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@@ -152,7 +152,7 @@ Functions</h2></td></tr>
<p>two elements a[i] and a[j] form an inversion if <code>a[i]</code> &gt; <code>a[j]</code> and i &lt; j</p>
<p>Time Complexity --&gt; <code>O(n.log n)</code></p>
<p>Space Complexity --&gt; <code>O(n)</code> ; additional array <code>temp[1..n]</code> </p>
<h3><a class="anchor" id="autotoc_md72"></a>
<h3><a class="anchor" id="autotoc_md73"></a>
Algorithm</h3>
<ol type="1">
<li>The idea is similar to merge sort, divide the array into two equal or almost equal halves in each step until the base case is reached.</li>

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<p>Implementation to check whether a number is a power of 2 or not.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
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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">std::vector</a> <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a89ab7d6c3e3ee72a8cbaa85127986185"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a89ab7d6c3e3ee72a8cbaa85127986185">math::power_of_two</a> (int n)</td></tr>
<tr class="memdesc:a89ab7d6c3e3ee72a8cbaa85127986185"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to test above algorithm. <a href="../../dd/d47/namespacemath.html#a89ab7d6c3e3ee72a8cbaa85127986185">More...</a><br /></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="../../d4/d38/power__of__two_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d4/d38/power__of__two_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>Implementation to check whether a number is a power of 2 or not. </p>
<p>This algorithm uses bit manipulation to check if a number is a power of 2 or not.</p>
<h3><a class="anchor" id="autotoc_md65"></a>
Algorithm</h3>
<p>Let the input number be n, then the bitwise and between n and n-1 will let us know whether the number is power of 2 or not</p>
<p>For Example, If N= 32 then N-1 is 31, if we perform bitwise and of these two numbers then the result will be zero, which indicates that it is the power of 2 If N=23 then N-1 is 22, if we perform bitwise and of these two numbers then the result will not be zero , which indicates that it is not the power of 2 </p><dl class="section note"><dt>Note</dt><dd>This implementation is better than naive recursive or iterative approach.</dd></dl>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/neha-hasija17">Neha Hasija</a> </dd></dl>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<p>Main function. </p>
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<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/ncr_modulo_p.cpp">Ncr Modulo P</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/number_of_positive_divisors.cpp">Number Of Positive Divisors</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/power_for_huge_numbers.cpp">Power For Huge Numbers</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/power_of_two.cpp">Power Of Two</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/prime_factorization.cpp">Prime Factorization</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/prime_numbers.cpp">Prime Numbers</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/primes_up_to_billion.cpp">Primes Up To Billion</a></li>

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<div class="textblock"><p>Implementation of <a href="https://en.wikipedia.org/wiki/Bogosort">Bogosort algorithm</a> </p>
<p>In computer science, bogosort (also known as permutation sort, stupid sort, slowsort, shotgun sort, random sort, monkey sort, bobosort or shuffle sort) is a highly inefficient sorting algorithm based on the generate and test paradigm. Two versions of this algorithm exist: a deterministic version that enumerates all permutations until it hits a sorted one, and a randomized version that randomly permutes its input.Randomized version is implemented here.</p>
<h3><a class="anchor" id="autotoc_md71"></a>
<h3><a class="anchor" id="autotoc_md72"></a>
Algorithm</h3>
<p>Shuffle the array untill array is sorted.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/imdeep2905">Deep Raval</a> </dd></dl>

