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<title>Selection Sort</title>
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<h1>Selection Sort Algorithm</h1>
<p class="editor-contents__short-description">In this tutorial, you will learn about the selection sort algorithm and its implementation in Python, Java, C, and C++.</p>
<div id="node-334" class="node node-algorithm clearfix" about="/dsa/selection-sort" typeof="sioc:Item foaf:Document">
<span property="dc:title" content="Selection Sort Algorithm" class="rdf-meta element-hidden"></span>
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<p id="definition">Selection sort is <a href="/dsa.html">a sorting algorithm</a> that selects the smallest element from an unsorted list in each iteration and places that element at the beginning of the unsorted list.</p>
<hr><h2 id="working">Working of Selection Sort</h2>
<ol><li>Set the first element as <code>minimum</code>.
<figure><img alt="Selection Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/Selection-sort-0-initial-array.png" title="New Array Initialized" width="330" height="85"><figcaption>Select first element as minimum</figcaption></figure></li>
<li>Compare <code>minimum</code> with the second element. If the second element is smaller than <code>minimum</code>, assign the second element as <code>minimum</code>.<br><br>
Compare <code>minimum</code> with the third element. Again, if the third element is smaller, then assign <code>minimum</code> to the third element otherwise do nothing. The process goes on until the last element.
<figure><img alt="Selection Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/Selection-sort-0-comparision.png" title="comparison" width="330" height="290"><figcaption>Compare minimum with the remaining elements</figcaption></figure></li>
<li>After each iteration, <code>minimum</code> is placed in the front of the unsorted list.
<figure><img alt="Selection Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/Selection-sort-0-swapping.png" title="swapping" width="330" height="122"><figcaption>Swap the first with minimum</figcaption></figure></li>
<li>For each iteration, indexing starts from the first unsorted element. Step 1 to 3 are repeated until all the elements are placed at their correct positions.
<figure><img alt="Selection Sort Steps" src="https://www.programiz.com/sites/tutorial2program/files/Selection-sort-0.png" title="Selection Sort Step 0" width="440" height="506"><figcaption>The first iteration</figcaption></figure><figure><img alt="Selection sort steps" src="https://www.programiz.com/sites/tutorial2program/files/Selection-sort-1.png" title="Selection sort steps 1" width="440" height="422"><figcaption>The second iteration</figcaption></figure><figure><img alt="Selection sort steps" src="https://www.programiz.com/sites/tutorial2program/files/Selection-sort-2.png" title="Selection sort steps 2" width="440" height="343"><figcaption>The third iteration</figcaption></figure><figure><img alt="Selection sort steps" src="https://www.programiz.com/sites/tutorial2program/files/Selection-sort-3_1.png" title="Selection sort steps 3" width="440" height="260"><figcaption>The fourth iteration</figcaption></figure></li>
</ol><hr><h2 id="algorithm">Selection Sort Algorithm</h2>
<pre style="max-height: 600px;"><code class="dsa hljs sql">selectionSort(array, size)
repeat (size - 1) times
<span class="hljs-keyword">set</span> the <span class="hljs-keyword">first</span> unsorted <span class="hljs-keyword">element</span> <span class="hljs-keyword">as</span> the <span class="hljs-keyword">minimum</span>
<span class="hljs-keyword">for</span> <span class="hljs-keyword">each</span> <span class="hljs-keyword">of</span> the unsorted elements
<span class="hljs-keyword">if</span> <span class="hljs-keyword">element</span> < currentMinimum
<span class="hljs-keyword">set</span> <span class="hljs-keyword">element</span> <span class="hljs-keyword">as</span> <span class="hljs-keyword">new</span> <span class="hljs-keyword">minimum</span>
swap <span class="hljs-keyword">minimum</span> <span class="hljs-keyword">with</span> <span class="hljs-keyword">first</span> unsorted <span class="hljs-keyword">position</span>
<span class="hljs-keyword">end</span> selectionSort</code></pre>
