**Solution:**

Question No. 01: The name of the algorithm being used for sorting the given array has given below.

Selection sort

Question No. 02: The Pseudo code for the algorithm used for sorting the given array has given below.

Pseudo code:

1 Selection sort (A)

{

2 For i 1 to A.lenght-1

{

3 imin i

4 for j i+1 to A.length

{

5 If (A[j] < A[imin])

Imin j

}

6 Temp A[i]

7 A[i] A[imin]

8 A[imin] Temp

}

}

Question No. 03: The step by stem analysis of the algorithm designed in question 2 is as follow,

The time taken by each statement (step) is given as follows,

b8c2d4d9-76e3-4841-94a7-e8c1a8202f51-image.png

Selection sort (A)
Cost
Times

{

For i 1 to A.length-1 |c1 | n

{

imin i--------------------> c2 n-1

for j i+1 to A.length

{ c3 n+n-1+…1=n(n+1)/2

If (A[j] < A[imin])

imin j

}

Temp A[i] c4 n-1

A[i] A[imin] c5 n-1

A[imin] Temp c6 n-1

}

}

Total time T(n) can be calculated as follows,

T(n)= c1n+c2(n-1)+c3(n(n+1)/2)+c4(n-1)+c5(n-1)+c6(n-1)

c1n+c2n-c2+c3 (n2+n/2) +c4n-c4+c5n-c5+c6n-c6 collect the like terms

c3n2/2+ (c1+c2+c3/2+c4+c5+c6) n + (-c2-c4-c5-c6)

This is equivalent to a polynomial an2+bn+c

Therefore T (n) = Big O (n2) by taking the highest order term of the equation.

Note: a, b, c in polynomial represents constants

// Ignoring constant terms

T(n) = O (n2)