{"id":96947,"date":"2021-06-17T09:00:42","date_gmt":"2021-06-17T03:30:42","guid":{"rendered":"https:\/\/data-flair.training\/blogs\/?p=96947"},"modified":"2021-06-26T19:29:24","modified_gmt":"2021-06-26T13:59:24","slug":"selection-sort","status":"publish","type":"post","link":"https:\/\/data-flair.training\/blogs\/selection-sort\/","title":{"rendered":"Selection Sort in Data Structure"},"content":{"rendered":"<p>Selection sort is a simple sorting where the control searches for the smallest element and puts it in the first index. In each iteration, it searches for the smallest element and puts it in its correct final position. The position of sorted elements does not change after swapping.<\/p>\n<ul>\n<li>Selection sort is an unstable algorithm<\/li>\n<li>Modification of Selection sort is possible to be a stable algorithm.<\/li>\n<\/ul>\n<h4>Procedure for Selection Sort<\/h4>\n<p>1. Swap the first element with the smallest element in the array. We have now n-1 elements to sort<\/p>\n<p>2. Find the smallest element in array from array[1] to array [n-1] and swap it with the second position<\/p>\n<p>3. For the next element, find the smallest element in the remaining array and swap it.<\/p>\n<h4>Selection Sort Algorithm<\/h4>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">Step 1:  for k = 1 to n-1\r\nstep 2: set small = arr[k]\r\nstep 3: set pos = k\r\nstep 4: repeat for j = k+1 to n -1\r\n             if small &gt; arr[j]\r\n             set small = arr[j]\r\n             set pos = j\r\n            [end of if]\r\n            [end of loop]\r\nstep 5: swap a[k] with arr[pos]\r\n            [end of loop]\r\nstep 6: Stop\r\n\r\n<\/pre>\n<h4>Pseudocode for Selection Sort<\/h4>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">selectionSort(array):\r\n     for i=0 to length(array):\r\n     Minimum element  = array[0]\r\n           for each unsorted elements:\r\n                   if element &lt; Minimum element\r\n           element = new minimum\r\n      swap minimum element with first unsorted position\r\nend selectionSort<\/pre>\n<h4>Working of Selection Sort<\/h4>\n<p>Let\u2019s Sort the following array by the insertion sort technique.<\/p>\n<p><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Selection_Sort_Example.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-97028\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Selection_Sort_Example.png\" alt=\"Selection Sort Example\" width=\"402\" height=\"42\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Selection_Sort_Example.png 402w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Selection_Sort_Example-300x31.png 300w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Selection_Sort_Example-150x16.png 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Selection_Sort_Example-320x33.png 320w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/a><\/p>\n<p>1st Iteration:<\/p>\n<p><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Selection-SOrt-First-Iteration.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-97029\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Selection-SOrt-First-Iteration.png\" alt=\"Selection Sort First Iteration\" width=\"402\" height=\"103\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Selection-SOrt-First-Iteration.png 402w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Selection-SOrt-First-Iteration-300x77.png 300w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Selection-SOrt-First-Iteration-150x38.png 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Selection-SOrt-First-Iteration-320x82.png 320w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/a><\/p>\n<p>2nd Iteration:<\/p>\n<p><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-2-Selection-SOrt.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-97030\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-2-Selection-SOrt.png\" alt=\"Iteration 2 Selection Sort\" width=\"402\" height=\"103\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-2-Selection-SOrt.png 402w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-2-Selection-SOrt-300x77.png 300w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-2-Selection-SOrt-150x38.png 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-2-Selection-SOrt-320x82.png 320w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/a><\/p>\n<p>3rd Iteration:<\/p>\n<p><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-3.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-97031\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-3.png\" alt=\"Iteration 3\" width=\"402\" height=\"66\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-3.png 402w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-3-300x49.png 300w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-3-150x25.png 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-3-320x53.png 320w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/a><\/p>\n<p>4th Iteration:<\/p>\n<p><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-4-Selection-Sort.