<hr><h2 id="code">Selection Sort Code in Python, Java, and C/C++</h2>
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<div id="py1" onclick="changepy()" class="tabbed-editor__node tabbed-editor__node--active"><a href="#python-code">Python</a></div>
<div id="java1" onclick="changejava()" class="tabbed-editor__node"><a href="#java-code">Java</a></div>
<div id="c1" onclick="changec()" class="tabbed-editor__node"><a href="#c-code">C</a></div>
<div id="cpp1" onclick="changecpp()" class="tabbed-editor__node"><a href="#cpp-code">C++</a></div>
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<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="python hljs"><span class="hljs-comment"># Selection sort in Python</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">selectionSort</span><span class="hljs-params">(array, size)</span>:</span>
<span class="hljs-keyword">for</span> step <span class="hljs-keyword">in</span> range(size):
min_idx = step
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(step + <span class="hljs-number">1</span>, size):
<span class="hljs-comment"># to sort in descending order, change > to < in this line</span>
<span class="hljs-comment"># select the minimum element in each loop</span>
<span class="hljs-keyword">if</span> array[i] < array[min_idx]:
min_idx = i
<span class="hljs-comment"># put min at the correct position</span>
(array[step], array[min_idx]) = (array[min_idx], array[step])
data = [<span class="hljs-number">-2</span>, <span class="hljs-number">45</span>, <span class="hljs-number">0</span>, <span class="hljs-number">11</span>, <span class="hljs-number">-9</span>]
size = len(data)
selectionSort(data, size)
<span class="hljs-keyword">print</span>(<span class="hljs-string">'Sorted Array in Ascending Order:'</span>)
<span class="hljs-keyword">print</span>(data)</code></pre></div>
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<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="java hljs"><span class="hljs-comment">// Selection sort in Java</span>
<span class="hljs-keyword">import</span> java.util.Arrays;
<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">SelectionSort</span> </span>{
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">selectionSort</span><span class="hljs-params">(<span class="hljs-keyword">int</span> array[])</span> </span>{
<span class="hljs-keyword">int</span> size = array.length;
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> step = <span class="hljs-number">0</span>; step < size - <span class="hljs-number">1</span>; step++) {
<span class="hljs-keyword">int</span> min_idx = step;
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = step + <span class="hljs-number">1</span>; i < size; i++) {
<span class="hljs-comment">// To sort in descending order, change > to < in this line.</span>
<span class="hljs-comment">// Select the minimum element in each loop.</span>
<span class="hljs-keyword">if</span> (array[i] < array[min_idx]) {
min_idx = i;
}
}
<span class="hljs-comment">// put min at the correct position</span>
<span class="hljs-keyword">int</span> temp = array[step];
array[step] = array[min_idx];
array[min_idx] = temp;
}
}
<span class="hljs-comment">// driver code</span>
<span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title">main</span><span class="hljs-params">(String args[])</span> </span>{
<span class="hljs-keyword">int</span>[] data = { <span class="hljs-number">20</span>, <span class="hljs-number">12</span>, <span class="hljs-number">10</span>, <span class="hljs-number">15</span>, <span class="hljs-number">2</span> };
SelectionSort ss = <span class="hljs-keyword">new</span> SelectionSort();
ss.selectionSort(data);
System.out.println(<span class="hljs-string">"Sorted Array in Ascending Order: "</span>);
System.out.println(Arrays.toString(data));
}
}</code></pre></div>
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<div class="code-editor__area" id="c-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="c hljs cpp"><span class="hljs-comment">// Selection sort in C</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><stdio.h></span></span>
<span class="hljs-comment">// function to swap the the position of two elements</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">swap</span><span class="hljs-params">(<span class="hljs-keyword">int</span> *a, <span class="hljs-keyword">int</span> *b)</span> </span>{
