Prof. V. S. Joe Irudayaraj - PowerPoint Presentation

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Prof. V. S. Joe Irudayaraj

Associate Professor of Computer Science

18SCS3101A

DESIGN AND ANALYSIS OF ALGORITHMS

III

M Sc/ MCA

ARRAY STRUCTURE

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ARRAY STRUCTURE

  What is an Array? Group of elements are represented in a single name called an Array. Array is a set of pairs, index and value. Array has consecutive memory locations. Array is a random access structure. Array is a homogeneous structure, that is it consists same type of data.

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ARRAY STRUCTURE

Operations on Array

1. Creation

2. Display

3. Updating4. Copying5. Joining

6. Concatenation7. Reversing8. Insertion

9. Deletion

10. Searching

11. Sorting

12. Merging

g

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DECLARATION AND INITIALIZATION

DECLARATION IN ‘C’

int a[10], char c[5], char * name[10];

INITIALIZATION IN ‘C’ 1. int a[ ] = {10,20,30,40,50};2. char c[ ] = {‘A’,’B’,’C’};

2. char * name = {“RAJA”,”RANI”};

g

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ARRAY CREATION

CREATE AN ARRAY OF ‘n’ ELEMENTS

ALGORITHM:

1. read n2. for i= 1 to n do

read a[i]

C PROGRAM:

1.

scanf

(“%

d”,&n);2. for(i

=1;i<=n;++i) scanf

(“%d”,&a[i] );

g

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ARRAY DISPLAY

DISPLAY AN ARRAY OF ‘n’ ELEMENTS

ALGORITHM:

for i= 1 to n do write a[i]

C PROGRAM:

for(

i

=1;i<=n;++

i

) printf(“%d ”,a[i] );

g

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ARRAY DISPLAY

Give number of elements

4

Give data one by one

10203040Given Data

10 20 30 40

g

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ARRAY DISPLAY IN REVERSE ORDER

DISPLAY AN ARRAY IN REVERSE ORDER

ALGORITHM:

for i= n downto 1 do

write a[i]

C PROGRAM:

for(

i

=

n;i>=1;--i)

printf(“%d ”,a[i] );

g

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ARRAY DISPLAY

Give number of elements

4

Give data one by one

10203040Given Data in reverse order

40 30 20 10

g

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ARRAY UPDATION

REPLACE DATA ‘x’ AT LOCATION ’j’ WHERE 1<=j<=n

(GIVEN : ARRAY OF ‘N’ ELEMENTS)

1. read x,j2. a[j]=x

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ARRAY DISPLAY

Given Array

10 20 30 40

Give new data to replace

80Give position3New Array10 20 80 40

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COPYING

COPY ARRAY A OF ‘m’ elements TO ARRAY B

for i= 1 to m do b[i] = a[i]

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JOINING

JOIN

ARRAY B OF ‘n’ elements

TO

ARRAY A of ‘m’ elements 1. for j= 1 to n do a[m+j

] = b[j]2. m = m+n

;

g

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REVERSING

REVERSE AN ARRAY OF ‘n’ ELEMENTS

for

i= 1 to n/2 do a[i] ↔ a[n-i+1]

g

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ARRAY CREATION and DISPLAY

CREATE and DISPLAY AN ARRAY OF ‘n’ ELEMENTS

ALGORITHM:

1. read n2. for i= 1 to n do

read a[i]

3. for i

= 1 to n do

write a[

i

]

g

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ARRAY DISPLAY

Give number of elements

4

Give data one by one

10203040Given Array

10 20 30 40

g

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REVERSING

REVERSE AN ARRAY OF ‘n’ ELEMENTS

for

i= 1 to n/2 do a[i] ↔ a[n-i+1]

g

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ARRAY DISPLAY

Given Array

10 20 30 40

Reversed Array

40 30 20 10

g

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ARRAY INSERTION

INSERT DATA ‘x’ AT LOCATION ’j’ WHERE 1<=j<=n

(GIVEN : ARRAY OF ‘n’ ELEMENTS)

1. read x2. read j3. for i

= n downto j do

a[i+1] = a[i]

4. a[j] = x

5. n = n+1

g

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ARRAY INSERTION

Given Array

10 20 30 40

Give new data to insert

100Give its position2New Array after insertion

10 100 20 30 40

g

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ARRAY INSERTION

Given Array

10 20 30 40

Give new data to insert

100Give its position1New Array after insertion

100 10 20 30 40

g

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ARRAY INSERTION

Given Array

10 20 30 40

Give new data to insert

100Give its position5New Array after insertion

10 20 30 40 100

g

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ARRAY INSERTION

INSERT DATA ‘x’ AT THE END OF AN ARRAY

(GIVEN : ARRAY OF ‘n’ ELEMENTS)

1. read x2. a[ n + 1] = x3. n = n+1

g

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ARRAY INSERTION

Given Array

10 20 30 40

Give new data to insert at rear

100New Array after insertion10 20 30 40 100

g

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ARRAY DELETION

DELETE DATA AT LOCATION ’j’ WHERE 1<=j<=n

(GIVEN : ARRAY OF ‘n’ ELEMENTS)

1. read j2. for i = j+1 to n do a[i-1] = a[

i] 3. n = n-1

g

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ARRAY DELETION

Given Array

10 20 30 40

Give data to delete

30New Array after deletion10 20 40

g

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ARRAY DELETION

Given Array

10 20 30 40

Give data to delete

40New Array after deletion10 20 30

g

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ARRAY DELETION

Given Array

10 20 30 40

Give data to delete

10New Array after deletion20 30 40

g

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ARRAY DELETION

DELETE DATA ‘x’ FROM AN ARRAY OF ‘n’ ELEMENTS

1. read x

2. for i = 1 to n do if (a[i]=x) break 3. if (

i=n+1) then {write(‘Not Found’); return;} else { for j= i+1 to n do

a[j-1] = a[j] n=n-1 }

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MERGING

MERGE TWO SORTED ARRAYS

ARRAY A OF ‘m’ ELEMENTS

WITH

ARRAY B OF ‘n’ ELEMENTS i=1; j=1a[m+1] = ∞ ; a[n+1]= ∞

for k= 1 to m+n do { if (a[

i] <= b[j]) then {c[k]=a[i]; i

=i+1}

else {c[k]=b[j]; j=j+1}

}

g

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MATRIX: MAGIC SQUARE

(4i, i = 1, 2, 3, …) n (n2

+1)Sum = -------------- 2Try for Singly Even Magic Square (4i+2, i =1, 2, 3, …)

162*

3*135*11108*9*

76

12*4

14*

15*

1

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8

16

35

7

ODD MAGIC SQUARE (2i, i = 1, 2, 3, …)492