Sorting Algorithms: Understanding the Basics and Importance, Slides of Data Structures and Algorithms

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Introduction to Sorting

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What is 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 }

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Types of Sorting Algorithms

There are many, many different types of sorting

algorithms, but the primary ones are:

● Bubble Sort ● Selection Sort ● Insertion Sort ● Merge Sort ● Shell Sort ● Heap Sort

● Quick Sort ● Radix Sort ● Swap Sort

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Review of Complexity

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.

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●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).

O(n), Ω(n), & Θ(n)

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Common Big-Oh’s

Time complexity Example O(1) constant Adding to the front of a linked list O(log N ) log^ Finding an entry in a sorted array O( N^ ) linear^ Finding an entry in an unsorted array O( N log N ) n-log-n Sorting n items by ‘divide-and-conquer’ O( N 2 ) quadratic Shortest path between two nodes in a graph O( N 3 ) cubic Simultaneous linear equations

(Binary) Finding 8:

9

50

22

21

8

5

1

(Linear) Finding 8:

9

50

22

21

8

5

Front 1 Initial: Final: 63

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

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)

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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

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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

Bob

Ann

Joe

Zöe

Dan

Pat

Sam

original array

Bob

Ann

Joe

Zöe

Dan

Pat

Sam

unstably sorted

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

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&

rio.ecs.umass.edu/ece242/slides/lect-sorting.ppt^5 7 8 10 20 Docsity.com

Insert Action: i=

temp

i = 1, first iteration

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

Insert Action: i=

temp

5

i = 2, second iteration

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

Insert Action: i=

temp

i = 4, forth iteration

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