03 ds and algorithm session 04

8/9/2019 03 DS and Algorithm Session 04

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Data Structures and Algorithms

Session 4Ver. 1.0

Objectives

In this session, you will learn to:

Identify the algorithms that can be used to sort data

Sort data by using bubble sort

Sort data by using selection sort

Sort data by using insertion sortSort data by using shell sort


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Session 4Ver. 1.0

Sorting Data

Suppose, you have to invite your friends and relatives for

your birthday party. For this, you need to give them a call.

You are looking for the telephone number of a friend named

Steve in a telephone directory with 1, records.

!owever, the records are stored randomly and not in anyparticular order.


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Session 4Ver. 1.0

Sorting Data (Contd.)

"o search for the telephone number of your friend in such a

directory, you would need to scan each entry in the directory

in a se#uential manner.

"his would be very time consuming.

!ow can you solve this problem$


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Session 4Ver. 1.0

% simple solution to save time, and search records

efficiently is sorting.

Sorting is the process of arranging data in some pre&defined

order or se#uence. "he order can be either ascending or

descending.If the data is ordered, you can directly go to the section that

stores the names starting with 'S(, thereby reducing the

number of records to be traversed.

Sorting Data (Contd.)


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Session 4Ver. 1.0

Sorting is implemented in a program by using an algorithm.

Some sorting algorithms are:

)ubble sort

Selection sort

Insertion sortShell sort

*erge sort

+uick sort

!eap sort

"o select an appropriate algorithm, you need to consider thefollowing:

-ecution time

Storage space

rogramming effort

Selecting a Sorting Algorithm


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Session 4Ver. 1.0

)ubble sort algorithm:

Is one of the simplest sorting algorithms

!as a #uadratic order of growth and is therefore suitable for

sorting small lists only

/orks by repeatedly scanning through the list, comparingad0acent elements, and swapping them if they are in the wrong

order

Sorting Data by Using Bubble Sort


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Session 4Ver. 1.0

"o understand the implementation of bubble sort algorithm,

consider an unsorted list of numbers stored in an array.

Imlementing Bubble Sort Algorithm

arr

210 43

2 6 75 3


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Session 4Ver. 1.0

et us sort this unsorted list.

Imlementing Bubble Sort Algorithm (Contd.)

arr

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2 6 75 3


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ass 1

n 2 3

4ompare the element stored at inde- with the element

stored at inde- 1.

arr

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2 6 75 3



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ass 1

n 2 3

4ompare the element stored at inde- 1 with the element

stored at inde- 5 and swap the values if the value at inde- 1

is greater than the value at inde- 5.


arr

210 43

6 7 32 5

No Change


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ass 1

n 2 3



is greater than the value at inde- 6.No Change


arr

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6 7 32 5


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ass 1

n 2 3



is greater than the value at inde- 7.Swap


arr

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6 7 32 5 3 7


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ass 1

n 2 3




Largest element is placed at its correct position ater !ass 1


arr

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6 3 72 5


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ass 5

n 2 3


stored at inde- 1 and swap the values if the value at inde-



arr

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6 3 72 5


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ass 5

n 2 3





arr

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ass 5

n 2 3





arr

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6 3 72 5 3 6


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ass 5

n 2 3




Second largest element is placed at its correct position ater !ass 2


arr

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3 6 72 5


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ass 6

n 2 3





arr

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3 6 72 5


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ass 6

n 2 3





arr

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3 6 72 53 5


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ass 6

n 2 3




"hird largest element is placed at its correct position ater !ass 3


arr

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ass 7

n 2 3





arr

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5 6 72 3


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ass 7

n 2 3




#o$rth largest element is placed at its correct position ater !ass 4


arr

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ass 7

n 2 3

%t the end of ass 7, the elements are sorted.


arr

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5 6 72 3


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/rite an algorithm to implement bubble sort.

%lgorithm for bubble sort:

1. Set pass 2 1.

5. 8epeat step 6 varying 0 from to n 9 1 9 pass.

6. If the element at inde- 0 is greater than the element at inde-0 1, swap the two elements.

7. Increment passby 1.

3. If pass;2 n 9 1, go to step 5.



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Session 4Ver. 1.0

"he efficiency of a sorting algorithm is measured in terms of

number of comparisons.

In bubble sort, there are n91 comparisons in ass 1, n 95

comparisons in ass 5, and so on.

"otal number of comparisons 2


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/hat is the order of growth of the bubble sort algorithm$

$ust a minute

%nswer:

"he bubble sort algorithm has a #uadratic order of growth.


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/hile implementing bubble sort algorithm, how many

comparisons will be performed in ass 1.

$ust a minute

%nswer:

n 91 comparisons


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roblem Statement:

/rite a program to store the marks of 1 students in an array.

