Quick sort

1. Quick Sort Analysis
3 3 3 3 3
J,i Pivot i+1 x
Worst case
q = Partion(A,p,r) …….> cn
Quicksort(A,p,q-1)--
Quicksort(A, q+1,r) 1,2 3,4,5
1
4,3,2,5
4,3,2 5
3
2
4
3,4
cn
cn
cn
cn
n-1 + n-2 +n-3 +n-4……………1 = O(n^2)

2. Merge Sort
7 3 2 16 20 24 5 9
2 3 5 7 9 16 20 24
7 3 2 16
2 3 7 16
20 24 5 9
5 9 20 24
7 3
3 7
i
5 9
5 9
i j
20 24
20 24
i j
2 16
2 16
j
7 ∞
i
2
i
16
j
20
i
24
j
5
i
9
j
3 ∞
j

3. 2 3 7 16
i
5 9 20 24
j
2 3 5 7 9 16 20 24
1 2 3 4 5 6 7 8
p q
=floor
(
p+r/2)
L R
A

4. Merge(A,p,q,r)
{
n1 = q-p+1
n2 = r-q
Let L[1…n1+1 ] and R [1
to n2 +1] be new arrays
for(i=1 to n1)
L[i] = A[p+i-1]
for (j=1 to n2)
R[j] =A[q+j]
L[n1+1] = ∞
R[n2+1]= ∞
i=1 ; j=1
for (k=p to r)
if(L[i]<= R[j]
A[k] =L[i]
i= i+1
else
A[k] =R[j]
j=j+1
}
2 3 7 16
i
5 9 20 24
j
2 3 5 7 9 16 20 24
1 2 3 4 5 6 7 8
p q
=floor
(
p+r/2)
L R
A

5. Mergesort (A,p,r)
{
If p<r
q = floor((p+r)/2)
mergesort(A,p,q)
mergesort(A,q+1,r)
merge(A,p,q,r)
}