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<div class="headertitle"><div class="title">binary_insertion_sort.cpp File Reference</div></div>
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<p><a href="https://en.wikipedia.org/wiki/Insertion_sort" target="_blank">Binary Insertion Sort Algorithm (Insertion Sort)</a>
<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 binary_insertion_sort.cpp:</div>
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<p><a href="../../d8/dcc/binary__insertion__sort_8cpp_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-namespaces" class="groupheader"><a id="namespaces" name="namespaces"></a>
Namespaces</h2></td></tr>
<tr class="memitem:sorting" id="r_sorting"><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:a034d8b276518a902962e87d3158b64fd" id="r_a034d8b276518a902962e87d3158b64fd"><td class="memTemplParams" colspan="2">template&lt;class T&gt; </td></tr>
<tr class="memitem:a034d8b276518a902962e87d3158b64fd template"><td class="memItemLeft" align="right" valign="top">int64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#a034d8b276518a902962e87d3158b64fd">sorting::binary_search</a> (std::vector&lt; T &gt; &amp;arr, T val, int64_t low, int64_t high)</td></tr>
<tr class="memdesc:a034d8b276518a902962e87d3158b64fd"><td class="mdescLeft">&#160;</td><td class="mdescRight">Binary search function to find the most suitable pace for an element. <br /></td></tr>
<tr class="memitem:a5f4bc75cca6dd8294af2d0e328006c68" id="r_a5f4bc75cca6dd8294af2d0e328006c68"><td class="memTemplParams" colspan="2">template&lt;typename T&gt; </td></tr>
<tr class="memitem:a5f4bc75cca6dd8294af2d0e328006c68 template"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#a5f4bc75cca6dd8294af2d0e328006c68">sorting::insertionSort_binsrch</a> (std::vector&lt; T &gt; &amp;arr)</td></tr>
<tr class="memdesc:a5f4bc75cca6dd8294af2d0e328006c68"><td class="mdescLeft">&#160;</td><td class="mdescRight">Insertion sort function to sort the vector. <br /></td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
<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>
</table>
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Insertion_sort" target="_blank">Binary Insertion Sort Algorithm (Insertion Sort)</a> </p>
<p>If the cost of comparisons exceeds the cost of swaps, as is the case for example with string keys stored by reference or with human interaction (such as choosing one of a pair displayed side-by-side), then using binary insertion sort may yield better performance. Binary insertion sort employs a binary search to determine the correct location to insert new elements, and therefore performs ⌈log2 n⌉ comparisons in the worst case. When each element in the array is searched for and inserted this is O(n log n). The algorithm as a whole still has a running time of O(n2) on average because of the series</p><ul>
<li>of swaps required for each insertion. However it has several advantages such as</li>
</ul>
<ol type="1">
<li>Easy to implement</li>
<li>For small set of data it is quite efficient</li>
<li>More efficient that other Quadratic complexity algorithms like Selection sort or bubble sort.</li>
<li>It is efficient to use it when the cost of comparison is high.</li>
<li>It's stable that is it does not change the relative order of elements with equal keys.</li>
<li>It can sort the array or list as it receives.</li>
</ol>
<p>Example execution steps:</p><ol type="1">
<li>Suppose initially we have <p class="formulaDsp">
\begin{bmatrix}40 &amp;30 &amp;20 &amp;50 &amp;10\end{bmatrix}
</p>
</li>
<li>We start traversing from 40 till we reach 10 when we reach at 30 we find that it is not at it's correct place so we take 30 and place it at a correct position thus the array will become <p class="formulaDsp">
\begin{bmatrix}30 &amp;40 &amp;20 &amp;50 &amp;10\end{bmatrix}
</p>
</li>
<li>In the next iteration we are at 20 we find that this is also misplaced so we place it at the correct sorted position thus the array in this iteration becomes <p class="formulaDsp">
\begin{bmatrix}20 &amp;30 &amp;40 &amp;50 &amp;10\end{bmatrix}
</p>
</li>
<li>We do not do anything with 50 and move on to the next iteration and select 10 which is misplaced and place it at correct position. Thus, we have <p class="formulaDsp">
\begin{bmatrix}10 &amp;20 &amp;30 &amp;40 &amp;50\end{bmatrix}
</p>
</li>
</ol>
<p class="definition">Definition in file <a class="el" href="../../d8/dcc/binary__insertion__sort_8cpp_source.html">binary_insertion_sort.cpp</a>.</p>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<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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<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit. </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d8/dcc/binary__insertion__sort_8cpp_source.html#l00143">143</a> of file <a class="el" href="../../d8/dcc/binary__insertion__sort_8cpp_source.html">binary_insertion_sort.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 143</span> {</div>
<div class="line"><span class="lineno"> 144</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 145</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 146</span>}</div>
