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<p>Counting Inversions using <a href="https://en.wikipedia.org/wiki/Merge_sort" target="_blank">Merge Sort</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cstdint&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 count_inversions.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:d5/d91/namespacesorting"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html">sorting</a></td></tr>
<tr class="memdesc:d5/d91/namespacesorting"><td class="mdescLeft">&#160;</td><td class="mdescRight">Sorting algorithms. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:d9/d13/namespaceinversion"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d13/namespaceinversion.html">inversion</a></td></tr>
<tr class="memdesc:d9/d13/namespaceinversion"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for counting inversions using Merge Sort algorithm. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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Functions</h2></td></tr>
<tr class="memitem:aad643c14734394e784a75169cb58132f"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:aad643c14734394e784a75169cb58132f"><td class="memTemplItemLeft" align="right" valign="top">uint32_t&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d26/count__inversions_8cpp.html#aad643c14734394e784a75169cb58132f">sorting::inversion::merge</a> (T *arr, T *temp, uint32_t left, uint32_t mid, uint32_t right)</td></tr>
<tr class="memdesc:aad643c14734394e784a75169cb58132f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to merge two sub-arrays. <a href="../../d2/d26/count__inversions_8cpp.html#aad643c14734394e784a75169cb58132f">More...</a><br /></td></tr>
<tr class="separator:aad643c14734394e784a75169cb58132f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae97a486e14101c4822ea8dc47f0d1661"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ae97a486e14101c4822ea8dc47f0d1661"><td class="memTemplItemLeft" align="right" valign="top">uint32_t&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d26/count__inversions_8cpp.html#ae97a486e14101c4822ea8dc47f0d1661">sorting::inversion::mergeSort</a> (T *arr, T *temp, uint32_t left, uint32_t right)</td></tr>
<tr class="memdesc:ae97a486e14101c4822ea8dc47f0d1661"><td class="mdescLeft">&#160;</td><td class="mdescRight">Implement merge Sort and count inverions while merging. <a href="../../d2/d26/count__inversions_8cpp.html#ae97a486e14101c4822ea8dc47f0d1661">More...</a><br /></td></tr>
<tr class="separator:ae97a486e14101c4822ea8dc47f0d1661"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3332498eabf6579ef059c0d0e9f4ec80"><td class="memTemplParams" colspan="2">template&lt;class T &gt; </td></tr>
<tr class="memitem:a3332498eabf6579ef059c0d0e9f4ec80"><td class="memTemplItemLeft" align="right" valign="top">uint32_t&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d26/count__inversions_8cpp.html#a3332498eabf6579ef059c0d0e9f4ec80">sorting::inversion::countInversion</a> (T *arr, const uint32_t size)</td></tr>
<tr class="memdesc:a3332498eabf6579ef059c0d0e9f4ec80"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function <a class="el" href="../../d2/d26/count__inversions_8cpp.html#a3332498eabf6579ef059c0d0e9f4ec80" title="Function countInversion() returns the number of inversion present in the input array....">countInversion()</a> returns the number of inversion present in the input array. Inversions are an estimate of how close or far off the array is to being sorted. <a href="../../d2/d26/count__inversions_8cpp.html#a3332498eabf6579ef059c0d0e9f4ec80">More...</a><br /></td></tr>
<tr class="separator:a3332498eabf6579ef059c0d0e9f4ec80"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a851ca6a0391d14fb49a97d55e4377497"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a851ca6a0391d14fb49a97d55e4377497"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d26/count__inversions_8cpp.html#a851ca6a0391d14fb49a97d55e4377497">sorting::inversion::show</a> (T *arr, const uint32_t array_size)</td></tr>
<tr class="memdesc:a851ca6a0391d14fb49a97d55e4377497"><td class="mdescLeft">&#160;</td><td class="mdescRight">UTILITY function to print array. <a href="../../d2/d26/count__inversions_8cpp.html#a851ca6a0391d14fb49a97d55e4377497">More...</a><br /></td></tr>
<tr class="separator:a851ca6a0391d14fb49a97d55e4377497"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d26/count__inversions_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test implementations. <a href="../../d2/d26/count__inversions_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><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/d26/count__inversions_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d2/d26/count__inversions_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 >Counting Inversions using <a href="https://en.wikipedia.org/wiki/Merge_sort" target="_blank">Merge Sort</a> </p>
<p >Program to count the number of inversions in an array using merge-sort.</p>
<p >The count of inversions help to determine how close the array is to be sorted in ASCENDING order.</p>
<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_md98"></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>
<li>Create a function merge that counts the number of inversions when two halves of the array are merged, create two indices i and j, i is the index for first half and j is an index of the second half. if <code>a[i]</code> is greater than <code>a[j]</code>, then there are (mid – i) inversions, Because left and right subarrays are sorted, so all the remaining elements in left-subarray (a[i+1], a[i+2] … a[mid]) will be greater than a[j].</li>
<li>Create a recursive function to divide the array into halves and find the answer by summing the number of inversions is the first half, number of inversion in the second half and the number of inversions by merging the two.</li>
<li>The base case of recursion is when there is only one element in the given half.</li>
<li>Print the answer</li>
