"><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>&#160; {</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>&#160; <span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = 5;</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>&#160; <span class="keywordflow">if</span> (argc == 2) {</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>&#160; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>&#160; } <span class="keywordflow">else</span> { <span class="comment">// if invalid input argument is given run tests</span></div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>&#160; <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>&#160; <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</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;Usage: ./qr_eigen_values [mat_size]\n&quot;</span>;</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>&#160; }</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>&#160; </div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> &lt; 2) {</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">fprintf</a>(stderr, <span class="stringliteral">&quot;Matrix size should be &gt; 2\n&quot;</span>);</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>&#160; <span class="keywordflow">return</span> -1;</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>&#160; }</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>&#160; </div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>&#160; <span class="comment">// initialize random number generator</span></div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>&#160; </div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>&#160; <span class="keywordtype">int</span> i, rows = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, columns = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>;</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>&#160; </div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; A(rows);</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>&#160; </div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; rows; i++) {</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>&#160; A[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(columns);</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>&#160; }</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>&#160; </div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>&#160; <span class="comment">/* create a random matrix */</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>&#160; <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#a33cb0a68c36aa26fd599c7c66da86ed7">create_matrix</a>(&amp;A);</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>&#160; </div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; A &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>&#160; </div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>&#160; clock_t t1 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>();</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eigen_vals = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a>(&amp;A);</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>&#160; <span class="keywordtype">double</span> dtime = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>() - t1) / CLOCKS_PER_SEC;</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>&#160; </div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</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;Eigen vals: &quot;</span>;</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>&#160; <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; eigen_vals[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</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;\nTime taken to compute: &quot;</span> &lt;&lt; dtime &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>&#160; </div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>&#160;}</div>
<p >main function </p>
<div class="fragment"><div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> {</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = 5;</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="keywordflow">if</span> (argc == 2) {</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> } <span class="keywordflow">else</span> { <span class="comment">// if invalid input argument is given run tests</span></div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</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;Usage: ./qr_eigen_values [mat_size]\n&quot;</span>;</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> }</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> </div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> &lt; 2) {</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">fprintf</a>(stderr, <span class="stringliteral">&quot;Matrix size should be &gt; 2\n&quot;</span>);</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> }</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> </div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> <span class="comment">// initialize random number generator</span></div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> </div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <span class="keywordtype">int</span> i, rows = <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, columns = <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>;</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> </div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; A(rows);</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> </div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; rows; i++) {</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> A[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(columns);</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> }</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> </div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> <span class="comment">/* create a random matrix */</span></div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#a9bbf469d5525a816b0d6ca812119093d">create_matrix</a>(&amp;A);</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> </div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; A &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> </div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> clock_t t1 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>();</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eigen_vals = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a>(&amp;A);</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <span class="keywordtype">double</span> dtime = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>() - t1) / CLOCKS_PER_SEC;</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> </div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</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;Eigen vals: &quot;</span>;</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; eigen_vals[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</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;\nTime taken to compute: &quot;</span> &lt;&lt; dtime &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> </div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span>}</div>
