Selection sort(sorting algorithm in data structure) and its time complexity

Selection sort
Presented by ASMITA
26/01/18
1

SORTING Algorithm
In computer science, a sorting algorithm is an
algorithm that puts elements of a list in a certain
order.
2

SELECTION SORT
 Selection sorting is conceptually the most simplest sorting
algorithm.
 This algorithm first finds the smallest element in the array
and exchanges it with the element in the first position, then
find the second smallest element and exchange it with the
element in the second position, and continues in this way
until the entire array is sorted.
 Keep doing n-1 times to place all n values in the sorted order.
3

How selection sorting works?
4

Selection sort
 input A sequence of n numbers <a1, a2,…..an>
 Output A reordering <a1,a2,….an>of the input sequences
such that a1<a2<a3…..<an
 Idea behind selection sort
Left hand Right hand
9 3 6 4 33
9 3 6 4 3 4
9 3 6 4 3 4 6
9 3 6 4 3 4 6 9
6

Pseudo-code for selection sort
 Selection sort(A) A[1….N]
 For i=1 to A.lenght-1
 {
 MIN=i
 For j=i + 1 to A.lenght
 {
 If (A[j] <A[MIN])
 {
 MIN= j
 }
 } // MIN.elements to its correct position
 Temp = A[i]
 A[i] =A[MIN]
 A[MIN] =temp
 }
6 3 1 2
1 2 3 4
i =1 j=2
MIN
1
7

 {
 MIN=I
 {
 {
 MIN= j
 }
6 3 1 2
1 2 3 4
i =1 j=2
MIN
1
6 3 1 2
1 2 3 4
i=1 j=3
MIN
2
6 3 1 2
1 2 3 4
i =1 j=4
MIN
3
If (A[j] <A[MIN]) If (A[j] <A[MIN])
3<6 1<3
9

 {
 MIN=i
 {
 {
 MIN= j
 }
1 2 3 4
i =2 j=3
MIN
2
1 2 3 4
i =2 j=3
MIN
2
1 2 3 4
i =2 j=5
MIN
4
If (A[j] <A[MIN]) If (A[j] <A[MIN])
6<3 2<3
1 3 6 2 1 3 6 21 3 6 2
10

 {
 MIN=i
 {
 {
 MIN= j
 }
1 2 3 4
i =3 j=4
MIN
3
1 2 3 4
i =3 j=5
MIN
4
1 2 3 4
MIN
4
If (A[j] <A[MIN])
3<6
1 2 6 3 1 2 3 61 2 6 3
11

Time complexity of selection sort
 Selection sort(A) A[1….N] cost times
 For i=1 to A.lenght-1 c1 n
 {
 MIN=I c2 n-1
 {
 { c3 n+n-1+…..1 // 2 n=n
 MIN= j = n(n+1)/2 3 n=n-1
 } 4 n=n-2
 } n-1 n=1
 Temp = A[i] c4 n-1
 A[i] =A[MIN] c5 n-1
 A[MIN] =temp c6 n-1
 }
12

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