</ol>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/rakshitraj" target="_blank">Rakshit Raj</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a3332498eabf6579ef059c0d0e9f4ec80" name="a3332498eabf6579ef059c0d0e9f4ec80"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3332498eabf6579ef059c0d0e9f4ec80">&#9670;&nbsp;</a></span>countInversion()</h2>
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template&lt;class T &gt; </div>
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<td class="memname">uint32_t sorting::inversion::countInversion </td>
<td>(</td>
<td class="paramtype">T *&#160;</td>
<td class="paramname"><em>arr</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const uint32_t&#160;</td>
<td class="paramname"><em>size</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</div><div class="memdoc">
<p>Function <a class="el" href="../../d2/d26/count__inversions_8cpp.html#a3332498eabf6579ef059c0d0e9f4ec80" title="Function countInversion() returns the number of inversion present in the input array....">countInversion()</a> returns the number of inversion present in the input array. Inversions are an estimate of how close or far off the array is to being sorted. </p>
<p >Number of inversions in a sorted array is 0. Number of inversion in an array[1...n] sorted in non-ascending order is n(n-1)/2, since each pair of elements contitute an inversion.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">arr</td><td>- array, data member of std::vector&lt;int&gt;, input for counting inversions </td></tr>
<tr><td class="paramname">array_size</td><td>- number of elementa in the array </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>number of inversions in input array, sorts the array </dd></dl>
<div class="fragment"><div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> {</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> temp;</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> temp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/reserve.html">reserve</a>(size);</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> temp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/assign.html">assign</a>(size, 0);</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(arr, temp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a>(), 0, size - 1);</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span>}</div>
<div class="ttc" id="aassign_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/assign.html">std::vector::assign</a></div><div class="ttdeci">T assign(T... args)</div></div>
<div class="ttc" id="adata_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/data.html">std::vector::data</a></div><div class="ttdeci">T data(T... args)</div></div>
<div class="ttc" id="agroup__sorting_html_gab6b14fea48d9841e29b9fc26be6e05d7"><div class="ttname"><a href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a></div><div class="ttdeci">void mergeSort(int *arr, int l, int r)</div><div class="ttdef"><b>Definition:</b> merge_sort.cpp:71</div></div>
<div class="ttc" id="areserve_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/reserve.html">std::vector::reserve</a></div><div class="ttdeci">T reserve(T... args)</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>
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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>
</tr>
</table>
</div><div class="memdoc">
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> {</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <a class="code hl_function" href="../../d2/d26/count__inversions_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// Run test implementations</span></div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="comment">// body(); // test your own array</span></div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span>}</div>
<div class="ttc" id="acount__inversions_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d2/d26/count__inversions_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Test implementations.</div><div class="ttdef"><b>Definition:</b> count_inversions.cpp:194</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aad643c14734394e784a75169cb58132f">&#9670;&nbsp;</a></span>merge()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">uint32_t sorting::inversion::merge </td>
<td>(</td>
<td class="paramtype">T *&#160;</td>
<td class="paramname"><em>arr</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T *&#160;</td>
<td class="paramname"><em>temp</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint32_t&#160;</td>
<td class="paramname"><em>left</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
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<td class="paramtype">uint32_t&#160;</td>
<td class="paramname"><em>mid</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint32_t&#160;</td>
<td class="paramname"><em>right</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
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<p>Function to merge two sub-arrays. </p>
<p ><a class="el" href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge()</a> function is called from <a class="el" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort()</a> to merge the array after it split for sorting by the <a class="el" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort()</a> funtion.</p>
<p >In this case the merge fuction will also count and return inversions detected when merging the sub arrays.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">arr</td><td>input array, data-menber of vector </td></tr>
<tr><td class="paramname">temp</td><td>stores the resultant merged array </td></tr>
<tr><td class="paramname">left</td><td>lower bound of <code>arr[]</code> and left-sub-array </td></tr>
<tr><td class="paramname">mid</td><td>midpoint, upper bound of left sub-array, <code>(mid+1)</code> gives the lower bound of right-sub-array </td></tr>
<tr><td class="paramname">right</td><td>upper bound of <code>arr[]</code> and right-sub-array </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>number of inversions found in merge step </dd></dl>
