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<div class="headertitle"><div class="title">recursive_bubble_sort.cpp File Reference</div></div>
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<p>This is an implementation of a recursive version of the <a href="https://www.geeksforgeeks.org/recursive-bubble-sort/" target="_blank">Bubble sort algorithm</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;cstdint&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 recursive_bubble_sort.cpp:</div>
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<p><a href="../../d3/df9/recursive__bubble__sort_8cpp_source.html">Go to the source code of this file.</a></p>
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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:ae3a775d99dbbb94c130a973df0cfddcf" id="r_ae3a775d99dbbb94c130a973df0cfddcf"><td class="memTemplParams" colspan="2">template&lt;typename T&gt; </td></tr>
<tr class="memitem:ae3a775d99dbbb94c130a973df0cfddcf template"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html#ae3a775d99dbbb94c130a973df0cfddcf">sorting::recursive_bubble_sort</a> (std::vector&lt; T &gt; *nums, uint64_t n)</td></tr>
<tr class="memdesc:ae3a775d99dbbb94c130a973df0cfddcf"><td class="mdescLeft">&#160;</td><td class="mdescRight">This is an implementation of the recursive_bubble_sort. A vector is passed to the function which is then dereferenced, so that the changes are reflected in the original vector. It also accepts a second parameter of type <span class="tt">int</span> and name <span class="tt">n</span>, which is the size of the array. <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>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p>This is an implementation of a recursive version of the <a href="https://www.geeksforgeeks.org/recursive-bubble-sort/" target="_blank">Bubble sort algorithm</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://adityaprakash.tech" target="_blank">Aditya Prakash</a> </dd></dl>
<p>The working principle of the Bubble sort algorithm.</p>
<p>Bubble sort is a simple sorting algorithm used to rearrange a set of ascending or descending order elements. Bubble sort gets its name from the fact that data "bubbles" to the top of the dataset.</p>
<h3 class="doxsection"><a class="anchor" id="autotoc_md118"></a>
Algorithm</h3>
<p>What is Swap?</p>
<p>Swapping two numbers means that we interchange their values. Often, an additional variable is required for this operation. This is further illustrated in the following:</p>
<p>void swap(int x, int y){ int z = x; x = y; y = z; }</p>
<p>The above process is a typical displacement process. When we assign a value to x, the old value of x is lost. That's why we create a temporary variable z to store the initial value of x. z is further used to assign the initial value of x to y, to complete swapping.</p>
<p>Recursion</p>
<p>While the recursive method does not necessarily have advantages over iterative versions, but it is useful to enhance the understanding of the algorithm and recursion itself. In Recursive Bubble sort algorithm, we firstly call the function on the entire array, and for every subsequent function call, we exclude the last element. This fixes the last element for that sub-array.Formally, for <span class="tt">ith</span> iteration, we consider elements up to n-i, where n is the number of elements in the array. Exit condition: n==1; i.e. the sub-array contains only one element.</p>
<p>Complexity Time complexity: O(n) best case; O(n²) average case; O(n²) worst case Space complexity: O(n)</p>
<p>We need to traverse the array <span class="tt">n * (n-1)</span> times. However, if the entire array is already sorted, then we need to traverse it only once. Hence, O(n) is the best case complexity </p>
<p class="definition">Definition in file <a class="el" href="../../d3/df9/recursive__bubble__sort_8cpp_source.html">recursive_bubble_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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<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="../../d3/df9/recursive__bubble__sort_8cpp_source.html#l00154">154</a> of file <a class="el" href="../../d3/df9/recursive__bubble__sort_8cpp_source.html">recursive_bubble_sort.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 154</span> {</div>
<div class="line"><span class="lineno"> 155</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"> 156</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 157</span>}</div>
<div class="ttc" id="arecursive__bubble__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="../../d3/df9/recursive__bubble__sort_8cpp_source.html#l00104">recursive_bubble_sort.cpp:104</a></div></div>
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<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>
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<td class="paramname"><span class="paramname"><em></em></span></td><td>)</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="../../d3/df9/recursive__bubble__sort_8cpp_source.html#l00104">104</a> of file <a class="el" href="../../d3/df9/recursive__bubble__sort_8cpp_source.html">recursive_bubble_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">// 1st example. Creating an array of type `int`.</span></div>