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<p>Function to test above algorithm. </p>
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<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p>This function finds whether a number is power of 2 or not </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>value for which we want to check prints the result, as "Yes, the number n is a power of 2" or "No, the number is not a power of 2" without quotes</td></tr>
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<p>Therefore, the direction ratios of the cross product are: J, A, N The following C++ Program calculates the direction ratios of the cross products of two vector. The program uses a function, <a class="el" href="../../df/d66/vector__cross__product_8cpp.html#abed307975124243d63fe2e118254defe" title="Function to calculate the cross product of the passed arrays containing the direction ratios of the t...">cross()</a> for doing so. The direction ratios for the first and the second vector has to be passed one by one seperated by a space character.</p>
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Example:</h3>
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<p><a href="https://gitpod.io/#https://github.com/TheAlgorithms/C-Plus-Plus"><img src="https://img.shields.io/badge/Gitpod-Ready--to--Code-blue?logo=gitpod" alt="Gitpod Ready-to-Code" class="inline"/></a> <a href="https://lgtm.com/projects/g/TheAlgorithms/C-Plus-Plus/context:cpp"><img src="https://img.shields.io/lgtm/grade/cpp/g/TheAlgorithms/C-Plus-Plus.svg?logo=lgtm&amp;logoWidth=18" alt="Language grade: C/C++" style="pointer-events: none;" class="inline"/></a> <a href="https://gitter.im/TheAlgorithms"><img src="https://img.shields.io/badge/Chat-Gitter-ff69b4.svg?label=Chat&amp;logo=gitter&amp;style=flat-square" alt="Gitter chat" style="pointer-events: none;" class="inline"/></a> <a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/CONTRIBUTING.md"><img src="https://img.shields.io/static/v1.svg?label=Contributions&amp;message=Welcome&amp;color=0059b3&amp;style=flat-square" alt="contributions welcome" style="pointer-events: none;" class="inline"/></a> <img src="https://img.shields.io/github/repo-size/TheAlgorithms/C-Plus-Plus?color=red&amp;style=flat-square" alt="GitHub repo size" class="inline"/> <a href="https://TheAlgorithms.github.io/C-Plus-Plus"><img src="https://github.com/TheAlgorithms/C-Plus-Plus/workflows/Doxygen%20CI/badge.svg" alt="Doxygen CI" style="pointer-events: none;" class="inline"/></a> <a href="https://github.com/TheAlgorithms/C-Plus-Plus/actions?query=workflow%3A%22Awesome+CI+Workflow%22"><img src="https://github.com/TheAlgorithms/C-Plus-Plus/workflows/Awesome%20CI%20Workflow/badge.svg" alt="Awesome CI" style="pointer-events: none;" class="inline"/></a></p>
<h1><a class="anchor" id="autotoc_md66"></a>
<h1><a class="anchor" id="autotoc_md67"></a>
Overview</h1>
<p>The repository is a collection of open-source implementation of a variety of algorithms implemented in C++ and licensed under <a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/LICENSE">MIT License</a>. The algorithms span a variety of topics from computer science, mathematics and statistics, data science, machine learning, engineering, etc.. The implementations and the associated documentation are meant to provide a learning resource for educators and students. Hence, one may find more than one implementation for the same objective but using a different algorithm strategies and optimizations.</p>
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<h1><a class="anchor" id="autotoc_md68"></a>
Features</h1>
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<li>The repository provides implementations of various algorithms in one of the most fundamental general purpose languages - <a href="https://en.wikipedia.org/wiki/C%2B%2B">C++</a>.</li>
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<li>Self-checks within programs ensure correct implementations with confidence.</li>
<li>Modular implementations and OpenSource licensing enable the functions to be utilized conveniently in other applications.</li>
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<h1><a class="anchor" id="autotoc_md68"></a>
<h1><a class="anchor" id="autotoc_md69"></a>
Documentation</h1>
<p><a href="https://TheAlgorithms.github.io/C-Plus-Plus">Online Documentation</a> is generated from the repository source codes directly. The documentation contains all resources including source code snippets, details on execution of the programs, diagrammatic representation of program flow, and links to external resources where necessary. The documentation also introduces interactive source code with links to documentation for C++ STL library functions used. Click on <a href="https://TheAlgorithms.github.io/C-Plus-Plus/files.html">Files menu</a> to see the list of all the files documented with the code.</p>
<p><a href="https://thealgorithms.github.io/C-Plus-Plus">Documentation of Algorithms in C++</a> by <a href="https://github.com/TheAlgorithms/C-Plus-Plus/graphs/contributors">The Algorithms Contributors</a> is licensed under <a href="https://creativecommons.org/licenses/by-sa/4.0/?ref=chooser-v1">CC BY-SA 4.0</a><br />
<a href="https://creativecommons.org/licenses/by-sa/4.0"><img src="https://mirrors.creativecommons.org/presskit/icons/cc.svg" alt="Creative Commons License" style="pointer-events: none; height:22px!important;margin-left: 3px;vertical-align:text-bottom;" class="inline"/><img src="https://mirrors.creativecommons.org/presskit/icons/by.svg" alt="Credit must be given to the creator" style="pointer-events: none; height:22px!important;margin-left: 3px;vertical-align:text-bottom;" class="inline"/><img src="https://mirrors.creativecommons.org/presskit/icons/sa.svg" alt="Adaptations must be shared under the same terms" style="pointer-events: none; height:22px!important;margin-left: 3px;vertical-align:text-bottom;" class="inline"/></a></p>
<h1><a class="anchor" id="autotoc_md69"></a>
<h1><a class="anchor" id="autotoc_md70"></a>
Contributions</h1>
<p>As a community developed and maintained repository, we welcome new un-plagiarized quality contributions. Please read our <a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/CONTRIBUTING.md">Contribution Guidelines</a>. </p>
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namespacemembers.html
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