<div class="ttc" id="aatoi_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">std::atoi</a></div><div class="ttdeci">T atoi(T... args)</div></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 class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
<div class="ttc" id="afprintf_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">std::fprintf</a></div><div class="ttdeci">T fprintf(T... args)</div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a9977ad12548c4a49dee9dc3f0685aa54"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a></div><div class="ttdeci">ll mat_size</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:45</div></div>
<div class="ttc" id="anamespaceqr__algorithm_html_a763896dbb4a7e95c4a1e614ac0819d66"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a></div><div class="ttdeci">std::valarray&lt; double &gt; eigen_values(std::valarray&lt; std::valarray&lt; double &gt;&gt; *A, bool print_intermediates=false)</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:98</div></div>
<div class="ttc" id="anamespaceqr__algorithm_html_a28e2fa3e803abaea6c568dc45d69d8cc"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a></div><div class="ttdeci">std::valarray&lt; double &gt; eigen_values(std::valarray&lt; std::valarray&lt; double &gt; &gt; *A, bool print_intermediates=false)</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:98</div></div>
<div class="ttc" id="aqr__eigen__values_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:210</div></div>
<div class="ttc" id="aqr__eigen__values_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:177</div></div>
<div class="ttc" id="aqr__eigen__values_8cpp_html_a33cb0a68c36aa26fd599c7c66da86ed7"><div class="ttname"><a href="../../de/d75/qr__eigen__values_8cpp.html#a33cb0a68c36aa26fd599c7c66da86ed7">create_matrix</a></div><div class="ttdeci">void create_matrix(std::valarray&lt; std::valarray&lt; double &gt;&gt; *A)</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:28</div></div>
<div class="ttc" id="aqr__eigen__values_8cpp_html_a9bbf469d5525a816b0d6ca812119093d"><div class="ttname"><a href="../../de/d75/qr__eigen__values_8cpp.html#a9bbf469d5525a816b0d6ca812119093d">create_matrix</a></div><div class="ttdeci">void create_matrix(std::valarray&lt; std::valarray&lt; double &gt; &gt; *A)</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:28</div></div>
<div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
<div class="ttc" id="atime_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a></div><div class="ttdeci">T time(T... args)</div></div>
<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a7558fd7779bf207157ced66f275951a0">&#9670;&nbsp;</a></span>mat_mul()</h2>
<a id="abb8bf4c55e10685a5eb2ad3797fde1ae" name="abb8bf4c55e10685a5eb2ad3797fde1ae"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abb8bf4c55e10685a5eb2ad3797fde1ae">&#9670;&nbsp;</a></span>mat_mul()</h2>
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<td class="memname">void mat_mul </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;&#160;</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &gt; &amp;&#160;</td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;&#160;</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &gt; &amp;&#160;</td>
<td class="paramname"><em>B</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; &gt; *&#160;</td>
<td class="paramname"><em>OUT</em>&#160;</td>
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<p>Perform multiplication of two matrices.</p><ul>
<p >Perform multiplication of two matrices.</p><ul>
<li>R2 must be equal to C1</li>
<li>Resultant matrix size should be R1xC2 <dl class="params"><dt>Parameters</dt><dd>
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<dl class="section return"><dt>Returns</dt><dd>pointer to resultant matrix </dd></dl>
</li>
</ul>
<div class="fragment"><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; {</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="keywordtype">int</span> R1 = A.size();</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordtype">int</span> C1 = A[0].size();</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordtype">int</span> R2 = B.size();</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordtype">int</span> C2 = B[0].size();</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="keywordflow">if</span> (C1 != R2) {</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">perror</a>(<span class="stringliteral">&quot;Matrix dimensions mismatch!&quot;</span>);</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; }</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; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; R1; i++) {</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; C2; j++) {</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; OUT[0][i][j] = 0.f;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; C1; k++) {</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; OUT[0][i][j] += A[i][k] * B[k][j];</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; }</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;}</div>
<div class="fragment"><div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordtype">int</span> R1 = A.size();</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordtype">int</span> C1 = A[0].size();</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordtype">int</span> R2 = B.size();</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordtype">int</span> C2 = B[0].size();</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">if</span> (C1 != R2) {</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">perror</a>(<span class="stringliteral">&quot;Matrix dimensions mismatch!&quot;</span>);</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</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> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; R1; i++) {</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; C2; j++) {</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> OUT[0][i][j] = 0.f;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; C1; k++) {</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> OUT[0][i][j] += A[i][k] * B[k][j];</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> }</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</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="ttc" id="aperror_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a></div><div class="ttdeci">T perror(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a1440a7779ac56f47a3f355ce4a8c7da0">&#9670;&nbsp;</a></span>test1()</h2>
