Computer Science II

1
Computer Science II

• Sorting

2
Some Sorting Methods

• Insertion sort
• Bubble sort
• Quicksort
• Merge sort

3
Insertion Sort

• Begins with an unsorted sequence of elements
  Ss0,s1,...,sn
• Adds each of these elements, one at a time, to a
  new sequence S, searching through the new list
  to determine the place to insert the new element

4
Insertion SortHow to do it
C
A
D
B
5
Insertion SortHow to do it
C
A
D
B

• Insert C

C
A
D
B
6
Insertion SortHow to do it
C
A
D
B

• Insert C
• Insert A, moving C down

C
A
D
B
A
C
D
B
7
Insertion SortHow to do it
C
A
D
B

• Insert C
• Insert A, moving C down
• Insert D

C
A
D
B
A
C
D
B
A
C
D
B
8
Insertion SortHow to do it
C
A
D
B

• Insert C
• Insert A, moving C down
• Insert D
• Insert B, moving C and D down

C
A
D
B
A
C
D
B
A
C
D
B
A
B
C
D
9
Bubble Sort

• Exchange sorting algorithm
• Moves larger elements up through array, by
  swapping adjacent elements that are out of
  order
• Each pass through the array bubbles the next
  largest element up to the slot it should occupy

10
Bubble SortHow to do it
C
A
D
B
11
Bubble SortHow to do it
C
A
D
B
A
C
B
D

• Swap C-A and D-B

12
Bubble SortHow to do it
C
A
D
B
A
C
B
D

• Swap C-A and D-B
• Swap C-B

A
B
C
D
13
Bubble SortHow to do it
C
A
D
B
A
C
B
D

• Swap C-A and D-B
• Swap C-B
• No swap

A
B
C
D
A
B
C
D
14
Bubble SortHow to do it
C
A
D
B
A
C
B
D

• Swap C-A and D-B
• Swap C-B
• No swap
• Last element, so were done!

A
B
C
D
A
B
C
D
A
B
C
D
15
Quicksort

• Exchange sorting algorithm
• Divide and conquer!
• A each stage, choose a pivot element, and
• Divide the remaining elements into those less
  than the pivot, and those greater than the pivot

16
Quicksort(A,p,r)

• 1. if p lt r
• 2. then q lt- Partition(A,p,r)
• 3. Quicksort(A,p,q)
• Quicksort(A,q1,r)
• Yes, this is recursive!

17
Partition(A,p,r)

• x lt- Ap
• i lt- p-1
• j lt- r1
• repeat
• repeat
• j lt- j - 1
• until Aj lt x
• repeat
• i lt- i 1
• until Ai gt x
• if iltj
• then Ai lt-gt Aj
• until i gt j
• return j

18
Paritition( )Example 1
A
F
J
D
E
G
C
H
1 2 3 4 5 6 7 8
0
9
Start
C
X
19
Paritition( )Example 1
A
F
J
D
E
G
C
H
1 2 3 4 5 6 7 8
0
9
J loop
C
X
20
Paritition( )Example 1
A
F
J
D
E
G
C
H
1 2 3 4 5 6 7 8
0
9
J loop
C
X
21
Paritition( )Example 1
A
F
J
D
E
G
C
H
1 2 3 4 5 6 7 8
0
9
J loop
C
X
22
Paritition( )Example 1
A
F
J
D
E
G
C
H
1 2 3 4 5 6 7 8
0
9
J loop
C
X
23
Paritition( )Example 1
A
F
J
D
E
G
C
H
1 2 3 4 5 6 7 8
0
9
J loop
C
X
24
Paritition( )Example 1
A
F
J
D
E
G
C
H
1 2 3 4 5 6 7 8
0
9
J loop
C
X
25
Paritition( )Example 1
A
F
J
D
E
G
C
H
1 2 3 4 5 6 7 8
0
9
I loop
C
X
26
Paritition( )Example 1
C
F
J
D
E
G
A
H
1 2 3 4 5 6 7 8
0
9
Swap
C
X
27
Paritition( )Example 1
C
F
J
D
E
G
A
H
1 2 3 4 5 6 7 8
0
9
J loop
C
X
28
Paritition( )Example 1
C
F
J
D
E
G
A
H
1 2 3 4 5 6 7 8
0
9
I loop
C
X
29
Paritition( )Example 1
G
F
J
D
E
C
A
H
1 2 3 4 5 6 7 8
0
9
Swap
C
X
30
Paritition( )Example 1
G
F
J
D
E
C
A
H
1 2 3 4 5 6 7 8
0
9
J Loop
C
X
31
Paritition( )Example 1
G
F
J
D
E
C
A
H
1 2 3 4 5 6 7 8
0
9
I Loop
C
X
32
Paritition( )Example 1
G
F
J
D
E
C
A
H
1 2 3 4 5 6 7 8
0
9
Done!
C
X
33
Partition(A,p,r)

