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Sunday, March 23, 2014
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Example of Selection sort for Data Structure in 'C'

6:31 AMSunday, March 23, 2014

Selection sort:

            In this technique of sorting, the fact of selecting the minimum element from n (size of the array) number of elements is used. The selected minimum element is interchanged with the first element of the array. Then leaving the first element, the minimum element is again picked from the remaining n-1 elements and interchanged with the second element. The same process of selecting minimum element and interchanging it from the respective element is repeated to obtain the sorted array. In total n-1 passes are applied to obtain the sorted array. As we select the minimum element in every pass this technique of sorting the elements is called as Selection sort. Let us understand this technique with the help of an analytical example before going into the algorithm and C function. Let us consider an array of size 10 with the following elements:

                  91 18 22 43 34 10 88 11 33 77
We can observe the elements and see that the elements are not in order. So to arrange the elements in ascending order we can apply the selection sort. 

In the first pass, we select the minimum element from the 10 elements as 10 with index 6. Interchange the element 10 with the element 91 (first element of the array). After this pass the array looks as follows:
                 10 18 22 43 34 91 88 11 33 77
In the second pass, we select the minimum element from 9 elements leaving the first element (as it is already sorted) as 11 with index 8. Interchange the element 11 with 18 (second element of the array). After this pass the array looks as follows:
                  10 11 22 43 34 91 88 18 33 77
In the third pass, we select the minimum element from 8 elements leaving the first two elements (as they are already sorted) as 18 with index 8. Interchange the element 18 with 22 (third element of the array). After this pass the array looks as follows:
                   10 11 18 43 34 91 88 22 33 77
In the fourth pass, we select the minimum element from 7 elements leaving the first three elements (as they are already sorted) as 22 with index 8. Interchange the element 22 with 43 (fourth element of the array). After this pass the array looks as follows:
                     10 11 18 22 34 91 88 43 33 77
 In the fifth pass, we select the minimum element from 6 elements leaving the first four elements (as they are already sorted) as 33 with index 9. Interchange the element 33 with 34 (fifth element of the array). After this pass the array looks as follows:
                      10 11 18 22 33 91 88 43 34 77
In the six pass, we select the minimum element from 5 elements leaving the first five elements (as they are already sorted) as 34 with index 9. Interchange the element 34 with 91 (sixth element of the array). After this pass the array looks as follows:
                       10 11 18 22 33 34 88 43 91 77
In the seventh pass, we select the minimum element from 4 elements leaving the first six elements (as they are already sorted) as 43 with index 8. Interchange the element 43 with 88 (seventh element of the array). After this pass the array looks as follows:
                       10 11 18 22 33 34 43 88 91 77
In the eighth pass, we select the minimum element from 3 elements leaving the first seven elements (as they are already sorted) as 77 with index 10. Interchange the element 77 with 88 (eighth element of the array). After this pass the array looks as follows:
                        10 11 18 22 33 34 43 77 91 88
In the ninth pass, we select the minimum element from 2 elements leaving the first three elements (as they are already sorted) as 88 with index 10. Interchange the element 77 with 91 (ninth element of the array). After this pass the array looks as follows:
                         10 11 18 22 33 34 43 77 88 91
The ninth pass is the last pass. We can observe from the last pass that after that pass we remain with the largest element of the array and is placed at its proper place. That is why we require only n-1 in this case 9 passes to sort the array.

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