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<p>Cycle sort is based on the idea that array to be sorted can be divided into cycles, which can individually be rotated to give a sorted result.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for cycle_sort2.cpp:</div>
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Functions</h2></td></tr>
<tr class="memitem:af82f47c25011c54bd19ae9cd775e52c1"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:af82f47c25011c54bd19ae9cd775e52c1"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d87/cycle__sort2_8cpp.html#af82f47c25011c54bd19ae9cd775e52c1">sorting::cycle_sort::swap</a> (T &amp;a, T &amp;b)</td></tr>
<tr class="memdesc:af82f47c25011c54bd19ae9cd775e52c1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to perform swapping. <a href="../../da/d87/cycle__sort2_8cpp.html#af82f47c25011c54bd19ae9cd775e52c1">More...</a><br /></td></tr>
<tr class="separator:af82f47c25011c54bd19ae9cd775e52c1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4c52eee647a17095f4893f6258893e15"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a4c52eee647a17095f4893f6258893e15"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d87/cycle__sort2_8cpp.html#a4c52eee647a17095f4893f6258893e15">sorting::cycle_sort::cycleSort</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;arr, int n)</td></tr>
<tr class="memdesc:a4c52eee647a17095f4893f6258893e15"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to perform cycle sort. <a href="../../da/d87/cycle__sort2_8cpp.html#a4c52eee647a17095f4893f6258893e15">More...</a><br /></td></tr>
<tr class="separator:a4c52eee647a17095f4893f6258893e15"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d87/cycle__sort2_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test implementations. <a href="../../da/d87/cycle__sort2_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></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="../../da/d87/cycle__sort2_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../da/d87/cycle__sort2_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Cycle sort is based on the idea that array to be sorted can be divided into cycles, which can individually be rotated to give a sorted result. </p>
<p>It is an in-place, unstable sorting algorithm, a comparison sort that is theoretically optimal in terms of the total number of memory writes to the original array. Each value is either written zero times, if it’s already in its correct position, or written one time to its correct position.</p>
<p>The array is divided into cycles. We begin with the cycle containing the first element. Find the correct position of first element and place it at its correct position, say j. Now we consider the old value of arr[j] and find its correct position. This process is continued until all the elements of the current cycle are placed at their correct position, i.e. until the starting point of the cycle is reached.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://www.github.com/VasuSehgal123">Vasu Sehgal</a> </dd></dl>
<dl class="section see"><dt>See also</dt><dd>more on <a href="https://en.wikipedia.org/wiki/Cycle_sort">Cycle sort</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a4c52eee647a17095f4893f6258893e15"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a4c52eee647a17095f4893f6258893e15">&#9670;&nbsp;</a></span>cycleSort()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">void sorting::cycle_sort::cycleSort </td>
<td>(</td>
<td class="paramtype"><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>arr</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Function to perform cycle sort. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">arr</td><td>vector of elements. </td></tr>
<tr><td class="paramname">n</td><td>size of the vector </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; {</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; </div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordtype">int</span> writes = 0; <span class="comment">// count number of memory writes</span></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">// traverse array elements and put it at it&#39;s correct positon</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; </div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> cycle_start = 0; cycle_start &lt;= n - 2; cycle_start++) {</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; T item = arr[cycle_start]; <span class="comment">// initialize item as starting point</span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; </div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="keywordtype">int</span> pos = cycle_start; <span class="comment">// Find position where we put the item.</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = cycle_start + 1; i &lt; n; i++) <span class="comment">// we basically count all smaller elements</span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="keywordflow">if</span> (arr[i] &lt; item) <span class="comment">// on the right side of the item.</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; pos++;</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; <span class="keywordflow">if</span> (pos == cycle_start)</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <span class="keywordflow">continue</span>; <span class="comment">// If item is already in correct position</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; </div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="keywordflow">while</span> (item == arr[pos])</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; pos += 1; <span class="comment">// ignore all duplicate elements</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; </div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; </div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <span class="keywordflow">if</span> (pos != cycle_start) {</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">swap</a>(item, arr[pos]); <span class="comment">// place the item at it&#39;s correct position</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; writes++;</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; }</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; </div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="keywordflow">while</span> (pos != cycle_start) { <span class="comment">// Rotate rest of the cycle</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; pos = cycle_start;</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="keywordflow">for</span> (<span class="keywordtype">int</span> i = cycle_start + 1; i &lt; n; i++) <span class="comment">// Find position where we put the element</span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <span class="keywordflow">if</span> (arr[i] &lt; item)</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; pos += 1;</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; </div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <span class="keywordflow">while</span> (item == arr[pos])</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; pos += 1; <span class="comment">// ignore all duplicate elements</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; </div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; </div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <span class="keywordflow">if</span> (item != arr[pos]) {</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/algorithm/swap.html">swap</a>(item, arr[pos]); <span class="comment">// place the item at it&#39;s correct position</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; writes++;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; }</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; }</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; </div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; <span class="comment">// Number of memory writes or swaps</span></div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; <span class="comment">// cout &lt;&lt; writes &lt;&lt; endl ;</span></div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; }</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>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void&#160;</td>
<td class="paramname"></td><td>)</td>
<td></td>
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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="l00142"></a><span class="lineno"> 142</span>&#160;{</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160; <a class="code" href="../../da/d87/cycle__sort2_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the tests</span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160;}</div>
<div class="ttc" id="acycle__sort2_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../da/d87/cycle__sort2_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_sort2.cpp:114</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#af82f47c25011c54bd19ae9cd775e52c1">&#9670;&nbsp;</a></span>swap()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">void sorting::cycle_sort::swap </td>
<td>(</td>
<td class="paramtype">T &amp;&#160;</td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T &amp;&#160;</td>
<td class="paramname"><em>b</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Function to perform swapping. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>element </td></tr>
<tr><td class="paramname">b</td><td>element </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; {</div>
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<td class="memname">static void test </td>
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<p>Test implementations. </p>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; arr2[i] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
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<p>This program computes the N^th Fibonacci number in modulo mod input argument .