Include a function to sort the elements of the array by using

the bubble sort algorithm. %fter sorting the array, display the

sorted list.

Activity% Sorting Data by Using Bubble Sort Algorithm


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Selection sort algorithm:



Scans through the list iteratively, selects one item in each

scan, and moves the item to its correct position in the list

Sorting Data by Using Selection Sort


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"o understand the implementation of selection sort

algorithm, consider an unsorted list of numbers stored in an

array.

Imlementing Selection Sort Algorithm

arr

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120 10 200105 20


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et us sort this unsorted list.

Imlementing Selection Sort Algorithm(Contd.)

arr

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120 10 200105 20


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ass 1

n 2 3

Search the minimum value in the array, arrAB to arrAn 9 1B.


arr

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120 10 200105 20

min


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ass 1

n 2 3


Swap the minimum value with the value at inde- .


arr

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120 10 200105 20

min

Swap

10510

S d l i h


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ass 1

n 2 3


Swap the minimum value with the value at inde- .


arr

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120 105 20010 20

"he smallest %al$e is placed at its correct location ater !ass 1

D S d Al i h


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ass 5

n 2 3

Search the minimum value in the array, arrA1B to arrAn 9 1B.

Swap the minimum value with the value at inde- 1.


arr

210 43

120 105 20010 20

min

20 120

Swap

D t St t d Al ith


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ass 5

n 2 3




arr

210 43

120 200 2010510arr

210 43

20 200 120

"he second smallest %al$e is placed at its correct location ater

!ass 2

10510

D t St t d Al ith


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ass 6

n 2 3

Search the minimum value in the array, arrA5B to arrAn91B.



arr

210 43

120 200 2010510arr

210 43

20 200

min

10 120105

D t St t d Al ith


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ass 6

n 2 3




arr

210 43

120 200 2010510arr

210 43

20 200

min"he third smallest %al$e is placed at its correct location ater !ass 3

12010510

D t St t d Al ith


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Session 4Ver. 1.0

ass 7

n 2 3




arr

210 43

120 200 2010510arr

210 43

20 200 12010 105

min

120 200

Swap

D t St t d Al ith


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ass 7

n 2 3




arr

210 43

120 200 2010510arr

210 43

20

"he o$rth smallest %al$e is placed at its correct location ater !ass 4

120 20010 105



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Session 4Ver. 1.0

ass 7

n 2 3

"he list is now sorted.


arr

210 43

120 200 2010510arr

210 43

20 20010 105 120



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Session 4Ver. 1.0

/rite an algorithm to implement selection sort.

%lgorithm for selection sort:

1. 8epeat steps 5 and 6 varying 0 from to n 9 5

5. Find the minimum value in arrA0B to arrAn 91B:

a. Set minCinde- 2 0

b. 8epeat step c varying i from 0 1 to n 9 1

c. If arrAiB ; arrAminCinde-B:

i. minCinde- 2 i

6. Swap arrA0B with arrAminCinde-B




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Session 4Ver. 1.0

In selection sort, there are n 9 1 comparisons during ass 1

to find the smallest element, n 9 5 comparisons during ass

5 to find the second smallest element, and so on.

"otal number of comparisons 2


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Session 4Ver. 1.0

8ead the following statement and specify whether it is true

or false:

"he efficiency of selection sort algorithm is same as that of the

bubble sort algorithm.

$ust a minute

%nswer:

"rue



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!ow many comparisons are performed in the second pass

of the selection sort algorithm$

$ust a minute

%nswer:

n 95



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Session 4Ver. 1.0

Insertion sort algorithm:



Is much more efficient than bubble sort, and selection sort, if

the list that needs to be sorted is nearly sorted

Sorting Data by Using Insertion Sort



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"o understand the implementation of insertion sort

algorithm, consider an unsorted list of numbers stored in an

array.

Imlementing Insertion Sort Algorithm

210 43

70 1030&0 20arr



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"o sort this list by using the insertion sort algorithm:

You need to divide the list into two sublists, sorted and

unsorted.

Imlementing Insertion Sort Algorithm(Contd.)

210 43

70 1030&0 20arr



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"o sort this list by using the insertion sort algorithm:

You need to divide the list into two sublists, sorted and

unsorted.

Initially, the sorted list has the first element and the unsorted

list has the remaining 7 elements.


Sorted ist Dnsorted ist

0

70 1030&0 20

21 43


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Session 4Ver. 1.0

ass 1

lace the first element from the unsorted list at its correct

position in the sorted list.



10

70 &0

32

30 10 20

4



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10

70 &0

32

30 10 20

4

ass 5





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30 70 &0 2010

ass 5





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30 70 &0 2010

ass 6





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30 70 &0

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ass 7





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Session 4Ver. 1.0

et us now write an algorithm to

implement insertion sort algorithm.