<div class="ttc" id="abinary__insertion__sort_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../d8/dcc/binary__insertion__sort_8cpp_source.html#l00104">binary_insertion_sort.cpp:104</a></div></div>
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<a id="aa8dca7b867074164d5f45b0f3851269d" name="aa8dca7b867074164d5f45b0f3851269d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">void test </td>
<td>(</td>
<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel static">static</span></span> </td>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d8/dcc/binary__insertion__sort_8cpp_source.html#l00104">104</a> of file <a class="el" href="../../d8/dcc/binary__insertion__sort_8cpp_source.html">binary_insertion_sort.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 104</span> {</div>
<div class="line"><span class="lineno"> 105</span> <span class="comment">/* descriptions of the following test */</span></div>
<div class="line"><span class="lineno"> 106</span> <span class="comment">/* 1st test:</span></div>
<div class="line"><span class="lineno"> 107</span><span class="comment"> [5, -3, -1, -2, 7] returns [-3, -2, -1, 5, 7] */</span></div>
<div class="line"><span class="lineno"> 108</span> std::vector&lt;int64_t&gt; arr1({5, -3, -1, -2, 7});</div>
<div class="line"><span class="lineno"> 109</span> std::cout &lt;&lt; <span class="stringliteral">&quot;1st test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 110</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a5f4bc75cca6dd8294af2d0e328006c68">sorting::insertionSort_binsrch</a>(arr1);</div>
<div class="line"><span class="lineno"> 111</span> assert(std::is_sorted(std::begin(arr1), std::end(arr1)));</div>
<div class="line"><span class="lineno"> 112</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 113</span> </div>
<div class="line"><span class="lineno"> 114</span> <span class="comment">/* 2nd test:</span></div>
<div class="line"><span class="lineno"> 115</span><span class="comment"> [12, 26, 15, 91, 32, 54, 41] returns [12, 15, 26, 32, 41, 54, 91] */</span></div>
<div class="line"><span class="lineno"> 116</span> std::vector&lt;int64_t&gt; arr2({12, 26, 15, 91, 32, 54, 41});</div>
<div class="line"><span class="lineno"> 117</span> std::cout &lt;&lt; <span class="stringliteral">&quot;2nd test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 118</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a5f4bc75cca6dd8294af2d0e328006c68">sorting::insertionSort_binsrch</a>(arr2);</div>
<div class="line"><span class="lineno"> 119</span> assert(std::is_sorted(std::begin(arr2), std::end(arr2)));</div>
<div class="line"><span class="lineno"> 120</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 121</span> </div>
<div class="line"><span class="lineno"> 122</span> <span class="comment">/* 3rd test:</span></div>
<div class="line"><span class="lineno"> 123</span><span class="comment"> [7.1, -2.5, -4.0, -2.1, 5.7] returns [-4.0, -2.5, -2.1, 5.7, 7.1] */</span></div>
<div class="line"><span class="lineno"> 124</span> std::vector&lt;float&gt; arr3({7.1, -2.5, -4.0, -2.1, 5.7});</div>
<div class="line"><span class="lineno"> 125</span> std::cout &lt;&lt; <span class="stringliteral">&quot;3rd test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 126</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a5f4bc75cca6dd8294af2d0e328006c68">sorting::insertionSort_binsrch</a>(arr3);</div>
<div class="line"><span class="lineno"> 127</span> assert(std::is_sorted(std::begin(arr3), std::end(arr3)));</div>
<div class="line"><span class="lineno"> 128</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 129</span> </div>
<div class="line"><span class="lineno"> 130</span> <span class="comment">/* 4th test:</span></div>
<div class="line"><span class="lineno"> 131</span><span class="comment"> [12.8, -3.7, -20.7, -7.1, 2.2] returns [-20.7, -7.1, -3.7, 2.2, 12.8] */</span></div>
<div class="line"><span class="lineno"> 132</span> std::vector&lt;float&gt; arr4({12.8, -3.7, -20.7, -7.1, 2.2});</div>
<div class="line"><span class="lineno"> 133</span> std::cout &lt;&lt; <span class="stringliteral">&quot;4th test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 134</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#a5f4bc75cca6dd8294af2d0e328006c68">sorting::insertionSort_binsrch</a>(arr4);</div>
<div class="line"><span class="lineno"> 135</span> assert(std::is_sorted(std::begin(arr4), std::end(arr4)));</div>
<div class="line"><span class="lineno"> 136</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 137</span>}</div>
<div class="ttc" id="anamespacesorting_html_a5f4bc75cca6dd8294af2d0e328006c68"><div class="ttname"><a href="../../d5/d91/namespacesorting.html#a5f4bc75cca6dd8294af2d0e328006c68">sorting::insertionSort_binsrch</a></div><div class="ttdeci">void insertionSort_binsrch(std::vector&lt; T &gt; &amp;arr)</div><div class="ttdoc">Insertion sort function to sort the vector.</div><div class="ttdef"><b>Definition</b> <a href="../../d8/dcc/binary__insertion__sort_8cpp_source.html#l00084">binary_insertion_sort.cpp:84</a></div></div>
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