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<p>test function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
<p >test function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
\[\begin{bmatrix} 5 &amp; 7\\ 7 &amp; 11 \end{bmatrix}\]
</p>
<p> which are approximately, {15.56158, 0.384227} </p>
<div class="fragment"><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160; {</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; X = {{5, 7}, {7, 11}};</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160; <span class="keywordtype">double</span> y[] = {15.56158, 0.384227}; <span class="comment">// corresponding y-values</span></div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160; </div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</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;------- Test 1 -------&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eig_vals = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a>(&amp;X);</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160; </div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 2; i++) {</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i + 1 &lt;&lt; <span class="stringliteral">&quot;/2 Checking for &quot;</span> &lt;&lt; y[i] &lt;&lt; <span class="stringliteral">&quot; --&gt; &quot;</span>;</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>&#160; <span class="keywordtype">bool</span> <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; 2 &amp;&amp; !<a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; j++) {</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160; <span class="keywordflow">if</span> (std::abs(y[i] - eig_vals[j]) &lt; 0.1) {</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>&#160; <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</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; eig_vals[j] &lt;&lt; <span class="stringliteral">&quot;) &quot;</span>;</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>&#160; }</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>&#160; }</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>&#160; assert(result); <span class="comment">// ensure that i^th expected eigen value was computed</span></div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</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;found\n&quot;</span>;</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160; }</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</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;Test 1 Passed\n\n&quot;</span>;</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> {</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; X = {{5, 7}, {7, 11}};</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="keywordtype">double</span> y[] = {15.56158, 0.384227}; <span class="comment">// corresponding y-values</span></div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> </div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</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;------- Test 1 -------&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eig_vals = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a>(&amp;X);</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> </div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 2; i++) {</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i + 1 &lt;&lt; <span class="stringliteral">&quot;/2 Checking for &quot;</span> &lt;&lt; y[i] &lt;&lt; <span class="stringliteral">&quot; --&gt; &quot;</span>;</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; 2 &amp;&amp; !<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; j++) {</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="keywordflow">if</span> (std::abs(y[i] - eig_vals[j]) &lt; 0.1) {</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</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; eig_vals[j] &lt;&lt; <span class="stringliteral">&quot;) &quot;</span>;</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> }</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> }</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> assert(result); <span class="comment">// ensure that i^th expected eigen value was computed</span></div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</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;found\n&quot;</span>;</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> }</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</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;Test 1 Passed\n\n&quot;</span>;</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span>}</div>
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0283886819c7c140a023582b7269e2d0">&#9670;&nbsp;</a></span>test2()</h2>
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<p>test function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
<p >test function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
\[\begin{bmatrix} -4&amp; 4&amp; 2&amp; 0&amp; -3\\ 4&amp; -4&amp; 4&amp; -3&amp; -1\\ 2&amp; 4&amp; 4&amp; 3&amp; -3\\ 0&amp; -3&amp; 3&amp; -1&amp;-1\\ -3&amp; -1&amp; -3&amp; -3&amp; 0 \end{bmatrix}\]
</p>
<p> which are approximately, {9.27648, -9.26948, 2.0181, -1.03516, -5.98994} </p>