1. 8epeat steps 5, 6, 7, and 3varying i from 1 to n 9 1

5. Set temp 2 arrAiB

6. Set 0 2 i 9 1

7. 8epeat until 0 becomes lessthan or arrA0B becomes less

than or e#ual to temp:

a. Shift the value at inde-

0 to inde- 0 1

b. Eecrement 0 by 1

3. Store temp at inde- 0 1

210 43

70 1030&0 20arr



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n 2 3

i 2 1




6. Set 0 2 i 9 1




0 to inde- 0 1

b. Eecrement 0 by 1


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70 1030&0 20arr



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a a S uc u es a d go s

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n 2 3

i 2 1


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70 1030&0 20arr

i



6. Set 0 2 i 9 1




0 to inde- 0 1

b. Eecrement 0 by 1




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g

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i 2 1

temp 2




6. Set 0 2 i 9 1




0 to inde- 0 1

b. Eecrement 0 by 1


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i



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i 2 1

temp 2


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b. Eecrement 0 by 1




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g

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n 2 3

i 2 1

temp 2

arrA0B ; temp


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0 to inde- 0 1

b. Eecrement 0 by 1




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g

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n 2 3

i 2 1

temp 2

arrA0B ; temp


210 43

70 1030&0 20arr

i'

Val$e temp is stored at its correct

position in the sorted list



6. Set 0 2 i 9 1




0 to inde- 0 1

b. Eecrement 0 by 1




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i 2 1


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b. Eecrement 0 by 1




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i 2 5


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b. Eecrement 0 by 1




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b. Eecrement 0 by 1




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i 2 5

temp 2 6


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6. Set 0 2 i 9 1




0 to inde- 0 1

b. Eecrement 0 by 1




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i 2 5

temp 2 6


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b. Eecrement 0 by 1




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i 2 5

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b. Eecrement 0 by 1




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temp 2 6


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b. Eecrement 0 by 1




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n 2 3

i 2 5

temp 2 6


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i''



6. Set 0 2 i 9 1

7. 8epeat until 0 becomes less

than or arrA0B becomes less



0 to inde- 0 1

b. Eecrement 0 by 1




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i 2 5

temp 2 6


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70



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0 to inde- 0 1

b. Eecrement 0 by 1




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i 2 5

temp 2 6

0 2 91


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i'

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0 to inde- 0 1

b. Eecrement 0 by 1




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i 2 5

temp 2 6

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0 to inde- 0 1

b. Eecrement 0 by 1




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0 to inde- 0 1

b. Eecrement 0 by 1




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b. Eecrement 0 by 1




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b. Eecrement 0 by 1




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temp 2 1


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b. Eecrement 0 by 1




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n 2 3i 2 7

temp 2 5


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0 to inde- 0 1

b. Eecrement 0 by 1




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temp 2 5


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&0arr 703010

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0 to inde- 0 1

b. Eecrement 0 by 1



l i i l i h


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temp 2 5


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&0arr 3010

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'



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0 to inde- 0 1

b. Eecrement 0 by 1



I l i I i S Al i h


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n 2 3i 2 7

temp 2 5


210 43

&0arr 3010

i

70

'

30



6. Set 0 2 i 9 1


than or arrA0B becomes lessthan or e#ual to temp:


0 to inde- 0 1

b. Eecrement 0 by 1



I l ti I ti S t Al ith


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n 2 3i 2 7

temp 2 5


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i

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'

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b. Eecrement 0 by 1





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n 2 3i 2 7

temp 2 5


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&0arr 10

i

703020



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0 to inde- 0 1

b. Eecrement 0 by 1


'




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n 2 3i 2 7


210 43

&0arr 10

i

703020

"he list is now sorted



6. Set 0 2 i 9 1




0 to inde- 0 1

b. Eecrement 0 by 1


'


D t i i th !" i # I ti S t Al ith


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Session 4Ver. 1.0

"o sort a list of siGe n by using insertion sort, you need toperform


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Session 4Ver. 1.0

% sales manager has to do a research on best seller colddrinks in the market for the year 57&5H. Eavid, the

software developer, has a list of all the cold drink brands

along with their sales figures stored in a file. Eavid has to

provide the sorted data to the sales manager. "he data in

the file is more or less sorted. /hich sorting algorithm willbe most efficient for sorting this data and why$

$ust a minute

%nswer:

Insertion sort provides better efficiency than bubble sort andselection sort when the list is partially sorted. "herefore, Eavid

should use the insertion sort algorithm.


