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<title>Algorithms_in_C++: math/fibonacci_matrix_exponentiation.cpp File Reference</title>
<title>TheAlgorithms/C++: math/fibonacci_matrix_exponentiation.cpp File Reference</title>
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<div id="projectname">TheAlgorithms/C++<span id="projectnumber">&#160;1.0.0</span>
</div>
<div id="projectbrief">Set of algorithms implemented in C++.</div>
<div id="projectbrief">All the algorithms implemented in C++</div>
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@@ -121,7 +138,9 @@ Include dependency graph for fibonacci_matrix_exponentiation.cpp:</div>
<div class="dyncontent">
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<p><a href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:abc3bc08249058d57cfc8f54a29d9cf9f" id="r_abc3bc08249058d57cfc8f54a29d9cf9f"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a> (uint64_t n, uint64_t mod)</td></tr>
@@ -138,6 +157,8 @@ Functions</h2></td></tr>
<dd>
[unknown author]() </dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d9/d89/fibonacci_8cpp.html" title="n-th Fibonacci number.">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>
<p class="definition">Definition in file <a class="el" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp_source.html">fibonacci_matrix_exponentiation.cpp</a>.</p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="abc3bc08249058d57cfc8f54a29d9cf9f" name="abc3bc08249058d57cfc8f54a29d9cf9f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abc3bc08249058d57cfc8f54a29d9cf9f">&#9670;&#160;</a></span>fibo()</h2>
@@ -164,11 +185,13 @@ Functions</h2></td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp_source.html#l00025">25</a> of file <a class="el" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp_source.html">fibonacci_matrix_exponentiation.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 25</span> {</div>
<div class="line"><span class="lineno"> 26</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(2, 0);</div>
<div class="line"><span class="lineno"> 27</span> <a class="code hl_classRef" 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,</div>
<div class="line"><span class="lineno"> 28</span> <a class="code hl_classRef" 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"><span class="lineno"> 29</span> <a class="code hl_classRef" 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="code hl_classRef" 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"><span class="lineno"> 26</span> std::vector&lt;uint64_t&gt; <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(2, 0);</div>
<div class="line"><span class="lineno"> 27</span> std::vector&lt;std::vector&lt;uint64_t&gt;&gt; transition(2,</div>
<div class="line"><span class="lineno"> 28</span> std::vector&lt;uint64_t&gt;(2, 0));</div>
<div class="line"><span class="lineno"> 29</span> std::vector&lt;std::vector&lt;uint64_t&gt;&gt; Identity(2, std::vector&lt;uint64_t&gt;(2, 0));</div>
<div class="line"><span class="lineno"> 30</span> n--;</div>
<div class="line"><span class="lineno"> 31</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[0] = 1, <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1] = 1;</div>
<div class="line"><span class="lineno"> 32</span> Identity[0][0] = 1;</div>
@@ -181,8 +204,8 @@ Functions</h2></td></tr>
<div class="line"><span class="lineno"> 39</span> </div>
<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">while</span> (n) {</div>
<div class="line"><span class="lineno"> 41</span> <span class="keywordflow">if</span> (n % 2) {</div>
<div class="line"><span class="lineno"> 42</span> <a class="code hl_classRef" 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,</div>
<div class="line"><span class="lineno"> 43</span> <a class="code hl_classRef" 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"><span class="lineno"> 42</span> std::vector&lt;std::vector&lt;uint64_t&gt;&gt; res(2,</div>
<div class="line"><span class="lineno"> 43</span> std::vector&lt;uint64_t&gt;(2, 0));</div>
<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 2; i++) {</div>
<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; 2; j++) {</div>
<div class="line"><span class="lineno"> 46</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; 2; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
@@ -201,8 +224,8 @@ Functions</h2></td></tr>
<div class="line"><span class="lineno"> 59</span> }</div>
<div class="line"><span class="lineno"> 60</span> n--;</div>
<div class="line"><span class="lineno"> 61</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 62</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; res1(</div>
<div class="line"><span class="lineno"> 63</span> 2, <a class="code hl_classRef" 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"><span class="lineno"> 62</span> std::vector&lt;std::vector&lt;uint64_t&gt;&gt; res1(</div>
<div class="line"><span class="lineno"> 63</span> 2, std::vector&lt;uint64_t&gt;(2, 0));</div>
<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 2; i++) {</div>
<div class="line"><span class="lineno"> 65</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; 2; j++) {</div>
<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt; 2; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
@@ -226,9 +249,8 @@ Functions</h2></td></tr>
<div class="line"><span class="lineno"> 84</span> (result[1] % mod * Identity[1][0] % mod) % mod) %</div>
<div class="line"><span class="lineno"> 85</span> mod;</div>
<div class="line"><span class="lineno"> 86</span>}</div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> composite_simpson_rule.cpp:117</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:77</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>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00117">composite_simpson_rule.cpp:117</a></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> <a href="../../de/dc3/fibonacci__sum_8cpp_source.html#l00077">fibonacci_sum.cpp:77</a></div></div>
</div><!-- fragment -->
</div>
</div>
@@ -247,26 +269,20 @@ Functions</h2></td></tr>
</table>
</div><div class="memdoc">
<p>Main function </p>
<p class="definition">Definition at line <a class="el" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp_source.html#l00108">108</a> of file <a class="el" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp_source.html">fibonacci_matrix_exponentiation.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 108</span> {</div>
<div class="line"><span class="lineno"> 109</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
<div class="line"><span class="lineno"> 110</span> uint64_t mod = 1000000007;</div>
<div class="line"><span class="lineno"> 111</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;Enter the value of N: &quot;</span>;</div>