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-97032\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-4-Selection-Sort.png\" alt=\"Iteration 4 Selection Sort\" width=\"402\" height=\"66\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-4-Selection-Sort.png 402w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-4-Selection-Sort-300x49.png 300w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-4-Selection-Sort-150x25.png 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-4-Selection-Sort-320x53.png 320w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/a><\/p>\n<p>5th Iteration:<\/p>\n<p><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-5.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-97033\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-5.png\" alt=\"Iteration 5\" width=\"402\" height=\"101\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-5.png 402w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-5-300x75.png 300w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-5-150x38.png 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-5-320x80.png 320w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/a><\/p>\n<p>6th Iteration:<\/p>\n<p><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-6.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-97034\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-6.png\" alt=\"Iteration 6\" width=\"402\" height=\"101\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-6.png 402w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-6-300x75.png 300w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-6-150x38.png 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-6-320x80.png 320w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/a><\/p>\n<p>7th Iteration:<\/p>\n<p><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-7.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-97035\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-7.png\" alt=\"Iteration 7\" width=\"402\" height=\"101\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-7.png 402w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-7-300x75.png 300w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-7-150x38.png 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-7-320x80.png 320w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/a><\/p>\n<p>8th Iteration:<\/p>\n<p><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-8.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-97036\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-8.png\" alt=\"Iteration 8\" width=\"402\" height=\"42\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-8.png 402w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-8-300x31.png 300w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-8-150x16.png 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/06\/Iteration-8-320x33.png 320w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/a><\/p>\n<p>In the above example, we can see the change in the order of three elements with the same value of \u20189\u2019 after sorting. Hence we can conclude that selection sort is not a stable algorithm.<\/p>\n<h4>Selection sort implementation in C<\/h4>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">#include&lt;stdio.h&gt;  \r\nint smallest_element(int[],int,int); \r\n\r\nvoid main ()  \r\n{  \r\n    int a[] = {32, 6, 76, 52, 29, 11, 94, 62, 73, 81};  \r\n    int i,pos,temp;  \r\n    for(i=0;i&lt;10;i++)  \r\n    {  \r\n        pos = smallest_element(a,10,i);  \r\n        temp = a[i];  \r\n        a[i]=a[pos];  \r\n        a[pos] = temp;  \r\n    }  \r\n    printf(\"sorted array:\\n\");  \r\n    for(i=0;i&lt;10;i++)  \r\n    {  \r\n        printf(\"%d \",a[i]);  \r\n    }  \r\n}  \r\nint smallest_element(int a[], int n, int i)  \r\n{  \r\n    int smallest,position,j;  \r\n    smallest = a[i];  \r\n    position = i;  \r\n    for(j=i+1;j&lt;10;j++)  \r\n    {  \r\n        if(a[j]&lt;smallest)  \r\n        {  \r\n            smallest = a[j];  \r\n            position=j;  \r\n        }  \r\n    }  \r\n    return position;  \r\n}  \r\n<\/pre>\n<h4>Selection sort implementation C++<\/h4>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">#include&lt;iostream&gt;\r\nusing namespace std;\r\nint smallest_element(int[],int,int); \r\n\r\nint main ()  \r\n{  \r\n    int a[] = {32, 6, 76, 52, 29, 11, 94, 62, 73, 81};  \r\n    int i,pos,temp;  \r\n    for(i=0;i&lt;10;i++)  \r\n    {  \r\n        pos = smallest_element(a,10,i);  \r\n        temp = a[i];  \r\n        a[i]=a[pos];  \r\n        a[pos] = temp;  \r\n    }  \r\n    cout &lt;&lt; \"sorted array:\\n\";  \r\n    for(i=0;i&lt;10;i++)  \r\n    {  \r\n        cout &lt;&lt; \" \" &lt;&lt; a[i];  \r\n    }  \r\n}  \r\nint smallest_element(int a[], int n, int i)  \r\n{  \r\n    int smallest,position,j;  \r\n    smallest = a[i];  \r\n    position = i;  \r\n    for(j=i+1;j&lt;10;j++)  \r\n    {  \r\n        if(a[j]&lt;smallest)  \r\n        {  \r\n            smallest = a[j];  \r\n            position=j;  \r\n        }  \r\n    }  \r\n    return position;  \r\n}  \r\n<\/pre>\n<h4>Implementation of Selection Sort in JAVA<\/h4>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">public class SelectionSort \r\n{\r\n  void selectionSort(int array[]) \r\n  {\r\n    int len = array.length;\r\n\r\n    for (int j = 0; j &lt; len - 1; j++) \r\n    {\r\n      int min_pos = j;\r\n\r\n      for (int i = j + 1; i &lt; len; i++) \r\n      {\r\n\r\n        if (array[i] &lt; array[min_pos]) \r\n        {\r\n          