<div class="line"><span class="lineno"> 106</span> std::cout &lt;&lt; <span class="stringliteral">&quot;1st test using `int`\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 107</span> <span class="keyword">const</span> uint64_t size = 6;</div>
<div class="line"><span class="lineno"> 108</span> std::vector&lt;int64_t&gt; arr;</div>
<div class="line"><span class="lineno"> 109</span> <span class="comment">// populating the array</span></div>
<div class="line"><span class="lineno"> 110</span> arr.push_back(22);</div>
<div class="line"><span class="lineno"> 111</span> arr.push_back(46);</div>
<div class="line"><span class="lineno"> 112</span> arr.push_back(94);</div>
<div class="line"><span class="lineno"> 113</span> arr.push_back(12);</div>
<div class="line"><span class="lineno"> 114</span> arr.push_back(37);</div>
<div class="line"><span class="lineno"> 115</span> arr.push_back(63);</div>
<div class="line"><span class="lineno"> 116</span> <span class="comment">// array populating ends</span></div>
<div class="line"><span class="lineno"> 117</span> </div>
<div class="line"><span class="lineno"> 118</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#ae3a775d99dbbb94c130a973df0cfddcf">sorting::recursive_bubble_sort</a>(&amp;arr, size);</div>
<div class="line"><span class="lineno"> 119</span> assert(std::is_sorted(std::begin(arr), std::end(arr)));</div>
<div class="line"><span class="lineno"> 120</span> std::cout &lt;&lt; <span class="stringliteral">&quot; 1st test passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 121</span> <span class="comment">// printing the array</span></div>
<div class="line"><span class="lineno"> 122</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; size; i++) {</div>
<div class="line"><span class="lineno"> 123</span> std::cout &lt;&lt; arr[i] &lt;&lt; <span class="stringliteral">&quot;, &quot;</span>;</div>
<div class="line"><span class="lineno"> 124</span> }</div>
<div class="line"><span class="lineno"> 125</span> std::cout &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 126</span> </div>
<div class="line"><span class="lineno"> 127</span> <span class="comment">// 2nd example. Creating an array of type `double`.</span></div>
<div class="line"><span class="lineno"> 128</span> std::cout &lt;&lt; <span class="stringliteral">&quot;2nd test using doubles\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 129</span> std::vector&lt;double&gt; double_arr;</div>
<div class="line"><span class="lineno"> 130</span> </div>
<div class="line"><span class="lineno"> 131</span> <span class="comment">// populating the array</span></div>
<div class="line"><span class="lineno"> 132</span> double_arr.push_back(20.4);</div>
<div class="line"><span class="lineno"> 133</span> double_arr.push_back(62.7);</div>
<div class="line"><span class="lineno"> 134</span> double_arr.push_back(12.2);</div>
<div class="line"><span class="lineno"> 135</span> double_arr.push_back(43.6);</div>
<div class="line"><span class="lineno"> 136</span> double_arr.push_back(74.1);</div>
<div class="line"><span class="lineno"> 137</span> double_arr.push_back(57.9);</div>
<div class="line"><span class="lineno"> 138</span> <span class="comment">// array populating ends</span></div>
<div class="line"><span class="lineno"> 139</span> </div>
<div class="line"><span class="lineno"> 140</span> <a class="code hl_function" href="../../d5/d91/namespacesorting.html#ae3a775d99dbbb94c130a973df0cfddcf">sorting::recursive_bubble_sort</a>(&amp;double_arr, size);</div>
<div class="line"><span class="lineno"> 141</span> assert(std::is_sorted(std::begin(double_arr), std::end(double_arr)));</div>
<div class="line"><span class="lineno"> 142</span> std::cout &lt;&lt; <span class="stringliteral">&quot; 2nd test passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 143</span> <span class="comment">// printing the array</span></div>
<div class="line"><span class="lineno"> 144</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; size; i++) {</div>
<div class="line"><span class="lineno"> 145</span> std::cout &lt;&lt; double_arr[i] &lt;&lt; <span class="stringliteral">&quot;, &quot;</span>;</div>
<div class="line"><span class="lineno"> 146</span> }</div>
<div class="line"><span class="lineno"> 147</span> std::cout &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 148</span>}</div>
<div class="ttc" id="anamespacesorting_html_ae3a775d99dbbb94c130a973df0cfddcf"><div class="ttname"><a href="../../d5/d91/namespacesorting.html#ae3a775d99dbbb94c130a973df0cfddcf">sorting::recursive_bubble_sort</a></div><div class="ttdeci">void recursive_bubble_sort(std::vector&lt; T &gt; *nums, uint64_t n)</div><div class="ttdoc">This is an implementation of the recursive_bubble_sort. A vector is passed to the function which is t...</div><div class="ttdef"><b>Definition</b> <a href="../../d3/df9/recursive__bubble__sort_8cpp_source.html#l00083">recursive_bubble_sort.cpp:83</a></div></div>
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