<div class="line"><span class="lineno"> 111</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Enter the value of N: &quot;</span>;</div>
<div class="line"><span class="lineno"> 112</span> uint64_t n = 0;</div>
<div class="line"><span class="lineno"> 113</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"><span class="lineno"> 114</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;th Fibonacci number in modulo &quot;</span> &lt;&lt; mod &lt;&lt; <span class="stringliteral">&quot;: &quot;</span></div>
<div class="line"><span class="lineno"> 115</span> &lt;&lt; <a class="code hl_function" href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(n, mod) &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"><span class="lineno"> 113</span> std::cin &gt;&gt; n;</div>
<div class="line"><span class="lineno"> 114</span> std::cout &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></div>
<div class="line"><span class="lineno"> 115</span> &lt;&lt; <a class="code hl_function" href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(n, mod) &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 116</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="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_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdef"><b>Definition</b> fibonacci_matrix_exponentiation.cpp:91</div></div>
<div class="ttc" id="afibonacci__matrix__exponentiation_8cpp_html_abc3bc08249058d57cfc8f54a29d9cf9f"><div class="ttname"><a href="#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:25</div></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="../../da/dc9/fibonacci__matrix__exponentiation_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="270" height="138"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
</div>
<div class="ttc" id="afibonacci__matrix__exponentiation_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdef"><b>Definition</b> <a href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp_source.html#l00091">fibonacci_matrix_exponentiation.cpp:91</a></div></div>
<div class="ttc" id="afibonacci__matrix__exponentiation_8cpp_html_abc3bc08249058d57cfc8f54a29d9cf9f"><div class="ttname"><a href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a></div><div class="ttdeci">uint64_t fibo(uint64_t n, uint64_t mod)</div><div class="ttdef"><b>Definition</b> <a href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp_source.html#l00025">fibonacci_matrix_exponentiation.cpp:25</a></div></div>
</div><!-- fragment -->
</div>
</div>
<a id="aa8dca7b867074164d5f45b0f3851269d" name="aa8dca7b867074164d5f45b0f3851269d"></a>
@@ -292,25 +308,22 @@ Here is the call graph for this function:</div>
</table>
</div><div class="memdoc">
<p>Function to test above algorithm </p>
<p class="definition">Definition at line <a class="el" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp_source.html#l00091">91</a> of file <a class="el" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp_source.html">fibonacci_matrix_exponentiation.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 91</span> {</div>
<div class="line"><span class="lineno"> 92</span> assert(<a class="code hl_function" href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(6, 1000000007) == 8);</div>
<div class="line"><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;test case:1 passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 93</span> std::cout &lt;&lt; <span class="stringliteral">&quot;test case:1 passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 94</span> assert(<a class="code hl_function" href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(5, 1000000007) == 5);</div>
<div class="line"><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 case:2 passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 95</span> std::cout &lt;&lt; <span class="stringliteral">&quot;test case:2 passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 96</span> assert(<a class="code hl_function" href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(10, 1000000007) == 55);</div>
<div class="line"><span class="lineno"> 97</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 case:3 passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 97</span> std::cout &lt;&lt; <span class="stringliteral">&quot;test case:3 passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 98</span> assert(<a class="code hl_function" href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(500, 100) == 25);</div>
<div class="line"><span class="lineno"> 99</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 case:3 passed\n&quot;</span>;</div>
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<div class="line"><span class="lineno"> 101</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 case:3 passed\n&quot;</span>;</div>
<div class="line"><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;--All tests passed--\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 101</span> std::cout &lt;&lt; <span class="stringliteral">&quot;test case:3 passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 102</span> std::cout &lt;&lt; <span class="stringliteral">&quot;--All tests passed--\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 103</span>}</div>
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<div class="headertitle"><div class="title">fibonacci_matrix_exponentiation.cpp</div></div>
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<a href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#include &lt;cassert&gt;</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="foldopen" id="foldopen00025" data-start="{" data-end="}">
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"><a class="line" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f"> 25</a></span>uint64_t <a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(uint64_t n, uint64_t mod) {</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> std::vector&lt;uint64_t&gt; result(2, 0);</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> std::vector&lt;std::vector&lt;uint64_t&gt;&gt; transition(2,</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> std::vector&lt;uint64_t&gt;(2, 0));</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> std::vector&lt;std::vector&lt;uint64_t&gt;&gt; Identity(2, std::vector&lt;uint64_t&gt;(2, 0));</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> n--;</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> result[0] = 1, result[1] = 1;</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> Identity[0][0] = 1;</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> Identity[0][1] = 0;</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> Identity[1][0] = 