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<a href="#func-members">Functions</a> </div>
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<div class="headertitle"><div class="title">fibonacci_matrix_exponentiation.cpp File Reference</div></div>
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<div class="contents">
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<p>This program computes the N^th Fibonacci number in modulo mod input argument .
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <cassert></code><br />
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<code>#include <cstdint></code><br />
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<code>#include <iostream></code><br />
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<code>#include <vector></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for fibonacci_matrix_exponentiation.cpp:</div>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:abc3bc08249058d57cfc8f54a29d9cf9f" id="r_abc3bc08249058d57cfc8f54a29d9cf9f"><td class="memItemLeft" align="right" valign="top">uint64_t </td><td class="memItemRight" valign="bottom"><a class="el" href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a> (uint64_t n, uint64_t mod)</td></tr>
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<tr class="separator:abc3bc08249058d57cfc8f54a29d9cf9f"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
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<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>This program computes the N^th Fibonacci number in modulo mod input argument . </p>
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<p>Takes O(logn) time to compute nth Fibonacci number</p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/villayatali123" target="_blank">villayatali123</a> </dd>
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<dd>
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[unknown author]() </dd></dl>
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<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>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="abc3bc08249058d57cfc8f54a29d9cf9f" name="abc3bc08249058d57cfc8f54a29d9cf9f"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#abc3bc08249058d57cfc8f54a29d9cf9f">◆ </a></span>fibo()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">uint64_t fibo </td>
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<td>(</td>
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<td class="paramtype">uint64_t</td> <td class="paramname"><span class="paramname"><em>n</em></span>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">uint64_t</td> <td class="paramname"><span class="paramname"><em>mod</em></span> )</td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>This function finds nth fibonacci number in a given modulus </p><dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">n</td><td>nth fibonacci number </td></tr>
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<tr><td class="paramname">mod</td><td>modulo number </td></tr>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><span class="lineno"> 25</span> {</div>
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<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<uint64_t></a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(2, 0);</div>
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<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<std::vector<uint64_t></a>> transition(2,</div>
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<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<uint64_t></a>(2, 0));</div>
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<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<std::vector<uint64_t></a>> Identity(2, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<uint64_t></a>(2, 0));</div>
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<div class="line"><span class="lineno"> 30</span> n--;</div>
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<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>
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<div class="line"><span class="lineno"> 32</span> Identity[0][0] = 1;</div>
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<div class="line"><span class="lineno"> 33</span> Identity[0][1] = 0;</div>
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<div class="line"><span class="lineno"> 34</span> Identity[1][0] = 0;</div>
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<div class="line"><span class="lineno"> 35</span> Identity[1][1] = 1;</div>
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<div class="line"><span class="lineno"> 36</span> </div>
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<div class="line"><span class="lineno"> 37</span> transition[0][0] = 0;</div>
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<div class="line"><span class="lineno"> 38</span> transition[1][0] = transition[1][1] = transition[0][1] = 1;</div>
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<div class="line"><span class="lineno"> 39</span> </div>
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<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">while</span> (n) {</div>
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<div class="line"><span class="lineno"> 41</span> <span class="keywordflow">if</span> (n % 2) {</div>
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<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<std::vector<uint64_t></a>> res(2,</div>
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<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<uint64_t></a>(2, 0));</div>
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<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 2; i++) {</div>
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<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < 2; j++) {</div>
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<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> < 2; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
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<div class="line"><span class="lineno"> 47</span> res[i][j] =</div>
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<div class="line"><span class="lineno"> 48</span> (res[i][j] % mod +</div>
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<div class="line"><span class="lineno"> 49</span> ((Identity[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] % mod * transition[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j] % mod)) %</div>
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<div class="line"><span class="lineno"> 50</span> mod) %</div>
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<div class="line"><span class="lineno"> 51</span> mod;</div>
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<div class="line"><span class="lineno"> 52</span> }</div>
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<div class="line"><span class="lineno"> 53</span> }</div>
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<div class="line"><span class="lineno"> 54</span> }</div>
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<div class="line"><span class="lineno"> 55</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 2; i++) {</div>
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<div class="line"><span class="lineno"> 56</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < 2; j++) {</div>
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<div class="line"><span class="lineno"> 57</span> Identity[i][j] = res[i][j];</div>
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<div class="line"><span class="lineno"> 58</span> }</div>
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<div class="line"><span class="lineno"> 59</span> }</div>
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<div class="line"><span class="lineno"> 60</span> n--;</div>
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<div class="line"><span class="lineno"> 61</span> } <span class="keywordflow">else</span> {</div>
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<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<std::vector<uint64_t></a>> res1(</div>