<div class="fragment"><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>&#160; {</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; X = {{-4, 4, 2, 0, -3},</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>&#160; {4, -4, 4, -3, -1},</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>&#160; {2, 4, 4, 3, -3},</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>&#160; {0, -3, 3, -1, -3},</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>&#160; {-3, -1, -3, -3, 0}};</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>&#160; <span class="keywordtype">double</span> y[] = {9.27648, -9.26948, 2.0181, -1.03516,</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>&#160; -5.98994}; <span class="comment">// corresponding y-values</span></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>&#160; </div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</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;------- Test 2 -------&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eig_vals = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a>(&amp;X);</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>&#160; </div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; X &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span></div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>&#160; &lt;&lt; <span class="stringliteral">&quot;Eigen values: &quot;</span> &lt;&lt; eig_vals &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>&#160; </div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 5; i++) {</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i + 1 &lt;&lt; <span class="stringliteral">&quot;/5 Checking for &quot;</span> &lt;&lt; y[i] &lt;&lt; <span class="stringliteral">&quot; --&gt; &quot;</span>;</div>
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<p>Algorithm that combines insertion sort and merge sort. <a href="https://en.wikipedia.org/wiki/Merge-insertion_sort">Wiki link</a>
<p>Algorithm that combines insertion sort and merge sort. <a href="https://en.wikipedia.org/wiki/Merge-insertion_sort" target="_blank">Wiki link</a>
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<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;array&gt;</code><br />
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Functions</h2></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Algorithm that combines insertion sort and merge sort. <a href="https://en.wikipedia.org/wiki/Merge-insertion_sort">Wiki link</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/sinkyoungdeok">@sinkyoungdeok</a> </dd>
<div class="textblock"><p >Algorithm that combines insertion sort and merge sort. <a href="https://en.wikipedia.org/wiki/Merge-insertion_sort" target="_blank">Wiki link</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/sinkyoungdeok" target="_blank">@sinkyoungdeok</a> </dd>
<dd>
<a href="https://github.com/kvedala">Krishna Vedala</a></dd></dl>
<a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a></dd></dl>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// }</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> ptr[j] = temp;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> }</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span>}</div>
<div class="ttc" id="adata_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array/data.html">std::array::data</a></div><div class="ttdeci">T data(T... args)</div></div>
<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a></div><div class="ttdeci">T end(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>&#160; {</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160; <a class="code" href="../../de/d7b/merge__insertion__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> {</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <a class="code hl_function" href="../../de/d7b/merge__insertion__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span>}</div>
<div class="ttc" id="amerge__insertion__sort_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../de/d7b/merge__insertion__sort_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Function to test code using random arrays.</div><div class="ttdef"><b>Definition:</b> merge_insertion_sort.cpp:132</div></div>
<div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
<div class="ttc" id="atime_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a></div><div class="ttdeci">T time(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#af4de4067a9a866ffd985c5b5055ccedf">&#9670;&nbsp;</a></span>merge()</h2>
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@@ -338,31 +337,31 @@ template&lt;typename T , size_t N&gt; </div>
</table>
</dd>
</dl>
<div class="fragment"><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="keywordtype">size_t</span> firstIndex = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a>;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="keywordtype">size_t</span> secondIndex = mid + 1;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; </div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <span class="keyword">auto</span> ptr = array-&gt;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/data.html">data</a>();</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;T, N + 1&gt;</a> tempArray{0};</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">// While there are elements in the left or right runs</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> index = min; index &lt;= <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a>; index++) {</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="comment">// If left run head exists and is &lt;= existing right run head.</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="keywordflow">if</span> (firstIndex &lt;= mid &amp;&amp;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; (secondIndex &gt; max || ptr[firstIndex] &lt;= ptr[secondIndex])) {</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; tempArray[index] = ptr[firstIndex];</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; firstIndex++;</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; tempArray[index] = ptr[secondIndex];</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; secondIndex++;</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; }</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; }</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; </div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; <span class="comment">// transfer to the initial array</span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/memcpy.html">memcpy</a>(ptr + min, tempArray.data() + min, (max - min) * <span class="keyword">sizeof</span>(T));</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; <span class="comment">// for (int index = min; index &lt;= max; index++) ptr[index] =</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; <span class="comment">// tempArray[index];</span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160;}</div>