0;</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> Identity[1][1] = 1;</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> transition[0][0] = 0;</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> transition[1][0] = transition[1][1] = transition[0][1] = 1;</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="keywordflow">while</span> (n) {</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordflow">if</span> (n % 2) {</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> std::vector&lt;std::vector&lt;uint64_t&gt;&gt; res(2,</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> std::vector&lt;uint64_t&gt;(2, 0));</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 2; i++) {</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; 2; j++) {</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> k = 0; k &lt; 2; k++) {</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> res[i][j] =</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> (res[i][j] % mod +</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> ((Identity[i][k] % mod * transition[k][j] % mod)) %</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> mod) %</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> mod;</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> }</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="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 2; i++) {</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; 2; j++) {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> Identity[i][j] = res[i][j];</div>
<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> }</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> n--;</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> std::vector&lt;std::vector&lt;uint64_t&gt;&gt; res1(</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> 2, std::vector&lt;uint64_t&gt;(2, 0));</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 2; i++) {</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; 2; j++) {</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> k = 0; k &lt; 2; k++) {</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> res1[i][j] =</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> (res1[i][j] % mod + ((transition[i][k] % mod *</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> transition[k][j] % mod)) %</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> mod) %</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> mod;</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="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 2; i++) {</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; 2; j++) {</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> transition[i][j] = res1[i][j];</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> }</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> }</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> n = n / 2;</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> }</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordflow">return</span> ((result[0] % mod * Identity[0][0] % mod) % mod +</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> (result[1] % mod * Identity[1][0] % mod) % mod) %</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> mod;</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span>}</div>
</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> </div>
<div class="foldopen" id="foldopen00091" data-start="{" data-end="}">
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"><a class="line" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 91</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> assert(<a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(6, 1000000007) == 8);</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> std::cout &lt;&lt; <span class="stringliteral">&quot;test case:1 passed\n&quot;</span>;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> assert(<a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(5, 1000000007) == 5);</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> std::cout &lt;&lt; <span class="stringliteral">&quot;test case:2 passed\n&quot;</span>;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> assert(<a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(10, 1000000007) == 55);</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> std::cout &lt;&lt; <span class="stringliteral">&quot;test case:3 passed\n&quot;</span>;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> assert(<a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(500, 100) == 25);</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> std::cout &lt;&lt; <span class="stringliteral">&quot;test case:3 passed\n&quot;</span>;</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> assert(<a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(500, 10000) == 4125);</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> std::cout &lt;&lt; <span class="stringliteral">&quot;test case:3 passed\n&quot;</span>;</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> std::cout &lt;&lt; <span class="stringliteral">&quot;--All tests passed--\n&quot;</span>;</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span>}</div>
</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="foldopen" id="foldopen00108" data-start="{" data-end="}">
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"><a class="line" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 108</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> uint64_t mod = 1000000007;</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Enter the value of N: &quot;</span>;</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> uint64_t n = 0;</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> std::cin &gt;&gt; n;</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> std::cout &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></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> &lt;&lt; <a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(n, mod) &lt;&lt; std::endl;</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span>}</div>
</div>
<div class="ttc" id="afibonacci__matrix__exponentiation_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdef"><b>Definition</b> <a href="#l00091">fibonacci_matrix_exponentiation.cpp:91</a></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> <a href="#l00025">fibonacci_matrix_exponentiation.cpp:25</a></div></div>
<div class="ttc" id="afibonacci__matrix__exponentiation_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition</b> <a href="#l00108">fibonacci_matrix_exponentiation.cpp:108</a></div></div>
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