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<p>Insertion Sort Algorithm.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for insertion_sort_recursive.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:"><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">for working with vectors <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a78cb2f3b97b6db2c062b2a1df05c9ea9" id="r_a78cb2f3b97b6db2c062b2a1df05c9ea9"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a78cb2f3b97b6db2c062b2a1df05c9ea9"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a> (T *arr, int n)</td></tr>
<tr class="memdesc:a78cb2f3b97b6db2c062b2a1df05c9ea9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Insertion Sort Function. <br /></td></tr>
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<tr class="memitem:a8fe6bac9e03f58abcc2ce26ef3de1b5f" id="r_a8fe6bac9e03f58abcc2ce26ef3de1b5f"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a8fe6bac9e03f58abcc2ce26ef3de1b5f"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#a8fe6bac9e03f58abcc2ce26ef3de1b5f">sorting::insertionSort</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; *arr)</td></tr>
<tr class="memdesc:a8fe6bac9e03f58abcc2ce26ef3de1b5f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Insertion Sort for a vector. <br /></td></tr>
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<tr class="memitem:a59914553f24088342c139645a02a8a49" id="r_a59914553f24088342c139645a02a8a49"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a59914553f24088342c139645a02a8a49"><td class="memTemplItemLeft" align="right" valign="top">static void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a59914553f24088342c139645a02a8a49">create_random_array</a> (T *arr, int N)</td></tr>
<tr class="memdesc:a59914553f24088342c139645a02a8a49"><td class="mdescLeft">&#160;</td><td class="mdescRight">Helper function to create a random array. <br /></td></tr>
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<tr class="memitem:a483bb8ccf42aaf7375a83e91490eda1e" id="r_a483bb8ccf42aaf7375a83e91490eda1e"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a> ()</td></tr>
<tr class="memdesc:a483bb8ccf42aaf7375a83e91490eda1e"><td class="mdescLeft">&#160;</td><td class="mdescRight">self test implementation <br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Insertion Sort Algorithm. </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Fandroid745" target="_blank">Dhanush S</a></dd></dl>
<p>Insertion sort is a simple sorting algorithm that builds the final sorted array one element at a time. It is much less efficient compared to other sorting algorithms like heap sort, merge sort, or quick sort.</p>
<p>However, it has several advantages:</p><ul>
<li>Easy to implement.</li>
<li>Efficient for small data sets.</li>
<li>More efficient than other O(n²) algorithms like selection sort or bubble sort.</li>
<li>Stable: it does not change the relative order of elements with equal keys.</li>
</ul>
<p>Insertion sort works similarly to how people sort playing cards in their hands. The algorithm iterates through the list and inserts each element into its correct position in the sorted portion of the array.</p>
<p>The time complexity of the algorithm is \(O(n^2)\), and in some cases, it can be \(O(n)\).</p>
<p>Example execution:</p><ol type="1">
<li>Start with the array [4, 3, 2, 5, 1].</li>
<li>Insert 3 in its correct position: [3, 4, 2, 5, 1].</li>
<li>Insert 2: [2, 3, 4, 5, 1].</li>
<li>Continue this until the array is sorted: [1, 2, 3, 4, 5]. </li>
</ol>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a59914553f24088342c139645a02a8a49" name="a59914553f24088342c139645a02a8a49"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a59914553f24088342c139645a02a8a49">&#9670;&#160;</a></span>create_random_array()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">static void create_random_array </td>
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<td class="paramtype">T *</td> <td class="paramname"><span class="paramname"><em>arr</em></span>, </td>
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<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>N</em></span>&#160;)</td>
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<p>Helper function to create a random array. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>Type of the array elements </td></tr>
</table>
</dd>
</dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">arr</td><td>Array to fill (must be pre-allocated) </td></tr>
<tr><td class="paramname">N</td><td>Number of elements in the array </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 94</span> {</div>
<div class="line"><span class="lineno"> 95</span> <span class="keywordflow">while</span> (N--) {</div>
<div class="line"><span class="lineno"> 96</span> <span class="keywordtype">double</span> r = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 10000 - 5000) / 100.f;</div>
<div class="line"><span class="lineno"> 97</span> arr[<a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>] = <span class="keyword">static_cast&lt;</span>T<span class="keyword">&gt;</span>(r);</div>
<div class="line"><span class="lineno"> 98</span> }</div>
<div class="line"><span class="lineno"> 99</span>}</div>
<div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition</b> sparse_table.cpp:47</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>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on successful exit. </dd></dl>
<p>run self test implementations</p>
<div class="fragment"><div class="line"><span class="lineno"> 149</span> {</div>
<div class="line"><span class="lineno"> 150</span> <a class="code hl_function" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">/// run self test implementations</span></div>
<div class="line"><span class="lineno"> 151</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 152</span>}</div>
<div class="ttc" id="ainsertion__sort__recursive_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdoc">self test implementation</div><div class="ttdef"><b>Definition</b> insertion_sort_recursive.cpp:105</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">&#9670;&#160;</a></span>tests()</h2>
