backup/C-Plus-Plus
1
0
Fork 0
mirror of https://github.com/TheAlgorithms/C-Plus-Plus.git synced 2026-03-21 20:31:43 +08:00
Code Issues Projects Releases Wiki Activity
Files
93021161c2a273df8447b17e09de6b3f2fc9c23f
C-Plus-Plus/d2/d0b/fast__power_8cpp.html
github-actions 93021161c2 Documentation for aaa08b0150
2020-06-19 16:07:44 +00:00

302 lines
26 KiB
HTML
Raw Blame History

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.8.18"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Algorithms_in_C++: math/fast_power.cpp File Reference</title>
<link href="../../tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../jquery.js"></script>
<script type="text/javascript" src="../../dynsections.js"></script>
<link href="../../navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../resize.js"></script>
<script type="text/javascript" src="../../navtreedata.js"></script>
<script type="text/javascript" src="../../navtree.js"></script>
<link href="../../search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../search/searchdata.js"></script>
<script type="text/javascript" src="../../search/search.js"></script>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
jax: ["input/TeX","output/HTML-CSS"],
});
</script>
<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
<link href="../../doxygen.css" rel="stylesheet" type="text/css" />
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr style="height: 56px;">
<td id="projectalign" style="padding-left: 0.5em;">
<div id="projectname">Algorithms_in_C++
&#160;<span id="projectnumber">1.0.0</span>
</div>
<div id="projectbrief">Set of algorithms implemented in C++.</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.8.18 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
var searchBox = new SearchBox("searchBox", "../../search",false,'Search');
/* @license-end */
</script>
<script type="text/javascript" src="../../menudata.js"></script>
<script type="text/javascript" src="../../menu.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
$(function() {
initMenu('../../',true,false,'search.php','Search');
$(document).ready(function() { init_search(); });
});
/* @license-end */</script>
<div id="main-nav"></div>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
<div id="nav-tree">
<div id="nav-tree-contents">
<div id="nav-sync" class="sync"></div>
</div>
</div>
<div id="splitbar" style="-moz-user-select:none;"
class="ui-resizable-handle">
</div>
</div>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
$(document).ready(function(){initNavTree('d2/d0b/fast__power_8cpp.html','../../'); initResizable(); });
/* @license-end */
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>
<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0"
name="MSearchResults" id="MSearchResults">
</iframe>
</div>
<div class="header">
<div class="summary">
<a href="#func-members">Functions</a> </div>
<div class="headertitle">
<div class="title">fast_power.cpp File Reference</div> </div>
</div><!--header-->
<div class="contents">
<p>Faster computation for \(a^b\).
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;cstdint&gt;</code><br />
<code>#include &lt;cstdlib&gt;</code><br />
<code>#include &lt;ctime&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for fast_power.cpp:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d30/fast__power_8cpp__incl.svg" width="506" height="112"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
</div>
</div>
</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a8399b847626e5bba983cab7c7918b445"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a8399b847626e5bba983cab7c7918b445"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a> (T <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, T b)</td></tr>
<tr class="separator:a8399b847626e5bba983cab7c7918b445"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0d4e3f0099a6975b74a314a35bd0f94d"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a0d4e3f0099a6975b74a314a35bd0f94d"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a> (T <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, T b)</td></tr>
<tr class="separator:a0d4e3f0099a6975b74a314a35bd0f94d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d0b/fast__power_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Faster computation for \(a^b\). </p>
<p>Program that computes \(a^b\) in \(O(logN)\) time. It is based on formula that:</p><ol type="1">
<li>if \(b\) is even: \(a^b = a^\frac{b}{2} \cdot a^\frac{b}{2} = {a^\frac{b}{2}}^2\)</li>
<li>if \(b\) is odd: \(a^b = a^\frac{b-1}{2} \cdot a^\frac{b-1}{2} \cdot a = {a^\frac{b-1}{2}}^2 \cdot a\)</li>
</ol>
<p>We can compute \(a^b\) recursively using above algorithm. </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a0d4e3f0099a6975b74a314a35bd0f94d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0d4e3f0099a6975b74a314a35bd0f94d">&#9670;&nbsp;</a></span>fast_power_linear()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename T &gt; </div>
<table class="memname">
<tr>
<td class="memname">double fast_power_linear </td>
<td>(</td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T&#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>Same algorithm with little different formula. It still calculates in \(O(\log N)\) </p>
<div class="fragment"><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="comment">// negative power. a^b = 1 / (a^-b)</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="keywordflow">if</span> (b &lt; 0)</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <span class="keywordflow">return</span> 1.0 / <a class="code" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, -b);</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; <span class="keywordtype">double</span> result = 1;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="keywordflow">while</span> (b) {</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="keywordflow">if</span> (b &amp; 1)</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; result = result * <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> * <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; b = b &gt;&gt; 1;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; }</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160;}</div>
</div><!-- fragment -->
</div>
</div>
<a id="a8399b847626e5bba983cab7c7918b445"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a8399b847626e5bba983cab7c7918b445">&#9670;&nbsp;</a></span>fast_power_recursive()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename T &gt; </div>
<table class="memname">
<tr>
<td class="memname">double fast_power_recursive </td>
<td>(</td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T&#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>algorithm implementation for \(a^b\) </p>