<span class="hljs-keyword">int</span> temp = *a;
*a = *b;
*b = temp;
}
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">selectionSort</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> size)</span> </span>{
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> step = <span class="hljs-number">0</span>; step < size - <span class="hljs-number">1</span>; step++) {
<span class="hljs-keyword">int</span> min_idx = step;
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = step + <span class="hljs-number">1</span>; i < size; i++) {
<span class="hljs-comment">// To sort in descending order, change > to < in this line.</span>
<span class="hljs-comment">// Select the minimum element in each loop.</span>
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[i] < <span class="hljs-built_in">array</span>[min_idx])
min_idx = i;
}
<span class="hljs-comment">// put min at the correct position</span>
swap(&<span class="hljs-built_in">array</span>[min_idx], &<span class="hljs-built_in">array</span>[step]);
}
}
<span class="hljs-comment">// function to print an array</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">printArray</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> size)</span> </span>{
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < size; ++i) {
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"%d "</span>, <span class="hljs-built_in">array</span>[i]);
}
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n"</span>);
}
<span class="hljs-comment">// driver code</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{
<span class="hljs-keyword">int</span> data[] = {<span class="hljs-number">20</span>, <span class="hljs-number">12</span>, <span class="hljs-number">10</span>, <span class="hljs-number">15</span>, <span class="hljs-number">2</span>};
<span class="hljs-keyword">int</span> size = <span class="hljs-keyword">sizeof</span>(data) / <span class="hljs-keyword">sizeof</span>(data[<span class="hljs-number">0</span>]);
selectionSort(data, size);
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Sorted array in Acsending Order:\n"</span>);
printArray(data, size);
}</code></pre></div>
</div>
<div class="code-editor__area" id="cpp-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="cpp hljs"><span class="hljs-comment">// Selection sort in C++</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><iostream></span></span>
<span class="hljs-keyword">using</span> <span class="hljs-keyword">namespace</span> <span class="hljs-built_in">std</span>;
<span class="hljs-comment">// function to swap the the position of two elements</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">swap</span><span class="hljs-params">(<span class="hljs-keyword">int</span> *a, <span class="hljs-keyword">int</span> *b)</span> </span>{
<span class="hljs-keyword">int</span> temp = *a;
*a = *b;
*b = temp;
}
<span class="hljs-comment">// function to print an array</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">printArray</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> size)</span> </span>{
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < size; i++) {
<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">array</span>[i] << <span class="hljs-string">" "</span>;
}
<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">endl</span>;
}
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">selectionSort</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> size)</span> </span>{
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> step = <span class="hljs-number">0</span>; step < size - <span class="hljs-number">1</span>; step++) {
<span class="hljs-keyword">int</span> min_idx = step;
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = step + <span class="hljs-number">1</span>; i < size; i++) {
<span class="hljs-comment">// To sort in descending order, change > to < in this line.</span>
<span class="hljs-comment">// Select the minimum element in each loop.</span>
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[i] < <span class="hljs-built_in">array</span>[min_idx])
min_idx = i;
}
<span class="hljs-comment">// put min at the correct position</span>
