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<div class="title">binary_exponent.cpp File Reference</div> </div>
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<p>C++ Program to find Binary Exponent Iteratively and Recursively.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for binary_exponent.cpp:</div>
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Functions</h2></td></tr>
<tr class="memitem:aeb48dce0725e63d19147944f41843c73"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dcf/binary__exponent_8cpp.html#aeb48dce0725e63d19147944f41843c73">binExpo</a> (int <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, int b)</td></tr>
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<tr class="memitem:a31dbf5f7ceb9c9eec831ef9f7782291f"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/dcf/binary__exponent_8cpp.html#a31dbf5f7ceb9c9eec831ef9f7782291f">binExpo_alt</a> (int <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, int b)</td></tr>
<tr class="separator:a31dbf5f7ceb9c9eec831ef9f7782291f"><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="../../de/dcf/binary__exponent_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../de/dcf/binary__exponent_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>C++ Program to find Binary Exponent Iteratively and Recursively. </p>
<p>Calculate \(a^b\) in \(O(\log(b))\) by converting \(b\) to a binary number. Binary exponentiation is also known as exponentiation by squaring. </p><dl class="section note"><dt>Note</dt><dd>This is a far better approach compared to naive method which provide \(O(b)\) operations.</dd></dl>
<p>Example: 10 in base 2 is 1010. </p><p class="formulaDsp">
\begin{eqnarray*} 2^{10_d} &amp;=&amp; 2^{1010_b} = 2^8 * 2^2\\ 2^1 &amp;=&amp; 2\\ 2^2 &amp;=&amp; (2^1)^2 = 2^2 = 4\\ 2^4 &amp;=&amp; (2^2)^2 = 4^2 = 16\\ 2^8 &amp;=&amp; (2^4)^2 = 16^2 = 256\\ \end{eqnarray*}
</p>
<p> Hence to calculate 2^10 we only need to multiply \(2^8\) and \(2^2\) skipping \(2^1\) and \(2^4\). </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="aeb48dce0725e63d19147944f41843c73"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aeb48dce0725e63d19147944f41843c73">&#9670;&nbsp;</a></span>binExpo()</h2>
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<td class="memname">int binExpo </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>b</em>&#160;</td>
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<td></td>
<td>)</td>
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<p>Recursive function to calculate exponent in \(O(\log(n))\) using binary exponent. </p>
<div class="fragment"><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; {</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <span class="keywordflow">if</span> (b == 0) {</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="keywordflow">return</span> 1;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; }</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <span class="keywordtype">int</span> res = <a class="code" href="../../de/dcf/binary__exponent_8cpp.html#aeb48dce0725e63d19147944f41843c73">binExpo</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b / 2);</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <span class="keywordflow">if</span> (b % 2) {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="keywordflow">return</span> res * res * <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">return</span> res * res;</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; }</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a31dbf5f7ceb9c9eec831ef9f7782291f">&#9670;&nbsp;</a></span>binExpo_alt()</h2>
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<td class="memname">int binExpo_alt </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>a</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>b</em>&#160;</td>
</tr>
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<td>)</td>
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<p>Iterative function to calculate exponent in \(O(\log(n))\) using binary exponent. </p>
<div class="fragment"><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; {</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="keywordtype">int</span> res = 1;</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="keywordflow">while</span> (b &gt; 0) {</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordflow">if</span> (b % 2) {</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; res = res * <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>;</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; }</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</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="l00049"></a><span class="lineno"> 49</span>&#160; b /= 2;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; }</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160;}</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>
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<p>Main function. </p>
<p>Give two numbers a, b</p>
<p>int resIterate = binExpo_alt(a, b);</p>
<p>Result of a^b (where '^' denotes exponentiation)</p>
<p><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; resIterate &lt;&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</p>
<div class="fragment"><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; {</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b;<span class="comment"></span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160;<span class="comment"> /// Give two numbers a, b</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160;<span class="comment"></span> <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="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> == 0 &amp;&amp; b == 0) {</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</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;Math error&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="l00061"></a><span class="lineno"> 61</span>&#160; } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (b &lt; 0) {</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</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;Exponent must be positive !!&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="l00063"></a><span class="lineno"> 63</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="keywordtype">int</span> resRecurse = <a class="code" href="../../de/dcf/binary__exponent_8cpp.html#aeb48dce0725e63d19147944f41843c73">binExpo</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b);<span class="comment"></span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160;<span class="comment"> /// int resIterate = binExpo_alt(a, b);</span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160;<span class="comment"></span><span class="comment"></span> </div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160;<span class="comment"> /// Result of a^b (where &#39;^&#39; denotes exponentiation)</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160;<span class="comment"></span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; resRecurse &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;<span class="comment"></span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160;<span class="comment"> /// std::cout &lt;&lt; resIterate &lt;&lt; std::endl;</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160;<span class="comment"></span> }</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160;}</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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