• x lt- Ar
• i lt- p
• j lt- r -1
• repeat
• do while (i lt j) and (Ai lt x)
• do i lt- i 1
• while (i lt j) and (Aj gt x)
• do j lt- j 1
• if i lt j
• then Ai lt-gt Aj
• until i gt j

34
Paritition( )Example 2
A
F
J
H
E
G
C
D
1 2 3 4 5 6 7 8
Start
X
35
Paritition( )Example 2
A
F
J
H
E
G
C
D
1 2 3 4 5 6 7 8
Hide pivot
D
X
36
Paritition( )Example 2
A
F
J
H
E
G
C
D
1 2 3 4 5 6 7 8
I loop
D
X
37
Paritition( )Example 2
A
F
J
H
E
G
C
D
1 2 3 4 5 6 7 8
J loop
D
X
38
Paritition( )Example 2
A
F
J
H
E
G
C
D
1 2 3 4 5 6 7 8
J loop
D
X
39
Paritition( )Example 2
A
F
J
H
E
G
C
D
1 2 3 4 5 6 7 8
J loop
D
X
40
Paritition( )Example 2
A
F
J
H
E
G
C
D
1 2 3 4 5 6 7 8
J loop
D
X
41
Paritition( )Example 2
G
F
J
H
E
A
C
D
1 2 3 4 5 6 7 8
Swap
D
X
42
Paritition( )Example 2
G
F
J
H
E
A
C
D
1 2 3 4 5 6 7 8
I loop
D
X
43
Paritition( )Example 2
G
F
J
H
E
A
C
D
1 2 3 4 5 6 7 8
J loop
D
X
44
Paritition( )Example 2
G
D
J
H
E
A
C
F
1 2 3 4 5 6 7 8
Return pivot
D
X
45
Paritition( )Example 2
G
D
J
H
E
A
C
F
1 2 3 4 5 6 7 8
Done!
D
X
46
Partition ( )

• How did they the two examples differ?
• Which example was better?
• No. 1?
• No.2
• Define better

47
Merge Sort

• Divide and Conquer
• Continually merges together large and larger
  sequences

48
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
5
3
2
6
1
8
7
4

• Start with three stacks
• Place all of the elements in stack 0

49
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
5
3
2
6
1
8
7
4

• Divide elements, one at time, between stacks 1
  and 2

50
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
5
3
2
6
7
4
1
1
8
8
2
6
7
5
3
4

• Divide elements, one at time, between stacks 1
  and 2

51
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
7
4
1
8
2
6
5
3

• Merge sequences of length one back onto stack 0

52
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
7
4
7
1
8
2
6
7
5
3
4

• Merge sequences of length one back onto stack 0

53
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
8
1
8
1
2
6
7
5
3
4

• Merge sequences of length one back onto stack 0

54
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
6
2
8
1
2
6
7
5
3
4

• Merge sequences of length one back onto stack 0

55
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
5
3
6
2
8
1
7
5
3
4

• Merge sequences of length one back onto stack 0

56
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
5
3
6
2
8
1
7
4

• Distribute sequences of two between stacks 1 and 2

57
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
5
3
6
2
8
1
3
7
5
4

• Distribute sequences of two between stacks 1 and 2

58
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
6
2
8
1
2
3
7
6
5
4

• Distribute sequences of two between stacks 1 and 2

59
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
1
8
8
1
2
3
7
6
5
4

• Distribute sequences of two between stacks 1 and 2

60
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
4
1
7
8
2
3
7
6
5
4

• Distribute sequences of two between stacks 1 and 2

61
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
4
1
7
8
2
3
6
5

• Merge sequences of two back onto stack 0

62
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
4
1
8
7
8
7
2
3
4
6
5
1

• Merge sequences of two back onto stack 0

63
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
6
5
3
2
8
7
2
3
4
6
5
1

• Merge sequences of two back onto stack 0

64
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
6
5
3
2
8
7
4
1

• Distribute sequences of four between stacks 1 and
  2

65
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
6
5
3
2
8
2
7
3
4
5
1
6

• Distribute sequences of four between stacks 1 and
  2

66
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
8
2
1
7
3
4
4
5
7
1
6
8

• Distribute sequences of four between stacks 1 and
  2

67
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
2
1
3
4
5
7
6
8

• Merge sequences of four back onto stack 0

68
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
6
5
2
1
4
3
4
3
5
7
2
6
8
1

• Merge sequences of four back onto stack 0

69
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
8
7
6
5
4
3
7
2
8
1

• Merge sequences of four back onto stack 0

70
Merge SortHow to do it
Stack 0
Stack 1
Stack 2
8
7
6
5
4
3
2
1

• Done!

71
Try this!

• Write a program to sort the following sequence of
  numbers using merge sort.
• 1 7 5 6 4 2 3 0