swap(&<span class="hljs-built_in">array</span>[min_idx], &<span class="hljs-built_in">array</span>[step]);
}
}
<span class="hljs-comment">// driver code</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{
<span class="hljs-keyword">int</span> data[] = {<span class="hljs-number">20</span>, <span class="hljs-number">12</span>, <span class="hljs-number">10</span>, <span class="hljs-number">15</span>, <span class="hljs-number">2</span>};
<span class="hljs-keyword">int</span> size = <span class="hljs-keyword">sizeof</span>(data) / <span class="hljs-keyword">sizeof</span>(data[<span class="hljs-number">0</span>]);
selectionSort(data, size);
<span class="hljs-built_in">cout</span> << <span class="hljs-string">"Sorted array in Acsending Order:\n"</span>;
printArray(data, size);
}</code></pre></div>
</div>
</div>
<hr><h2 id="complexity">Selection Sort Complexity</h2>
<div class="table-responsive">
<table border="0"><tbody><tr><th><strong>Time Complexity</strong></th>
<td> </td>
</tr><tr><td>Best</td>
<td>O(n<sup>2</sup>)</td>
</tr><tr><td>Worst</td>
<td>O(n<sup>2</sup>)</td>
</tr><tr><td>Average</td>
<td>O(n<sup>2</sup>)</td>
</tr><tr><th><strong>Space Complexity</strong></th>
<td>O(1)</td>
</tr><tr><th><strong>Stability</strong></th>
<td>No</td>
</tr></tbody></table></div>
<hr><div class="table-responsive">
<table border="0"><tbody><tr><th>Cycle</th>
<th>Number of Comparison</th>
</tr><tr><td>1st</td>
<td>(n-1)</td>
</tr><tr><td>2nd</td>
<td>(n-2)</td>
</tr><tr><td>3rd</td>
<td>(n-3)</td>
</tr><tr><td>...</td>
<td>...</td>
</tr><tr><td>last</td>
<td>1</td>
</tr></tbody></table></div>
<p>Number of comparisons: <code>(n - 1) + (n - 2) + (n - 3) + ..... + 1 = n(n - 1) / 2</code> nearly equals to <code>n<sup>2</sup></code>.</p>
<p><strong>Complexity</strong> = <code>O(n<sup>2</sup>)</code></p>
<p>Also, we can analyze the complexity by simply observing the number of loops. There are 2 loops so the complexity is <code>n*n = n<sup>2</sup></code>.</p>
<p><strong>Time Complexities:</strong></p>
<ul><li><strong>Worst Case Complexity:</strong> <code>O(n<sup>2</sup>)</code><br>
If we want to sort in ascending order and the array is in descending order then, the worst case occurs.</li>
<li><strong>Best Case Complexity:</strong> <code>O(n<sup>2</sup>)</code><br>
It occurs when the array is already sorted</li>
<li><strong>Average Case Complexity:</strong> <code>O(n<sup>2</sup>)</code><br>
It occurs when the elements of the array are in jumbled order (neither ascending nor descending).</li>
</ul><p></p><div class="clearfix"></div><p>The time complexity of the selection sort is the same in all cases. At every step, you have to find the minimum element and put it in the right place. The minimum element is not known until the end of the array is not reached.</p>
<p><strong>Space Complexity:</strong></p>
<p>Space complexity is <code>O(1)</code> because an extra variable <code>temp</code> is used.</p>
<hr><h2 id="application">Selection Sort Applications</h2>
<p>The selection sort is used when</p>
<ul><li>a small list is to be sorted</li>
<li>cost of swapping does not matter</li>
<li>checking of all the elements is compulsory</li>
<li>cost of writing to a memory matters like in flash memory (number of writes/swaps is <code>O(n)</code> as compared to <code>O(n<sup>2</sup>)</code> of bubble sort)</li>
</ul><hr><h2>Similar Sorting Algorithms</h2>
<ol><li><a href="/dsa/bubble-sort.html">Bubble Sort</a></li>
<li><a href="/dsa/quick-sort.html">Quicksort</a></li>
<li><a href="/dsa/insertion-sort.html">Insertion Sort</a></li>
<li><a href="/dsa/merge-sort.html">Merge Sort</a></li>
</ol></div>
</div>
<div class="tutorial-toc"><div class="tutorial-toc__inner"><h3 class="tutorial-toc__title">Table of Contents
<button class="btn btn--clear align-items-center">
<svg class="programiz-icon"><use xlink:href="/sites/all/themes/programiz/assets/feather-sprite.svg#x"></use></svg></button></h3><div class="tutorial-toc__links"><ul><li><a href="#definition">Definition</a></li>
<li><a href="#working">Working of Selection Sort</a></li>
<li><a href="#algorithm">Selection Sort Algorithm</a></li>
<li><a href="#code">Selection Sort Code in Python, Java, and C/C++</a></li>
<li><a href="#complexity">Complexity</a></li>
<li><a href="#application">Applications</a></li>
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