30.%20Sorting%201-dimensional%20Arrays - PowerPoint PPT Presentation

About This Presentation

Title:

30.%20Sorting%201-dimensional%20Arrays

Description:

30. Sorting 1-dimensional Arrays Bubble Sort Insertion Sort – PowerPoint PPT presentation

Number of Views:64

Avg rating:3.0/5.0

Slides: 41

Provided by: VanL98

Learn more at: https://www.cs.cornell.edu

Category:

more less

Transcript and Presenter's Notes

Title: 30.%20Sorting%201-dimensional%20Arrays

1
30. Sorting 1-dimensional Arrays

Bubble Sort
Insertion Sort

2
Searching for an item in an unorganized
collection?

May need to look through the whole collection to
find the target item
E.g., find value x in vector v
Linear search

f is index of first occurrence
of value x in vector v.
f is -1 if x not found.
k 1while kltlength(v) v(k)x k k
1
end
if kgtlength(v) f -1 signal for x not
foundelse f k
end

Linear Search f is index of first occurrence
of value x in vector v.
f is -1 if x not found.
k 1while kltlength(v) v(k)x k k
1
end
if kgtlength(v) f -1 signal for x not
foundelse f k
end

12
15
35
33
42
45
v
x
31
5

Linear Search f is index of first occurrence
of value x in vector v.
f is -1 if x not found.
k 1while kltlength(v) v(k)x k k
1
end
if kgtlength(v) f -1 signal for x not
foundelse f k
end

Linear Search f is index of first occurrence
of value x in vector v.
f is -1 if x not found.
k 1while kltlength(v) v(k)x k k
1
end
if kgtlength(v) f -1 signal for x not
foundelse f k
end

12
15
35
33
42
45
v
x
31
7

Linear Search f is index of first occurrence
of value x in vector v.
f is -1 if x not found.
k 1while kltlength(v) v(k)x k k
1
end
if kgtlength(v) f -1 signal for x not
foundelse f k
end

45
v
x
31
What if v is sorted?
8
Sorting data allows us to search more easily
2008 Boston Marathon Top Women Finishers
Place Bib Name Official Time State Country Ctz
1 F7 Tune, Dire 22525 ETH
2 F8 Biktimirova, Alevtina 22527 RUS
3 F4 Jeptoo, Rita 22634 KEN
4 F2 Prokopcuka, Jelena 22812 LAT
5 F5 Magarsa, Askale Tafa 22948 ETH
6 F9 Genovese, Bruna 23052 ITA
7 F12 Olaru, Nuta 23356 ROM
8 F6 Guta, Robe Tola 23437 ETH
9 F1 Grigoryeva, Lidiya 23537 RUS
10 F35 Hood, Stephanie A. 24444 IL USA CAN
11 F14 Robson, Denise C. 24554 NS CAN
12 F11 Chemjor, Magdaline 24625 KEN
13 F101 Sultanova-Zhdanova, Firaya 24717 FL USA RUS
14 F15 Mayger, Eliza M. 24736 AUS
15 F24 Anklam, Ashley A. 24843 MN USA
Name Score Grade
Jorge 92.1
Ahn 91.5
Oluban 90.6
Chi 88.9
Minale 88.1
Bell 87.3
9
The bubble process
30
50
10
60
40
Compare adjacent values. Swap if out of order.
20
10
The bubble process
30
50
10
60
Compare adjacent values. Swap if out of order.
20
40
11
The bubble process
30
50
10
Compare adjacent values. Swap if out of order.
20
60
40
12
The bubble process
30
50
Compare adjacent values. Swap if out of order.
10
20
60
40
13
The bubble process
30
Compare adjacent values. Swap if out of order.
10
50
20
60
40
14
The bubble process
10
The smallest (lightest) value bubbles to the
top Done in one pass through the vector
30
50
20
60
40
Bubble.m
15
The second bubble process
10
30
50
20
60
Compare adjacent values. Swap if out of order.
40
16
The second bubble process
10
30
50
20
Compare adjacent values. Swap if out of order.
40
60
17
The second bubble process
10
30
50
Compare adjacent values. Swap if out of order.
20
40
60
18
The second bubble process
10
30
Compare adjacent values. Swap if out of order.
20
50
40
60
19
The second bubble process
10
After two bubble processes, the first two
components are sorted. Repeatedly apply the
bubble process to sort the whole array
20
30
50
40
60
20
Sort vector x using the Bubble Sort algorithm
x
Apply Bubble to x x,C,S Bubble(x)
21
Sort vector x using the Bubble Sort algorithm
x
Bubble x x,C,S Bubble(x)
Bubble x(26) x(26),C,S Bubble(x(26))
Bubble x(36) x(36),C,S Bubble(x(36))
Bubble x(46) x(46),C,S Bubble(x(46))
Bubble x(56) x(56),C,S Bubble(x(56))
BubbleSort1.m
22
Possible to get a sorted vector before n-1
bubble processes
10
After 2 bubble processes Start 3rd bubble
process
20
30
50
40
60
23
Possible to get a sorted vector before n-1
bubble processes
10
In the 3rd bubble process
20
30
50
40
60
24
Possible to get a sorted vector before n-1
bubble processes
10
In the 3rd bubble process
20
30
40
50
60
25
Possible to get a sorted vector before n-1
bubble processes
After the 3rd bubble process Vector is
completely sorted (in this example) How to
improve BubbleSort to quit early?
10
20
30
40
50
60
26
Possible to get a sorted vector before n-1
bubble processes
After the 3rd bubble process Vector is
completely sorted (in this example) How to
improve BubbleSort to quit early?
10
20
30
40
50
60
Keep track of the swaps! No swap is done when
vector is sorted.
BubbleSort.m
27
The Insertion Process

Given a sorted array x, insert a number y such
that the result is sorted

2
3
6
9
8
28
Insertion
2
3
6
9
8
Just swap 8 9
29
Insertion
2
3
6
9
8
2
3
6
9
8
2
3
6
9
8
30
Insertion
2
3
6
9
8
2
3
6
9
8
Compare adjacent components swap 9 4
4
2
3
6
9
8
31
Insertion
2
3
6
9
8
2
3
6
9
8
4
2
3
6
9
8
Compare adjacent components swap 8 4
2
3
6
9
8
4
32
Insertion
2
3
6
9
8
2
3
6
9
8
4
2
3
6
9
8
2
3
6
9
8
4
Compare adjacent components swap 6 4
2
3
6
9
8
4
33
Insertion
2
3
6
9
8
2
3
6
9
8
4
2
3
6
9
8
2
3
6
9
8
4
2
3
6
9
8
4
Compare adjacent components DONE! No more swaps.
2
3
6
9
8
4
Insert.m
34
Sort vector x using the Insertion Sort algorithm
Need to start with a sorted subvector. How do
you find one?
x
Length 1 subvector is sorted
Insert x(2) x(12),C,S Insert(x(12))
Insert x(3) x(13),C,S Insert(x(13))
Insert x(4) x(14),C,S Insert(x(14))
Insert x(5) x(15),C,S Insert(x(15))
Insert x(6) x(16),C,S Insert(x(16))
InsertionSort.m
35
Bubble Sort vs. Insertion Sort

Both involve comparing adjacent values and swaps
On average, which is more efficient?

36
Other efficiency considerations

Worst case, best case, average case
Use of subfunction incurs an overhead
Memory use and access
Example Rather than directing the insert
process to a subfunction, have it done in-line.
Also, Insertion sort can be done in-place,
i.e., using only the memory space of the
original vector.