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<p>An algorithm to calculate the sum of <a href="https://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci Sequence</a>: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\).
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<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 fibonacci_sum.cpp:</div>
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<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft">&#160;</td><td class="mdescRight">for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html" title="STL class.">std::vector</a> <br /></td></tr>
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<tr class="memdesc:d3/dc9/namespacefibonacci__sum"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for the sum of the Fibonacci Sequence: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\). <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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using&#160;</td><td class="memItemRight" valign="bottom"><b>math::fibonacci_sum::matrix</b> = <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint64_t &gt; &gt;</td></tr>
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<tr class="memitem:aadb40ac4c74a7efc0680b83eeee138aa"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a> (uint64_t n)</td></tr>
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<tr class="memitem:a493fbaa7a94e3b7ca573111237bb3742"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a> (uint64_t n, uint64_t m)</td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dc3/fibonacci__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">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="../../de/dc3/fibonacci__sum_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../de/dc3/fibonacci__sum_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>An algorithm to calculate the sum of <a href="https://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci Sequence</a>: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\). </p>
<p>An algorithm to calculate the sum of Fibonacci Sequence: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\) where \(\mathrm{F}(i)\) denotes the i-th Fibonacci Number . Note that F(0) = 0 and F(1) = 1. The value of the sum is calculated using matrix exponentiation. Reference source: <a href="https://stackoverflow.com/questions/4357223/finding-the-sum-of-fibonacci-numbers">https://stackoverflow.com/questions/4357223/finding-the-sum-of-fibonacci-numbers</a> </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/SarthakSahu1009">Sarthak Sahu</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a493fbaa7a94e3b7ca573111237bb3742"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a493fbaa7a94e3b7ca573111237bb3742">&#9670;&nbsp;</a></span>fiboSum()</h2>
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<td class="memname">uint64_t math::fibonacci_sum::fiboSum </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>m</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</div><div class="memdoc">
<p>Function to compute sum of fibonacci sequence from n to m. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>start of sequence </td></tr>
<tr><td class="paramname">m</td><td>end of sequence </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>uint64_t the sum of sequence </dd></dl>
<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; <span class="keywordflow">return</span> (<a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(m + 2) - <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(n + 1)); </div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; }</div>
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Here is the call graph for this function:</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<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="l00135"></a><span class="lineno"> 135</span>&#160; {</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160; <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the tests</span></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a9c83cca09a3e4ff2a25c816a9303448e">&#9670;&nbsp;</a></span>multiply()</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a> math::fibonacci_sum::multiply </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a> &amp;&#160;</td>
<td class="paramname"><em>T</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a> &amp;&#160;</td>
<td class="paramname"><em>A</em>&#160;</td>
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<p>Function to multiply two matrices </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">T</td><td>matrix 1 </td></tr>
<tr><td class="paramname">A</td><td>martix 2 </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>resultant matrix </dd></dl>
<div class="fragment"><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; {</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a> <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(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="l00040"></a><span class="lineno"> 40</span>&#160; </div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="comment">// multiplying matrices</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[0][0] = T[0][0]*A[0][0] + T[0][1]*A[1][0];</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[0][1] = T[0][0]*A[0][1] + T[0][1]*A[1][1];</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1][0] = T[1][0]*A[0][0] + T[1][1]*A[1][0];</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1][1] = T[1][0]*A[0][1] + T[1][1]*A[1][1];</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; <span class="keywordflow">return</span> <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a7cf5feaf168b88e74544da59ed830311">&#9670;&nbsp;</a></span>power()</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a> math::fibonacci_sum::power </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a>&#160;</td>
<td class="paramname"><em>T</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint64_t&#160;</td>
<td class="paramname"><em>ex</em>&#160;</td>
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<p>Function to compute A^n where A is a matrix. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">T</td><td>matrix </td></tr>
<tr><td class="paramname">ex</td><td>power </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>resultant matrix </dd></dl>
<div class="fragment"><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; {</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a> A{{1, 1}, {1, 0}};</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordflow">if</span> (ex == 0 || ex == 1) {</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordflow">return</span> T;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; }</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; </div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; T = <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a>(T, ex / 2);</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; T = <a class="code" href="../../d8/d77/namespacemachine__learning.html#a7491744dcfc8844338d55065d0cd0c79">multiply</a>(T, T);</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="keywordflow">if</span> (ex &amp; 1) {</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; T = <a class="code" href="../../d8/d77/namespacemachine__learning.html#a7491744dcfc8844338d55065d0cd0c79">multiply</a>(T, A);</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="keywordflow">return</span> T;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aadb40ac4c74a7efc0680b83eeee138aa">&#9670;&nbsp;</a></span>result()</h2>
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<td class="memname">uint64_t math::fibonacci_sum::result </td>
<td>(</td>
<td class="paramtype">uint64_t&#160;</td>
<td class="paramname"><em>n</em></td><td>)</td>
<td></td>
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<p>Function to compute sum of fibonacci sequence from 0 to n. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>number </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>uint64_t ans, the sum of sequence </dd></dl>
<div class="fragment"><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; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a> T{{1, 1}, {1, 0}};</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; T = <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a>(T, n);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; uint64_t <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = T[0][1];</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> - 1);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&nbsp;</a></span>test()</h2>
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<td class="memname">static void test </td>
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<p>Function for testing fiboSum function. test cases and assert statement. </p><dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
<div class="fragment"><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; uint64_t n = 0, m = 3;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; uint64_t <a class="code" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a> = <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; assert(<a class="code" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a> == 4);</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 1!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; </div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; n = 3;</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; m = 5;</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; uint64_t <a class="code" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a> = <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; assert(<a class="code" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a> == 10);</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;Passed Test 2!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; </div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; n = 5;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; m = 7;</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; uint64_t <a class="code" href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a> = <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; assert(<a class="code" href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a> == 26);</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 3!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; </div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; n = 7;</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; m = 10;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; uint64_t test_4 = <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; assert(test_4 == 123);</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 4!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160; </div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160; n = 9;</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; m = 12;</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; uint64_t test_5 = <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; assert(test_5 == 322);</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed Test 5!&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160;}</div>
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<div class="ttc" id="afibonacci__sum_8cpp_html_a7cf5feaf168b88e74544da59ed830311"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">math::fibonacci_sum::power</a></div><div class="ttdeci">math::fibonacci_sum::matrix power(math::fibonacci_sum::matrix T, uint64_t ex)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:56</div></div>
<div class="ttc" id="aheavy__light__decomposition_8cpp_html_af31ec5409537703d9c8a47350386b32a"><div class="ttname"><a href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a></div><div class="ttdeci">static void test_3()</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:592</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 class="ttdoc">STL class.</div></div>
<div class="ttc" id="aheavy__light__decomposition_8cpp_html_a458410412185a5f09199deaff7157a8d"><div class="ttname"><a href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a></div><div class="ttdeci">static void test_2()</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:549</div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:91</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="afibonacci__sum_8cpp_html_a493fbaa7a94e3b7ca573111237bb3742"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a></div><div class="ttdeci">uint64_t fiboSum(uint64_t n, uint64_t m)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:89</div></div>
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