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<td class="memname">static void tests </td>
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<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<p>self test implementation </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 105</span> {</div>
<div class="line"><span class="lineno"> 106</span> <span class="keywordtype">int</span> arr1[10] = {78, 34, 35, 6, 34, 56, 3, 56, 2, 4};</div>
<div class="line"><span class="lineno"> 107</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;Test 1... &quot;</span>;</div>
<div class="line"><span class="lineno"> 108</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr1, 10);</div>
<div class="line"><span class="lineno"> 109</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr1, arr1 + 10));</div>
<div class="line"><span class="lineno"> 110</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;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 111</span> </div>
<div class="line"><span class="lineno"> 112</span> <span class="keywordtype">int</span> arr2[5] = {5, -3, 7, -2, 1};</div>
<div class="line"><span class="lineno"> 113</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;Test 2... &quot;</span>;</div>
<div class="line"><span class="lineno"> 114</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr2, 5);</div>
<div class="line"><span class="lineno"> 115</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr2, arr2 + 5));</div>
<div class="line"><span class="lineno"> 116</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;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 117</span> </div>
<div class="line"><span class="lineno"> 118</span> <span class="keywordtype">float</span> arr3[5] = {5.6, -3.1, -3.0, -2.1, 1.8};</div>
<div class="line"><span class="lineno"> 119</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;Test 3... &quot;</span>;</div>
<div class="line"><span class="lineno"> 120</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr3, 5);</div>
<div class="line"><span class="lineno"> 121</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr3, arr3 + 5));</div>
<div class="line"><span class="lineno"> 122</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;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 123</span> </div>
<div class="line"><span class="lineno"> 124</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> arr4({5.6, -3.1, -3.0, -2.1, 1.8});</div>
<div class="line"><span class="lineno"> 125</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;Test 4... &quot;</span>;</div>
<div class="line"><span class="lineno"> 126</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(&amp;arr4);</div>
<div class="line"><span class="lineno"> 127</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4)));</div>
<div class="line"><span class="lineno"> 128</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;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 129</span> </div>
<div class="line"><span class="lineno"> 130</span> <span class="keywordtype">int</span> arr5[50];</div>
<div class="line"><span class="lineno"> 131</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;Test 5... &quot;</span>;</div>
<div class="line"><span class="lineno"> 132</span> <a class="code hl_function" href="#a59914553f24088342c139645a02a8a49">create_random_array</a>(arr5, 50);</div>
<div class="line"><span class="lineno"> 133</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr5, 50);</div>
<div class="line"><span class="lineno"> 134</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr5, arr5 + 50));</div>
<div class="line"><span class="lineno"> 135</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;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 136</span> </div>
<div class="line"><span class="lineno"> 137</span> <span class="keywordtype">float</span> arr6[50];</div>
<div class="line"><span class="lineno"> 138</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;Test 6... &quot;</span>;</div>
<div class="line"><span class="lineno"> 139</span> <a class="code hl_function" href="#a59914553f24088342c139645a02a8a49">create_random_array</a>(arr6, 50);</div>
<div class="line"><span class="lineno"> 140</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a>(arr6, 50);</div>
<div class="line"><span class="lineno"> 141</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(arr6, arr6 + 50));</div>
<div class="line"><span class="lineno"> 142</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;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 143</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>
<div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a></div><div class="ttdeci">T begin(T... args)</div></div>
<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a></div><div class="ttdeci">T end(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="ainsertion__sort__recursive_8cpp_html_a59914553f24088342c139645a02a8a49"><div class="ttname"><a href="#a59914553f24088342c139645a02a8a49">create_random_array</a></div><div class="ttdeci">static void create_random_array(T *arr, int N)</div><div class="ttdoc">Helper function to create a random array.</div><div class="ttdef"><b>Definition</b> insertion_sort_recursive.cpp:94</div></div>
<div class="ttc" id="ais_sorted_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a></div><div class="ttdeci">T is_sorted(T... args)</div></div>
<div class="ttc" id="anamespacesorting_html_a78cb2f3b97b6db2c062b2a1df05c9ea9"><div class="ttname"><a href="../../d5/d91/namespacesorting.html#a78cb2f3b97b6db2c062b2a1df05c9ea9">sorting::insertionSort</a></div><div class="ttdeci">void insertionSort(T *arr, int n)</div><div class="ttdoc">Insertion Sort Function.</div><div class="ttdef"><b>Definition</b> insertion_sort.cpp:59</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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