<div class="fragment"><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="keywordtype">size_t</span> firstIndex = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a>;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordtype">size_t</span> secondIndex = mid + 1;</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keyword">auto</span> ptr = array-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array/data.html">data</a>();</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;T, N + 1&gt;</a> tempArray{0};</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> <span class="comment">// While there are elements in the left or right runs</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> index = min; index &lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a>; index++) {</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// If left run head exists and is &lt;= existing right run head.</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">if</span> (firstIndex &lt;= mid &amp;&amp;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> (secondIndex &gt; max || ptr[firstIndex] &lt;= ptr[secondIndex])) {</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> tempArray[index] = ptr[firstIndex];</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> firstIndex++;</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> tempArray[index] = ptr[secondIndex];</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> secondIndex++;</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> }</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> }</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// transfer to the initial array</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/memcpy.html">memcpy</a>(ptr + min, tempArray.data() + min, (max - min) * <span class="keyword">sizeof</span>(T));</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// for (int index = min; index &lt;= max; index++) ptr[index] =</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="comment">// tempArray[index];</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</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 class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
<div class="ttc" id="amemcpy_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/memcpy.html">std::memcpy</a></div><div class="ttdeci">T memcpy(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a7161278f18e83b671c6454b139cc5674">&#9670;&nbsp;</a></span>mergeSort()</h2>
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@@ -433,35 +432,35 @@ template&lt;typename T , size_t N&gt; </div>
</table>
</dd>
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<div class="fragment"><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; {</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; <span class="comment">// prerequisite</span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; <span class="keywordflow">if</span> ((max - min) &lt;= threshold) {</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; <a class="code" href="../../de/d7b/merge__insertion__sort_8cpp.html#a0cba4fbf287ab8cb978ed7f8fef886b1">InsertionSort</a>(array, min, max);</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; <span class="comment">// get the middle point</span></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; <span class="keywordtype">size_t</span> mid = (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a> + <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a>) &gt;&gt; 1;</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; </div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; <span class="comment">// apply merge sort to both parts of this</span></div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; <a class="code" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(array, min, mid, threshold);</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; <a class="code" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(array, mid, max, threshold);</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; </div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; <span class="comment">// and finally merge all that sorted stuff</span></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; <a class="code" href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge</a>(array, min, max, mid);</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; }</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160;}</div>
<div class="fragment"><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> <span class="comment">// prerequisite</span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keywordflow">if</span> ((max - min) &lt;= threshold) {</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <a class="code hl_function" href="../../de/d7b/merge__insertion__sort_8cpp.html#a0cba4fbf287ab8cb978ed7f8fef886b1">InsertionSort</a>(array, min, max);</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="comment">// get the middle point</span></div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keywordtype">size_t</span> mid = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a> + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">min</a>) &gt;&gt; 1;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> </div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// apply merge sort to both parts of this</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(array, min, mid, threshold);</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(array, mid, max, threshold);</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> </div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="comment">// and finally merge all that sorted stuff</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <a class="code hl_function" href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge</a>(array, min, max, mid);</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> }</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span>}</div>
<div class="ttc" id="agroup__sorting_html_ga460c61cd948203b4816bef2accb3fc73"><div class="ttname"><a href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge</a></div><div class="ttdeci">void merge(int *arr, int l, int m, int r)</div><div class="ttdef"><b>Definition:</b> merge_sort.cpp:33</div></div>
<div class="ttc" id="agroup__sorting_html_gab6b14fea48d9841e29b9fc26be6e05d7"><div class="ttname"><a href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a></div><div class="ttdeci">void mergeSort(int *arr, int l, int r)</div><div class="ttdef"><b>Definition:</b> merge_sort.cpp:71</div></div>