<div class="fragment"><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; {</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; <span class="comment">// negative power. a^b = 1 / (a^-b)</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; <span class="keywordflow">if</span> (b &lt; 0)</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <span class="keywordflow">return</span> 1.0 / <a class="code" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, -b);</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; </div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordflow">if</span> (b == 0)</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <span class="keywordflow">return</span> 1;</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; T bottom = <a class="code" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b &gt;&gt; 1);</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="comment">// Since it is integer division b/2 = (b-1)/2 where b is odd.</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <span class="comment">// Therefore, case2 is easily solved by integer division.</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="keywordtype">double</span> result;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; <span class="keywordflow">if</span> ((b &amp; 1) == 0) <span class="comment">// case1</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; result = bottom * bottom;</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">else</span> <span class="comment">// case2</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; result = bottom * bottom * <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160;}</div>
</div><!-- fragment -->
</div>
</div>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">int main </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Main function </p>
<div class="fragment"><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; {</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/sync_with_stdio.html">std::ios_base::sync_with_stdio</a>(<span class="keyword">false</span>);</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; <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;Testing...&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="l00073"></a><span class="lineno"> 73</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 20; i++) {</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 20 - 10;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="keywordtype">int</span> b = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 20 - 10;</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/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> &lt;&lt; <span class="stringliteral">&quot;Calculating &quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt;&lt; <span class="stringliteral">&quot;^&quot;</span> &lt;&lt; b &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="l00077"></a><span class="lineno"> 77</span>&#160; assert(<a class="code" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b) == <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b));</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; assert(<a class="code" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b) == <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b));</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; </div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------ &quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt;&lt; <span class="stringliteral">&quot;^&quot;</span> &lt;&lt; b &lt;&lt; <span class="stringliteral">&quot; = &quot;</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; &lt;&lt; <a class="code" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b) &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="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; int64_t <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &gt;&gt; b;</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; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt;&lt; <span class="stringliteral">&quot;^&quot;</span> &lt;&lt; b &lt;&lt; <span class="stringliteral">&quot; = &quot;</span> &lt;&lt; <a class="code" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b)</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; &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="l00089"></a><span class="lineno"> 89</span>&#160; </div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> &lt;&lt; <span class="stringliteral">&quot;^&quot;</span> &lt;&lt; b &lt;&lt; <span class="stringliteral">&quot; = &quot;</span> &lt;&lt; <a class="code" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b) &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="l00091"></a><span class="lineno"> 91</span>&#160; </div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160;}</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="../../d2/d0b/fast__power_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="246" height="256"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
</div>
</div>
</div>
</div>
</div><!-- contents -->
</div><!-- doc-content -->
<div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
<div class="ttc" id="afast__power_8cpp_html_a8399b847626e5bba983cab7c7918b445"><div class="ttname"><a href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a></div><div class="ttdeci">double fast_power_recursive(T a, T b)</div><div class="ttdef"><b>Definition:</b> fast_power.cpp:26</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="amatrix__exponentiation_8cpp_html_a9ecd98ce0064e2f7f97bb6a92f58ee72"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a></div><div class="ttdeci">vector&lt; ll &gt; a</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:53</div></div>
<div class="ttc" id="arand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a></div><div class="ttdeci">T rand(T... args)</div></div>
<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="async_with_stdio_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/ios_base/sync_with_stdio.html">std::ios_base::sync_with_stdio</a></div><div class="ttdeci">T sync_with_stdio(T... args)</div></div>
<div class="ttc" id="atime_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a></div><div class="ttdeci">T time(T... args)</div></div>
<div class="ttc" id="afast__power_8cpp_html_a0d4e3f0099a6975b74a314a35bd0f94d"><div class="ttname"><a href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a></div><div class="ttdeci">double fast_power_linear(T a, T b)</div><div class="ttdef"><b>Definition:</b> fast_power.cpp:50</div></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="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d2/d0b/fast__power_8cpp.html">fast_power.cpp</a></li>
<li class="footer">Generated on Fri Jun 19 2020 16:06:44 for Algorithms_in_C++ by
<a href="http://www.doxygen.org/index.html">
<img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
</ul>
</div>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink