Selection sort in C

In the C standard, the selection sorting technique exists where the smallest among the unsorted elements of the array is selected at each time and is then inserted into its appropriate place within the array.

Selection sort iterated through the array and only then finds the smallest element within the iterated array and swaps it with the first element within the list if it is smaller when compared to the first element.

In the next step, it again iterated throughout the array and got the second element and this process repeated until all the elements are sorted.

Selection sort in the C programming language is considered as the assaulting algorithm which works by finding the smallest number from the array and then replacing it to the very first position in the array.

The next array that is to be traversed will then start from the index position to the next position where the smallest of the elements is placed.

Consider an example where the array ‘arr’ consists of ‘n’ number of elements. It needs to be sorted by making use of ‘n-1’ selection passes.

• Pass the smallest element present within the array when found along with its index ‘position’. After doing so, then swap the arr[0] and arr[position]. This will make sure that arr[0] is sorted and we will be left with ‘n-1’ number of elements that needs to be sorted.
• After the first step, during the second pass, position of the smallest element present in the subarray arr[n - 1] will be selected. After doing so, then swap the arr[1] and arr[position]. This will make sure that arr[0] and arr[1] is sorted and we will be left with ‘n - 2’ number of elements that needs to be sorted.
• In the n - 1th pass present, the position of the smaller element will be between the index numbers arr[n - 1] and arr[n - 2] which needs to be found. Then later swap the arr[position] and arr[n - 1].

Therefore, by following the above explained process, the elements arr[0], arr[1], arr[2],...., arr[n-1] are sorted.

Algorithm for selection sort:

• Find the minimum element in the array and swap it with the element in the 1st position.
• Find the minimum element again in the remaining array[2, n] and swap it with the element at 2nd position. Now we have two elements at their correct positions.
• We have to do this n-1 times to sort the array.

E.g.:

#include<stdio.h>  
int smallest(int[],int,int);  
void main ()  
{  
int a[10] = {10, 9, 7, 101, 23, 44, 12, 78, 34, 23};  
int i,j,k,pos,temp;  
for(i=0;i<10;i++)  
{  
pos = smallest(a,10,i);  
temp = a[i];  
a[i]=a[pos];  
a[pos] = temp;  
}  
printf("\n Printing the sorted elements using selection sort \n");  
for(i=0;i<10;i++)  
{  
printf("%d\n",a[i]);  
}  
}  


int smallest(int a[], int n, int i)  
{  
int small,pos,j;  
small = a[i];  
pos = i;  
for(j=i+1;j<10;j++)  
{  
if(a[j]<small)  
{  
small = a[j];  
pos=j;  
}  
}  
return pos;  
} 

Output:

Printing the sorted elements using selection sort:
7
9
10
12
23
23
34
44
78
101

Time complexities:

• Worst case complexity: if we want to sort in ascending order and the array is in descending order then, the worst case occurs. It equates to O(n²)
• Best case complexity: best case always occurs when the array is already sorted. It equates to O(n²)
• Average case complexity: It occurs when the elements of the array are in jumbled order that is either ascending order or descending order. It equates to O(n²)

The time complexity is always the same in all three cases. At each and every step, one has to find the minimum element and should put it in the correct position.

The least or the minimum element is not known until the end of the array is reached.

Space complexity:

Space complexity is always O(1) as the temporary variable is used.

Applications:

• Selection sort is used when a small list needs to be sorted.
• It is opted when the cost of swapping does not matter.
• It can also be used when the checking of all the elements is necessary
• The cost of writing the memory matters such as the flash memory.