<div class="ttc" id="amerge__insertion__sort_8cpp_html_a0cba4fbf287ab8cb978ed7f8fef886b1"><div class="ttname"><a href="../../de/d7b/merge__insertion__sort_8cpp.html#a0cba4fbf287ab8cb978ed7f8fef886b1">sorting::merge_insertion::InsertionSort</a></div><div class="ttdeci">static void InsertionSort(std::array&lt; T, N &gt; *A, size_t start, size_t end)</div><div class="ttdoc">Insertion merge algorithm.</div><div class="ttdef"><b>Definition:</b> merge_insertion_sort.cpp:37</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&nbsp;</a></span>test()</h2>
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<p>Function to test code using random arrays. </p>
<dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
<div class="fragment"><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; {</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160; constexpr <span class="keywordtype">size_t</span> size = 30;</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, size&gt;</a> array{0};</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160; <span class="comment">// input</span></div>
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<p>main function </p>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</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;Type in decimal number between 0 up to 4000 (exclusive): &quot;</span>;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; in Upper Roman Numerals is &quot;</span> &lt;&lt; <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; in Lower Roman Numerals is &quot;</span> &lt;&lt; <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160;}</div>
<p >main function </p>
<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="keywordtype">int</span> n;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</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;\t\tRoman numbers converter\n\n&quot;</span>;</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</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;Type in decimal number between 0 up to 4000 (exclusive): &quot;</span>;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; in Upper Roman Numerals is &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; in Lower Roman Numerals is &quot;</span> &lt;&lt; <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span>}</div>
<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></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 class="ttc" id="adecimal__to__roman__numeral_8cpp_html_a003fb4e1b08279fe4cd50fbbc2782c2d"><div class="ttname"><a href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a></div><div class="ttdeci">std::string tolowerRoman(int n)</div><div class="ttdef"><b>Definition:</b> decimal_to_roman_numeral.cpp:24</div></div>
@@ -191,13 +190,13 @@ Functions</h2></td></tr>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/d85/decimal__to__roman__numeral_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="307" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<a id="a003fb4e1b08279fe4cd50fbbc2782c2d" name="a003fb4e1b08279fe4cd50fbbc2782c2d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a003fb4e1b08279fe4cd50fbbc2782c2d">&#9670;&nbsp;</a></span>tolowerRoman()</h2>
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@@ -212,48 +211,48 @@ Here is the call graph for this function:</div>
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<p>to convert to lowercase Roman Numeral the function works recursively </p>
<div class="fragment"><div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; {</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; <span class="keywordflow">if</span> (n &lt; 4)</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, n);</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; <span class="keywordflow">if</span> (n &lt; 6)</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, 5 - n) + <span class="stringliteral">&quot;v&quot;</span>;</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <span class="keywordflow">if</span> (n &lt; 9)</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;v&quot;</span>) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, n - 5);</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordflow">if</span> (n &lt; 11)</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, 10 - n) + <span class="stringliteral">&quot;x&quot;</span>;</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <span class="keywordflow">if</span> (n &lt; 40)</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, n / 10) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <span class="keywordflow">if</span> (n &lt; 60)</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, 5 - n / 10) + <span class="charliteral">&#39;l&#39;</span> + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="keywordflow">if</span> (n &lt; 90)</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;l&quot;</span>) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, n / 10 - 5) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keywordflow">if</span> (n &lt; 110)</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, 10 - n / 10) + <span class="stringliteral">&quot;c&quot;</span> + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="keywordflow">if</span> (n &lt; 400)</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, n / 100) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="keywordflow">if</span> (n &lt; 600)</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, 5 - n / 100) + <span class="charliteral">&#39;d&#39;</span> + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordflow">if</span> (n &lt; 900)</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;d&quot;</span>) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, n / 100 - 5) +</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="keywordflow">if</span> (n &lt; 1100)</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, 10 - n / 100) + <span class="stringliteral">&quot;m&quot;</span> + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <span class="keywordflow">if</span> (n &lt; 4000)</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;m&#39;</span>, n / 1000) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 1000);</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="keywordflow">return</span> <span class="stringliteral">&quot;?&quot;</span>;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160;}</div>
<p >to convert to lowercase Roman Numeral the function works recursively </p>