min_pos= i;\r\n        }\r\n      }\r\n      \r\n      int temp = array[j];\r\n      array[j] = array[min_pos];\r\n      array[min_pos] = temp;\r\n    }\r\n    System.out.println(\"Sorted Array: \");\r\n    for (int i = 0; i &lt; len; i++) \r\n    {\r\n        System.out.print(array[i] +\" \");\r\n        \r\n    }\r\n    \r\n  }\r\n\r\n  public static void main(String args[]) \r\n  {\r\n    int[] array = { 32, 6, 76, 52, 29, 11, 94, 62, 73, 81 };\r\n    SelectionSort ss = new SelectionSort();\r\n    ss.selectionSort(array);\r\n    \r\n    \r\n  }\r\n}\r\n<\/pre>\n<h4>Selection sort implementation in Python<\/h4>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">def selectionSort(array, length):\r\n   \r\n    for i in range(length):\r\n        min_pos = i\r\n\r\n        for j in range(i + 1, length):\r\n         \r\n            if array[j] &lt; array[min_pos]:\r\n                min_pos = j\r\n         \r\n        (array[i], array[min_pos]) = (array[min_pos], array[i])\r\n\r\n\r\narray = [32, 6, 76, 52, 29, 11, 94, 62, 73, 81]\r\nlength = len(array)\r\nselectionSort(array, length)\r\nprint('Sorted Array:')\r\nprint(array)\r\n<\/pre>\n<h4>Complexity of Selection Sort<\/h4>\n<table>\n<tbody>\n<tr>\n<td><span style=\"font-weight: 400;\">iteration<\/span><\/td>\n<td><span style=\"font-weight: 400;\">comparisons<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">1<\/span><\/td>\n<td><span style=\"font-weight: 400;\">(n-1)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td><span style=\"font-weight: 400;\">(n-2)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">3<\/span><\/td>\n<td><span style=\"font-weight: 400;\">(n-3)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">.<\/span><\/td>\n<td><span style=\"font-weight: 400;\">.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">.<\/span><\/td>\n<td><span style=\"font-weight: 400;\">.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">.<\/span><\/td>\n<td><span style=\"font-weight: 400;\">.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">n-1<\/span><\/td>\n<td><span style=\"font-weight: 400;\">1<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Total number of comparison :<\/p>\n<p>(n-1) + (n-2) + (n-3) \u2026\u2026\u2026. + 1<\/p>\n<p>= n(n-1)\/2 \u2248 n^2 ( complexity)<\/p>\n<p><strong>1. Best Case Complexity<\/strong><\/p>\n<p>Array is already sorted.<\/p>\n<p><strong>2. Average Case Complexity<\/strong><\/p>\n<p>elements in the array are jumbled i.e. they are neither in ascending or descending order.<\/p>\n<p><strong>3. Worst-Case Complexity<\/strong><\/p>\n<p>Array is sorted in the opposite of the required order.<\/p>\n<p><strong>4. Space complexity<\/strong><\/p>\n<p>An extra variable, temp, is used to swap the variables.<\/p>\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td><b>scenario<\/b><\/td>\n<td><b>complexity<\/b><\/td>\n<\/tr>\n<tr>\n<td rowspan=\"3\"><b>Time Complexity<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Average case<\/span><\/td>\n<td><span style=\"font-weight: 400;\">O(n^<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Best case<\/span><\/td>\n<td><span style=\"font-weight: 400;\">O(n^<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Worst case<\/span><\/td>\n<td><span style=\"font-weight: 400;\">O(n^<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">)<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Space complexity<\/b><\/td>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">O(1)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>Applications of Selection Sort<\/h4>\n<p>Selection sort can be used:<\/p>\n<p>1. when a small dataset needs to be sorted<\/p>\n<p>2. in algorithms where the cost of swapping does not matter.<\/p>\n<p>3. in scenarios where there is a need to check all elements.<\/p>\n<p>4. In situations where the cost of writing in flash memory matters. It has a write\/swap complexity of O(n) while that of bubble sort is O(n^2).<\/p>\n<h3>Conclusion<\/h3>\n<p>Selection sort is an unstable algorithm that is good for sorting small datasets. Time taken by this algorithm is more but it is beneficial to scenarios where we have memory limitations. Selection sort is simple and easy to implement. In further articles, we see other sorting techniques which are based on different algorithms techniques.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Selection sort is a simple sorting where the control searches for the smallest element and puts it in the first index. In each iteration, it searches for the smallest element and puts it in&#46;&#46;&#46;<\/p>\n","protected":false},"author":7,"featured_media":97027,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24020],"tags":[24577,24579,24582,24578,24580,24581],"class_list":["post-96947","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-structure-tutorials","tag-selection-sort","tag-selection-sort-algorithm","tag-selection-sort-implementation","tag-selection-sort-in-data-structure","tag-selection-sort-pseudocode","tag-working-of-selection-sort"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Selection Sort in Data Structure - DataFlair<\/title>\n<meta name=\"description\" content=\"Learn Selection sort which is a simple sorting method. 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