Sorting Data by Using Shell Sort


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Session 4Ver. 1.0

Shell sort algorithm:Insertion sort is an efficient algorithm only if the list is already

partially sorted and results in an inefficient solution in an

average case.

"o overcome this limitation, a computer scientist, E.. Shell

proposed an improvement over the insertion sort algorithm."he new algorithm was called shell sort after the name of its

proposer.

Sorting Data by Using Shell Sort


Imlementing Shell Sort Algorithm


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Session 4Ver. 1.0

Shell sort algorithm:Improves insertion sort by comparing the elements separated

by a distance of several positions to form multiple sublists

%pplies insertion sort on each sublist to move the elements

towards their correct positions

!elps an element to take a bigger step towards its correctposition, thereby reducing the number of comparisons

Imlementing Shell Sort Algorithm


Imlementing Shell Sort Algorithm (Contd )


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Session 4Ver. 1.0

"o understand the implementation of shell sort algorithm,consider an unsorted list of numbers stored in an array.

Imlementing Shell Sort Algorithm (Contd.)

210 43

70 104030 &0arr 20

5 6 7 & ( 10

(0 110 75 60 45




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"o apply shell sort on this array, you need to:Select the distance by which the elements in a group will be

separated to form multiple sublists.

%pply insertion sort on each sublist to move the elements

towards their correct positions.


210 43

70 104030 &0arr 20

5 6 7 & ( 10

(0 110 75 60 45




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ist 1 2


210 43

arr

5 6 7 & ( 10

Increment 2 6

ass 2 1

630 (

70 60(010

741 10

30 45110&0ist 5 2

&52

40 7520ist 6 2

70 104030 &0 20 (0 110 75 60 45




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630 (

70 60(010

741 10

30 45110&0ist 5 2

&52

40 7520ist 6 2

%pply insertion sort to sort the

three lists"he lists are sorted

10 (07060 30 110&045

20 7540

ist 1 2




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10 602030 45arr 40

5 6 7 & ( 10

70 &0 75 (0 110

630 ( 741 10

30ist 5 2

&52

75ist 6 2

30

75

10 60 70 (0 45 &0 110

20 40

ist 1 2




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70 &0 75 (0 110

Increment 2 5ass 2 5ist 1 2

420 6

10 704520

531 7

30 &04060ist 5 2

75 110

& 10

(0

(




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ist 1 2

420 6

10 704520

531 7

30 &04060ist 5 2

75 110

& 10

(0

(

%pply insertion sort on each sublist




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Session 4Ver. 1.0


ist 1 2

420 6

10 704520

531 7

30 &06040ist 5 2

75 110

& 10

(0

(

"he lists are now sorted




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Session 4Ver. 1.0


ist 1 2

420 6

10 704520

531 7

30 &06040ist 5 2

75 110

& 10

(0

(

210 43

10 402030 45arr 60

5 6 7 & ( 10

70 &0 75 (0 110




115/120

Session 4Ver. 1.0


210 43

10 402030 45arr 60

5 6 7 & ( 10

70 &0 75 (0 110

Increment 2 1ass 2 6

%pply insertion sort to sort the list




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Session 4Ver. 1.0


210 43

10 403020 45arr 60

5 6 7 & ( 10

70 75 &0 (0 110

Increment 2 1ass 2 6

"he list is now sorted


$ust a minute


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Session 4Ver. 1.0

/hich of the following sorting algorithms compares theelements separated by a distance of several positions to

sort the data$ "he options are:

1. Insertion sort

5. Selection sort

6. )ubble sort7. Shell sort

$ust a minute

%nswer:

7. Shell sort


Summary


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Session 4Ver. 1.0

In this session, you learned that:Sorting is a process of arranging data in some pre&defined

order of a key value. "he order can be either ascending or

descending.

"here are various sorting algorithms that are used to sort data.

Some of them are:

)ubble sort

Selection sort

Insertion sort

Shell sort

*erge sort

+uick sort

!eap sort

Summary


Summary (Contd.)


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Session 4Ver. 1.0

"o select an appropriate algorithm, you need to consider thefollowing:

-ecution time

Storage space

rogramming effort

)ubble sort and selection algorithms have a #uadratic order of

growth, and are therefore suitable for sorting small lists only.

Insertion sort performs different number of comparisons

depending on the initial ordering of elements. /hen the

elements are already in the sorted order, insertion sort needs

to make very few comparisons.

Insertion sort is an efficient algorithm than bubble sort andselection sort if the list that needs to be sorted is nearly sorted.

Summary (Contd.)


Summary (Contd.)


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Shell sort improves insertion sort by comparing the elementsseparated by a distance of several positions. "his helps an

element to take a bigger step towards its correct position,

thereby reducing the number of comparisons.

y ( )

03 ds and algorithm session 04

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