<div class="fragment"><div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> {</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> <span class="keywordflow">if</span> (n &lt; 4)</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, n);</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="keywordflow">if</span> (n &lt; 6)</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, 5 - n) + <span class="stringliteral">&quot;v&quot;</span>;</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keywordflow">if</span> (n &lt; 9)</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;v&quot;</span>) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, n - 5);</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keywordflow">if</span> (n &lt; 11)</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;i&#39;</span>, 10 - n) + <span class="stringliteral">&quot;x&quot;</span>;</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keywordflow">if</span> (n &lt; 40)</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, n / 10) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordflow">if</span> (n &lt; 60)</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, 5 - n / 10) + <span class="charliteral">&#39;l&#39;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordflow">if</span> (n &lt; 90)</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;l&quot;</span>) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, n / 10 - 5) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordflow">if</span> (n &lt; 110)</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;x&#39;</span>, 10 - n / 10) + <span class="stringliteral">&quot;c&quot;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 10);</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordflow">if</span> (n &lt; 400)</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, n / 100) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">if</span> (n &lt; 600)</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, 5 - n / 100) + <span class="charliteral">&#39;d&#39;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">if</span> (n &lt; 900)</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;d&quot;</span>) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, n / 100 - 5) +</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keywordflow">if</span> (n &lt; 1100)</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;c&#39;</span>, 10 - n / 100) + <span class="stringliteral">&quot;m&quot;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 100);</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordflow">if</span> (n &lt; 4000)</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;m&#39;</span>, n / 1000) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a003fb4e1b08279fe4cd50fbbc2782c2d">tolowerRoman</a>(n % 1000);</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordflow">return</span> <span class="stringliteral">&quot;?&quot;</span>;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span>}</div>
<div class="ttc" id="adecimal__to__roman__numeral_8cpp_html_a88203bd297e8405160c132faa1187780"><div class="ttname"><a href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a></div><div class="ttdeci">std::string fill(char c, int n)</div><div class="ttdef"><b>Definition:</b> decimal_to_roman_numeral.cpp:15</div></div>
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Here is the call graph for this function:</div>
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<a id="a214743638eff1336f835310049aef979" name="a214743638eff1336f835310049aef979"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a214743638eff1336f835310049aef979">&#9670;&nbsp;</a></span>toupperRoman()</h2>
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@@ -268,41 +267,41 @@ Here is the call graph for this function:</div>
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<p>to convert to uppercase Roman Numeral the function works recursively </p>
<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="keywordflow">if</span> (n &lt; 4)</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;I&#39;</span>, n);</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="keywordflow">if</span> (n &lt; 6)</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;I&#39;</span>, 5 - n) + <span class="stringliteral">&quot;V&quot;</span>;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keywordflow">if</span> (n &lt; 9)</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;V&quot;</span>) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;I&#39;</span>, n - 5);</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <span class="keywordflow">if</span> (n &lt; 11)</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;I&#39;</span>, 10 - n) + <span class="stringliteral">&quot;X&quot;</span>;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="keywordflow">if</span> (n &lt; 40)</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;X&#39;</span>, n / 10) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 10);</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="keywordflow">if</span> (n &lt; 60)</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;X&#39;</span>, 5 - n / 10) + <span class="charliteral">&#39;L&#39;</span> + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 10);</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <span class="keywordflow">if</span> (n &lt; 90)</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;L&quot;</span>) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;X&#39;</span>, n / 10 - 5) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 10);</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <span class="keywordflow">if</span> (n &lt; 110)</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;X&#39;</span>, 10 - n / 10) + <span class="stringliteral">&quot;C&quot;</span> + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 10);</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="keywordflow">if</span> (n &lt; 400)</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;C&#39;</span>, n / 100) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 100);</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="keywordflow">if</span> (n &lt; 600)</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;C&#39;</span>, 5 - n / 100) + <span class="charliteral">&#39;D&#39;</span> + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 100);</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <span class="keywordflow">if</span> (n &lt; 900)</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;D&quot;</span>) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;C&#39;</span>, n / 100 - 5) +</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 100);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="keywordflow">if</span> (n &lt; 1100)</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;C&#39;</span>, 10 - n / 100) + <span class="stringliteral">&quot;M&quot;</span> + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 100);</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="keywordflow">if</span> (n &lt; 4000)</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;M&#39;</span>, n / 1000) + <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 1000);</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <span class="keywordflow">return</span> <span class="stringliteral">&quot;?&quot;</span>;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160;}</div>
