Quick Sort

2

Quick Sort

• Divide: • Pick any element p as the pivot, e.g, the first element• Partition the remaining elements into

FirstPart, which contains all elements < pSecondPart, which contains all elements ≥ p

• Recursively sort the FirstPart and SecondPart

• Combine: no work is necessary since sorting is done in place

3

Quick Sort

x < p p p ≤ x

PartitionFirstPart SecondPart

ppivot

A:

Recursive call

x < p p p ≤ x

SortedFirstPart

SortedSecondPart

Sorted

4

Quick SortQuick-Sort(A, left, right)if left ≥ right return

else middle ← Partition(A, left,

right) Quick-Sort(A, left, middle–1 ) Quick-Sort(A, middle+1, right)

end if

5

Partitionp

p x < p p ≤ x

p p ≤ xx < p

A:

A:

A:p

6

Partition Example

A: 4 8 6 3 5 1 7 2

7

Partition Example

A: 4 8 6 3 5 1 7 2

i=0

j=1

8

Partition Example

A:

j=1

4 8 6 3 5 1 7 2

i=0

8

9

Partition Example

A: 4 8 6 3 5 1 7 26

i=0

j=2

10

Partition Example

A: 4 8 6 3 5 1 7 2

i=0

383

j=3

i=1

11

Partition Example

A: 4 3 6 8 5 1 7 2

i=1

5

j=4

12

Partition Example

A: 4 3 6 8 5 1 7 2

i=1

1

j=5

13

Partition Example

A: 4 3 6 8 5 1 7 2

i=2

1 6

j=5

14

Partition Example

A: 4 3 8 5 7 2

i=2

1 6 7

j=6

15

Partition Example

A: 4 3 8 5 7 2

i=2

1 6 22 8

i=3

j=7

16

Partition Example

A: 4 3 2 6 7 8

i=3

1 5

j=8

17

Partition Example

A: 4 1 6 7 8

i=3

2 542 3

18

A: 3 6 7 81 542

x < 4 4 ≤ x

pivot incorrect position

Partition Example

19

Partition(A, left, right)1. x ← A[left]2. i ← left3. for j ← left+1 to right4. if A[j] < x then 5. i ← i + 16. swap(A[i], A[j])7. end if8. end for j9. swap(A[i], A[left])10. return in = right – left +1

Time: cn for some constant c Space: constant

20

4 8 6 3 5 1 7 22 3 1 5 6 7 84

Quick-Sort(A, 0, 7)Partition

A:

21

2 3 1

5 6 7 84

2 1 3

Quick-Sort(A, 0, 7)Quick-Sort(A, 0, 2)

A:

, partition

22

2

5 6 7 84

1

1 3

Quick-Sort(A, 0, 7)Quick-Sort(A, 0, 0) , base case, return

23

2

5 6 7 84

1

33

Quick-Sort(A, 0, 7)Quick-Sort(A, 1, 1) , base case

24

5 6 7 842 1 3

2 1 3

Quick-Sort(A, 0, 7)Quick-Sort(A, 2, 2), returnQuick-Sort(A, 0, 2), return

25

42 1 3

5 6 7 86 7 85

Quick-Sort(A, 0, 7)Quick-Sort(A, 2, 2), returnQuick-Sort(A, 4, 7) , partition

26

4

5

6 7 87 866

2 1 3

Quick-Sort(A, 0, 7)Quick-Sort(A, 5, 7) , partition

27

4

5

6

7 887

2 1 3

Quick-Sort(A, 0, 7)Quick-Sort(A, 6, 7) , partition

28

4

5

6

7

2 1 3

Quick-Sort(A, 0, 7)Quick-Sort(A, 7, 7)

8

, return, base case

8

29

4

5

6 87

2 1 3

Quick-Sort(A, 0, 7)Quick-Sort(A, 6, 7) , return

30

4

5

2 1 3

Quick-Sort(A, 0, 7)Quick-Sort(A, 5, 7) , return

6 87

31

42 1 3

Quick-Sort(A, 0, 7)Quick-Sort(A, 4, 7) , return

5 6 87

32

42 1 3

Quick-Sort(A, 0, 7)Quick-Sort(A, 0, 7) , done!

5 6 87