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
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Functions</h2></td></tr>
<tr class="memitem:abc3bc08249058d57cfc8f54a29d9cf9f"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a> (uint64_t n, uint64_t mod)</td></tr>
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<tr class="memitem:ae1a3968e7947464bee7714f6d43b7002"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a> ()</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="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>This program computes the N^th Fibonacci number in modulo mod input argument . </p>
<p>Takes O(logn) time to compute nth Fibonacci number</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/villayatali123">villayatali123</a> </dd>
<dd>
[unknown author]() </dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d9/d89/fibonacci_8cpp.html" title="Generate fibonacci sequence.">fibonacci.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="../../de/d47/string__fibonacci_8cpp.html" title="This Programme returns the Nth fibonacci as a string.">string_fibonacci.cpp</a>, <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> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="abc3bc08249058d57cfc8f54a29d9cf9f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abc3bc08249058d57cfc8f54a29d9cf9f">&#9670;&nbsp;</a></span>fibo()</h2>
<div class="memitem">
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<td class="memname">uint64_t fibo </td>
<td>(</td>
<td class="paramtype">uint64_t&#160;</td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint64_t&#160;</td>
<td class="paramname"><em>mod</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>This function finds nth fibonacci number in a given modulus </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>nth fibonacci number </td></tr>
<tr><td class="paramname">mod</td><td>modulo number </td></tr>
</table>
</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/container/vector.html">std::vector&lt;uint64_t&gt;</a> <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(2,0);</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; transition(2,<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2,0));</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; Identity(2,<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2,0));</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; n--;</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[0]=1, <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1]=1;</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; Identity[0][0]=1; Identity[0][1]=0;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; Identity[1][0]=0; Identity[1][1]=1;</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; transition[0][0]=0;</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; transition[1][0]=transition[1][1]=transition[0][1]=1;</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; <span class="keywordflow">while</span>(n)</div>
<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; <span class="keywordflow">if</span>(n%2)</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; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; res(2, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2,0));</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=0;i&lt;2;i++)</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="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; {</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordflow">for</span>(<span class="keywordtype">int</span> k=0;k&lt;2;k++)</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; res[i][j]=(res[i][j]%mod+((Identity[i][k]%mod*transition[k][j]%mod))%mod)%mod;</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; }</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; <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; {</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; {</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; Identity[i][j]=res[i][j];</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; }</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; n--;</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; <span class="keywordflow">else</span>{</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; res1(2, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2,0));</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</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="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</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> k=0;k&lt;2;k++)</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; {</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; res1[i][j]=(res1[i][j]%mod+((transition[i][k]%mod*transition[k][j]%mod))%mod)%mod;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; }</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; }</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</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="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; {</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; transition[i][j]=res1[i][j];</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; }</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; } </div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; n=n/2;</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> ((result[0]%mod*Identity[0][0]%mod)%mod+(<a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1]%mod*Identity[1][0]%mod)%mod)%mod;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160;}</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>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; uint64_t &gt;</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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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void&#160;</td>
<td class="paramname"></td><td>)</td>
<td></td>
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</div><div class="memdoc">
<p>Main function </p>
<div class="fragment"><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160;{</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; <a class="code" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; uint64_t mod=1000000007;</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;Enter the value of N: &quot;</span>;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; uint64_t n=0; <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="l00112"></a><span class="lineno"> 112</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;th Fibonacci number in modulo &quot;</span> &lt;&lt; mod &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>&lt;&lt; <a class="code" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>( n , mod) &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="l00113"></a><span class="lineno"> 113</span>&#160;}</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="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__matrix__exponentiation_8cpp_html_abc3bc08249058d57cfc8f54a29d9cf9f"><div class="ttname"><a href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a></div><div class="ttdeci">uint64_t fibo(uint64_t n, uint64_t mod)</div><div class="ttdef"><b>Definition:</b> fibonacci_matrix_exponentiation.cpp:23</div></div>
<div class="ttc" id="afibonacci__matrix__exponentiation_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition:</b> fibonacci_matrix_exponentiation.cpp:88</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae1a3968e7947464bee7714f6d43b7002">&#9670;&nbsp;</a></span>test()</h2>
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<td class="memname">void test </td>
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<td class="paramname"></td><td>)</td>
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<p>Function to test above algorithm </p>
<div class="fragment"><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; assert(<a class="code" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(6, 1000000007 ) == 8);</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</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 case:1 passed\n&quot;</span>;</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; assert(<a class="code" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(5, 1000000007 ) == 5);</div>
<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;test case:2 passed\n&quot;</span>;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; assert(<a class="code" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(10 , 1000000007) == 55);</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 case:3 passed\n&quot;</span>;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; assert(<a class="code" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(500 , 100) == 25);</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</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 case:3 passed\n&quot;</span>;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; assert(<a class="code" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(500 , 10000) == 4125);</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</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 case:3 passed\n&quot;</span>;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</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;--All tests passed--\n&quot;</span>;</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160;}</div>
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var fibonacci__matrix__exponentiation_8cpp =
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