<p >to convert to uppercase Roman Numeral the function works recursively </p>
<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="keywordflow">if</span> (n &lt; 4)</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;I&#39;</span>, n);</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">if</span> (n &lt; 6)</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;I&#39;</span>, 5 - n) + <span class="stringliteral">&quot;V&quot;</span>;</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">if</span> (n &lt; 9)</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;V&quot;</span>) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;I&#39;</span>, n - 5);</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keywordflow">if</span> (n &lt; 11)</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;I&#39;</span>, 10 - n) + <span class="stringliteral">&quot;X&quot;</span>;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">if</span> (n &lt; 40)</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;X&#39;</span>, n / 10) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 10);</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">if</span> (n &lt; 60)</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;X&#39;</span>, 5 - n / 10) + <span class="charliteral">&#39;L&#39;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 10);</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">if</span> (n &lt; 90)</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;L&quot;</span>) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;X&#39;</span>, n / 10 - 5) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 10);</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordflow">if</span> (n &lt; 110)</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;X&#39;</span>, 10 - n / 10) + <span class="stringliteral">&quot;C&quot;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 10);</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordflow">if</span> (n &lt; 400)</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;C&#39;</span>, n / 100) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 100);</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">if</span> (n &lt; 600)</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;C&#39;</span>, 5 - n / 100) + <span class="charliteral">&#39;D&#39;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 100);</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordflow">if</span> (n &lt; 900)</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;D&quot;</span>) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;C&#39;</span>, n / 100 - 5) +</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 100);</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">if</span> (n &lt; 1100)</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;C&#39;</span>, 10 - n / 100) + <span class="stringliteral">&quot;M&quot;</span> + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 100);</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keywordflow">if</span> (n &lt; 4000)</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(<span class="charliteral">&#39;M&#39;</span>, n / 1000) + <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a214743638eff1336f835310049aef979">toupperRoman</a>(n % 1000);</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keywordflow">return</span> <span class="stringliteral">&quot;?&quot;</span>;</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span>}</div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/d85/decimal__to__roman__numeral_8cpp_a214743638eff1336f835310049aef979_cgraph.svg" width="208" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/d85/decimal__to__roman__numeral_8cpp_a214743638eff1336f835310049aef979_cgraph.svg" width="208" height="62"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
</div>
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<tr bgcolor="#f0f0f0"><td class="entry"><b>m_root</b> (defined in <a class="el" href="../../dd/d2f/class_trie.html">Trie</a>)</td><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
<tr bgcolor="#f0f0f0" class="odd"><td class="entry"><b>m_root</b> (defined in <a class="el" href="../../dd/d2f/class_trie.html">Trie</a>)</td><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></td><td class="entry"><span class="mlabel">private</span></td></tr>
<tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>removeWord</b>(const std::string &amp;word) (defined in <a class="el" href="../../dd/d2f/class_trie.html">Trie</a>)</td><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
<tr><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html#a95216ffc56cb9f8cede982cecb872af4">removeWordHelper</a>(const std::string &amp;word, std::shared_ptr&lt; TrieNode &gt; curr, size_t index)</td><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></td><td class="entry"><span class="mlabel">inline</span><span class="mlabel">private</span></td></tr>
<tr class="odd"><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html#a26941759ecf94d67a27d4a610bc0f63d">removeWordHelper</a>(const std::string &amp;word, std::shared_ptr&lt; TrieNode &gt; curr, size_t index)</td><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></td><td class="entry"><span class="mlabel">inline</span><span class="mlabel">private</span></td></tr>
<tr class="even"><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html#a411e77126930a0942dd7b65e96b15206">search</a>(const std::string &amp;word)</td><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
<tr><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html#a6af57e9f25d0d0a2d59eea5a4a802908">Trie</a>()</td><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
<tr class="odd"><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html#a6af57e9f25d0d0a2d59eea5a4a802908">Trie</a>()</td><td class="entry"><a class="el" href="../../dd/d2f/class_trie.html">Trie</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
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