<div class="fragment"><div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> {</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> uint32_t i = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>; <span class="comment">/* i --&gt; index of left sub-array */</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> uint32_t j = mid + 1; <span class="comment">/* j --&gt; index for right sub-array */</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> uint32_t k = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>; <span class="comment">/* k --&gt; index for resultant array temp */</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> uint32_t inv_count = 0; <span class="comment">// inversion count</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordflow">while</span> ((i &lt;= mid) &amp;&amp; (j &lt;= right)) {</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keywordflow">if</span> (arr[i] &lt;= arr[j]) {</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> temp[k++] = arr[i++];</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> temp[k++] = arr[j++];</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> inv_count +=</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> (mid - i +</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> 1); <span class="comment">// tricky; may vary depending on selection of sub-array</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> }</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> }</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="comment">// Add remaining elements from the larger subarray to the end of temp</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keywordflow">while</span> (i &lt;= mid) {</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> temp[k++] = arr[i++];</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> }</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keywordflow">while</span> (j &lt;= right) {</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> temp[k++] = arr[j++];</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> }</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="comment">// Copy temp[] to arr[]</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keywordflow">for</span> (k = left; k &lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a>; k++) {</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> arr[k] = temp[k];</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> }</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keywordflow">return</span> inv_count;</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span>}</div>
<div class="ttc" id="aleft_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a></div><div class="ttdeci">T left(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae97a486e14101c4822ea8dc47f0d1661">&#9670;&nbsp;</a></span>mergeSort()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">uint32_t sorting::inversion::mergeSort </td>
<td>(</td>
<td class="paramtype">T *&#160;</td>
<td class="paramname"><em>arr</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T *&#160;</td>
<td class="paramname"><em>temp</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint32_t&#160;</td>
<td class="paramname"><em>left</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint32_t&#160;</td>
<td class="paramname"><em>right</em>&#160;</td>
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<td></td>
<td>)</td>
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<p>Implement merge Sort and count inverions while merging. </p>
<p >The <a class="el" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort()</a> function implements Merge Sort, a Divide and conquer algorithm, it divides the input array into two halves and calls itself for each sub-array and then calls the <a class="el" href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge()</a> function to merge the two halves.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">arr</td><td>- array to be sorted </td></tr>
<tr><td class="paramname">temp</td><td>- merged resultant array </td></tr>
<tr><td class="paramname">left</td><td>- lower bound of array </td></tr>
<tr><td class="paramname">right</td><td>- upper bound of array </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>number of inversions in array </dd></dl>
<div class="fragment"><div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> {</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> uint32_t mid = 0, inv_count = 0;</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keywordflow">if</span> (right &gt; left) {</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="comment">// midpoint to split the array</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> mid = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">right</a> + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>) / 2;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="comment">// Add inversions in left and right sub-arrays</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> inv_count += <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(arr, temp, left, mid); <span class="comment">// left sub-array</span></div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> inv_count += <a class="code hl_function" href="../../d5/d4c/group__sorting.html#gab6b14fea48d9841e29b9fc26be6e05d7">mergeSort</a>(arr, temp, mid + 1, right);</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> </div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="comment">// inversions in the merge step</span></div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> inv_count += <a class="code hl_function" href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge</a>(arr, temp, left, mid, right);</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> }</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="keywordflow">return</span> inv_count;</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span>}</div>