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<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<uint64_t></a>(2, 0));</div>
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<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 2; i++) {</div>
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<div class="line"><span class="lineno"> 65</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < 2; j++) {</div>
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<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> < 2; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
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<div class="line"><span class="lineno"> 67</span> res1[i][j] =</div>
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<div class="line"><span class="lineno"> 68</span> (res1[i][j] % mod + ((transition[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] % mod *</div>
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<div class="line"><span class="lineno"> 69</span> transition[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j] % mod)) %</div>
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<div class="line"><span class="lineno"> 70</span> mod) %</div>
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<div class="line"><span class="lineno"> 71</span> mod;</div>
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<div class="line"><span class="lineno"> 72</span> }</div>
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<div class="line"><span class="lineno"> 73</span> }</div>
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<div class="line"><span class="lineno"> 74</span> }</div>
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<div class="line"><span class="lineno"> 75</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 2; i++) {</div>
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<div class="line"><span class="lineno"> 76</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < 2; j++) {</div>
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<div class="line"><span class="lineno"> 77</span> transition[i][j] = res1[i][j];</div>
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<div class="line"><span class="lineno"> 78</span> }</div>
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<div class="line"><span class="lineno"> 79</span> }</div>
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<div class="line"><span class="lineno"> 80</span> n = n / 2;</div>
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<div class="line"><span class="lineno"> 81</span> }</div>
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<div class="line"><span class="lineno"> 82</span> }</div>
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<div class="line"><span class="lineno"> 83</span> <span class="keywordflow">return</span> ((result[0] % mod * Identity[0][0] % mod) % mod +</div>
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<div class="line"><span class="lineno"> 84</span> (result[1] % mod * Identity[1][0] % mod) % mod) %</div>
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<div class="line"><span class="lineno"> 85</span> mod;</div>
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<div class="line"><span class="lineno"> 86</span>}</div>
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<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>
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<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>
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<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">◆ </a></span>main()</h2>
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<td class="memname">int main </td>
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<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<p>Main function </p>
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<div class="fragment"><div class="line"><span class="lineno"> 108</span> {</div>
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<div class="line"><span class="lineno"> 109</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
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<div class="line"><span class="lineno"> 110</span> uint64_t mod = 1000000007;</div>
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<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> << <span class="stringliteral">"Enter the value of N: "</span>;</div>
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<div class="line"><span class="lineno"> 112</span> uint64_t n = 0;</div>
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<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> >> n;</div>
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<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> << n << <span class="stringliteral">"th Fibonacci number in modulo "</span> << mod << <span class="stringliteral">": "</span></div>
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<div class="line"><span class="lineno"> 115</span> << <a class="code hl_function" href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(n, mod) << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 116</span>}</div>
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<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>
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<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="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>
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<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>
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<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>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">◆ </a></span>test()</h2>
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<td class="memname">static void test </td>
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<p>Function to test above algorithm </p>
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<div class="fragment"><div class="line"><span class="lineno"> 91</span> {</div>
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<div class="line"><span class="lineno"> 92</span> assert(<a class="code hl_function" href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(6, 1000000007) == 8);</div>
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<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> << <span class="stringliteral">"test case:1 passed\n"</span>;</div>
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<div class="line"><span class="lineno"> 94</span> assert(<a class="code hl_function" href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(5, 1000000007) == 5);</div>
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<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> << <span class="stringliteral">"test case:2 passed\n"</span>;</div>
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<div class="line"><span class="lineno"> 96</span> assert(<a class="code hl_function" href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(10, 1000000007) == 55);</div>
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<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> << <span class="stringliteral">"test case:3 passed\n"</span>;</div>
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<div class="line"><span class="lineno"> 98</span> assert(<a class="code hl_function" href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(500, 100) == 25);</div>
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<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> << <span class="stringliteral">"test case:3 passed\n"</span>;</div>
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<div class="line"><span class="lineno"> 100</span> assert(<a class="code hl_function" href="#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(500, 10000) == 4125);</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> << <span class="stringliteral">"test case:3 passed\n"</span>;</div>
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<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> << <span class="stringliteral">"--All tests passed--\n"</span>;</div>
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<div class="line"><span class="lineno"> 103</span>}</div>
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