Introduction to Sorting

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# Introduction to Sorting - PowerPoint PPT Presentation

By Saad Malik. Introduction to Sorting. Sorting: an operation that segregates items into groups according to specified criterion. A = { 3 1 6 2 1 3 4 5 9 0 } A = { 0 1 1 2 3 3 4 5 6 9 }. What is Sorting?. Consider : Sorting Books in Library (Dewey system)

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Sorting: an operation that segregates items into groups according to specified criterion.

A = { 3 1 6 2 1 3 4 5 9 0 }

A = { 0 1 1 2 3 3 4 5 6 9 }

What is Sorting?

Consider:

Sorting Books in Library (Dewey system)

Sorting Individuals by Height (Feet and Inches)

Sorting Movies in Blockbuster (Alphabetical)

Sorting Numbers (Sequential)

Why Sort and Examples
There are many, many different types of sorting algorithms, but the primary ones are: Types of Sorting Algorithms
• Bubble Sort
• Selection Sort
• Insertion Sort
• Merge Sort
• Shell Sort
• Heap Sort
• Quick Sort
• Swap Sort

Most of the primary sorting algorithms run on different space and time complexity.

Time Complexity is defined to be the time the computer takes to run a program (or algorithm in our case).

Space complexity is defined to be the amount of memory the computer needs to run a program.

Review of Complexity

Complexity in general, measures the algorithms efficiency in internal factors such as the time needed to run an algorithm.

External Factors (not related to complexity):

Size of the input of the algorithm

Speed of the Computer

Quality of the Compiler

Complexity (cont.)
O(n), Ω(n), & Θ(n)
• An algorithm or function T(n) is O(f(n)) whenever T(n)\'s rate of growth is less than or equal to f(n)\'s rate.
• An algorithm or function T(n) is Ω(f(n)) whenever T(n)\'s rate of growth is greater than or equal to f(n)\'s rate.
• An algorithm or function T(n) is Θ(f(n)) if and only if the rate of growth of T(n) is equal to f(n).

Time complexity

Example

constant

O(1)

N

log

O(log

)

Finding an entry in a sorted array

N

linear

O(

)

Finding an entry in an unsorted array

N

N

n-log-n

O(

log

)

Sorting n items by ‘divide-and-conquer’

2

N

O(

)

Shortest path between two nodes in a graph

3

N

cubic

O(

)

Simultaneous linear equations

1

1

5

5

8

8

(Binary) Finding 8:

(Linear) Finding 8:

9

9

21

21

22

22

50

50

Common Big-Oh’s

Front

Initial:

1

0

Final:

6

3

http://www.cs.sjsu.edu/faculty/lee/cs146/23FL3Complexity.ppt

Big-Oh to Primary Sorts
• Bubble Sort = n²
• Selection Sort = n²
• Insertion Sort = n²
• Merge Sort = n log(n)
• Quick Sort = n log(n)
Time Efficiency
• How do we improve the time efficiency of a program?
• The 90/10 Rule

90% of the execution time of a program is spent in

executing 10% of the code

• So, how do we locate the critical 10%?
• software metrics tools
• global counters to locate bottlenecks (loop executions,

function calls)

Time Efficiency Improvements

Possibilities (some better than others!)

• Move code out of loops that does not belong there

(just good programming!)

• Remove any unnecessary I/O operations (I/O operations

are expensive time-wise)

• Code so that the compiled code is more efficient

Moral - Choose the most appropriate algorithm(s) BEFORE

program implementation

Ann

98

Ann

98

Bob

90

Joe

98

Dan

75

Bob

90

Joe

98

Sam

90

Pat

86

Pat

86

Sam

90

Zöe

86

Zöe

86

Dan

75

original array

stably sorted

Stable sort algorithms
• A stable sort keeps equal elements in the same order
• This may matter when you are sorting data according to some characteristic
• Example: sorting students by test scores

www.cis.upenn.edu/~matuszek/cit594-2002/ Slides/searching.ppt

Ann

98

Joe

98

Bob

90

Ann

98

Dan

75

Bob

90

Joe

98

Sam

90

Pat

86

Zöe

86

Sam

90

Pat

86

Zöe

86

Dan

75

original array

unstably sorted

Unstable sort algorithms
• An unstable sort may or may not keep equal elements in the same order
• Stability is usually not important, but sometimes it is important

www.cis.upenn.edu/~matuszek/cit594-2002/ Slides/searching.ppt

Selection Sorting

Step:

• 1. select the smallest element
• among data[i]~ data[data.length-1];
• 2. swap it with data[i];
• 3. if not finishing, repeat 1&2

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rio.ecs.umass.edu/ece242/slides/lect-sorting.ppt

Pseudo-code for Insertion Sorting
• Place ith item in proper position:
• temp = data[i]
• shift those elements data[j] which greater than temp to right by one position
• place temp in its proper position

rio.ecs.umass.edu/ece242/slides/lect-sorting.ppt

Insert Action: i=1

temp

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i = 1, first iteration

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---

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rio.ecs.umass.edu/ece242/slides/lect-sorting.ppt

Insert Action: i=2

temp

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i = 2, second iteration

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rio.ecs.umass.edu/ece242/slides/lect-sorting.ppt

Insert Action: i=3

temp

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i = 3, third iteration

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rio.ecs.umass.edu/ece242/slides/lect-sorting.ppt

Insert Action: i=4

temp

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i = 4, forth iteration

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---

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rio.ecs.umass.edu/ece242/slides/lect-sorting.ppt

Sorting Webpage

http://www.cs.ubc.ca/spider/harrison/Java/sorting-demo.html