<div class="ttc" id="agroup__sorting_html_ga460c61cd948203b4816bef2accb3fc73"><div class="ttname"><a href="../../d5/d4c/group__sorting.html#ga460c61cd948203b4816bef2accb3fc73">merge</a></div><div class="ttdeci">void merge(int *arr, int l, int m, int r)</div><div class="ttdef"><b>Definition:</b> merge_sort.cpp:33</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a851ca6a0391d14fb49a97d55e4377497">&#9670;&nbsp;</a></span>show()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">void sorting::inversion::show </td>
<td>(</td>
<td class="paramtype">T *&#160;</td>
<td class="paramname"><em>arr</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const uint32_t&#160;</td>
<td class="paramname"><em>array_size</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
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</div><div class="memdoc">
<p>UTILITY function to print array. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">arr[]</td><td>array to print </td></tr>
<tr><td class="paramname">array_size</td><td>size of input array arr[] </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> {</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Printing array: \n&quot;</span>;</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="keywordflow">for</span> (uint32_t i = 0; i &lt; array_size; i++) {</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <a class="code hl_classRef" 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; arr[i];</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> }</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span>}</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>
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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>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
</table>
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<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">static</span></span> </td>
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<p>Test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> {</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="comment">// Test 1</span></div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr1 = {</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84,</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67,</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50,</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33,</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16,</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1};</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> uint32_t size1 = arr1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> uint32_t inv_count1 = 4950;</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> uint32_t result1 = <a class="code hl_function" href="../../d2/d26/count__inversions_8cpp.html#a3332498eabf6579ef059c0d0e9f4ec80">sorting::inversion::countInversion</a>(arr1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a>(), size1);</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> assert(inv_count1 == result1);</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="comment">// Test 2</span></div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> arr2 = {22, 66, 75, 23, 11, 87, 2, 44, 98, 43};</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> uint32_t size2 = arr2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> uint32_t inv_count2 = 20;</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> uint32_t result2 = <a class="code hl_function" href="../../d2/d26/count__inversions_8cpp.html#a3332498eabf6579ef059c0d0e9f4ec80">sorting::inversion::countInversion</a>(arr2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a>(), size2);</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> assert(inv_count2 == result2);</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <span class="comment">// Test 3</span></div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> arr3 = {33.1, 45.2, 65.4, 76.5, 1.0,</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> 2.9, 5.4, 7.7, 88.9, 12.4};</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> uint32_t size3 = arr3.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> uint32_t inv_count3 = 21;</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> uint32_t result3 = <a class="code hl_function" href="../../d2/d26/count__inversions_8cpp.html#a3332498eabf6579ef059c0d0e9f4ec80">sorting::inversion::countInversion</a>(arr3.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a>(), size3);</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> assert(inv_count3 == result3);</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="comment">// Test 4</span></div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;char&gt;</a> arr4 = {<span class="charliteral">&#39;a&#39;</span>, <span class="charliteral">&#39;b&#39;</span>, <span class="charliteral">&#39;c&#39;</span>, <span class="charliteral">&#39;d&#39;</span>, <span class="charliteral">&#39;e&#39;</span>};</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> uint32_t size4 = arr4.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> uint32_t inv_count4 = 0;</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> uint32_t result4 = <a class="code hl_function" href="../../d2/d26/count__inversions_8cpp.html#a3332498eabf6579ef059c0d0e9f4ec80">sorting::inversion::countInversion</a>(arr4.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/data.html">data</a>(), size4);</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> assert(inv_count4 == result4);</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span>}</div>
<div class="ttc" id="acount__inversions_8cpp_html_a3332498eabf6579ef059c0d0e9f4ec80"><div class="ttname"><a href="../../d2/d26/count__inversions_8cpp.html#a3332498eabf6579ef059c0d0e9f4ec80">sorting::inversion::countInversion</a></div><div class="ttdeci">uint32_t countInversion(T *arr, const uint32_t size)</div><div class="ttdoc">Function countInversion() returns the number of inversion present in the input array....</div><div class="ttdef"><b>Definition:</b> count_inversions.cpp:164</div></div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
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