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Data Structures

Data Structures

Reference

http://www.algolist.net

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Algorithm :- Outline the essence of a computational procedure , step by step instructions .

Program :- an implementation of an algorithm in some programming language

Data Structure :- Organization of data needed to solve the problem .

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What is an Algorithm?

Algorithm: Finite set of instructions that, if

followed, accomplishes a particular task.

Describe: Representation of algorithm can

written By :-

in natural language ( English ) / pseudo-

code / diagrams / etc.

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Any computing algorithm will have AT MOST

five kinds of components:

• Data structures to hold data

• Instructions change data values

• Conditional expressions to make

decisions

• Control structures to act on decisions

• Modules to make the algorithm

manageable by abstraction, i.e., grouping

related components

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Relations between Problems, Algorithms and Programs

Problem

Algorithm Algorithm

Program ProgramProgram Program

. . . .

. . . . . . . .

What is a Good Algorithm?

Efficient :-

Running Time Space Used

Efficiency as function of input size :-

The number of bits in an input number Number of data elements ( numbers , points )

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WORST- / AVERAGE- / BEST-CASE

Worst-case running time of an algorithm

The longest running time for any input of size n An upper bound on the running time for any input

guarantee that the algorithm will never take longer Example: Sort a set of numbers in increasing order; and the

data is in decreasing order The worst case can occur fairly often

E.g. in searching a database for a particular piece of information

Best-case running timesort a set of numbers in increasing order; and the data is already in increasing order

Average-case running timeAverage number of steps taken on any instance of size n

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Pseudo- code -: A mixture of natural language and high –

level programming concepts that describes the main ideas behind a generic implementation of a data structure or algorithm

Eg:- Algorithm arrayMax ( A, n )

input : An array A sorting n integers Output : The Maximum element in A

currentMax A[0]for i 1 to n-1 do if currentMax < A[i] then currentMax

A[i]return currentMax

Pseudo – Code

It is more structured than usual language but less formal than a programming language .

Expressions:

Use standard mathematical symbols to

describe numeric and Boolean expression .

Use for assignment ( “=“ in java )

Use = for the equality relationship( “==“ in

java ) 10

Pseudo- Code

Programming Constructs :- decision structures :- if …. Then … [ else ]

while – loops : while .. Do repeat – loops : repeat … until .. for – loop : for .. Do array indexing : A[i] , A[I,j]

Methods : Calls : object method ( args ) returns : return value 11

Simple Algorithm

Find sum n numbers between any given range numbers

1 -Start

2 -Read N

3 -Sum =0

4 -For I= 1 to N

4.1 sum = sum + I

4.1 next I

5 -print Sum

6 -End 12

Basic Structure of C++ Language

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Documentation Section

Link Section

Definition Section

Global Declaration Section

Subprogram SectionFunction 1…..Function n

main(){Declaration SectionExecutable Section }

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Language

Built-in User-defined

Data

OperatorsAssignment) = (

Arithmetic)%,/,*,-,+( Relational)=!,==,=> ,> ,=< ,<(

Logical)|| , ( &&Unary)-- ,++(

Data Operators

Atomicint (2 bytes)

char (1 byte)float (4 bytes)

double (8 bytes)

Tokens

The smallest element in the C language is the token. Tokens can be:

Numeric constants : 123, 98.6, 1000000 Character constants : ‘A’, ‘a’, ‘$’, ‘4’ String constants : “UMBC”, “I like ice cream.”,

“123”, “CAR”, “car” Keywords : int , while, for Names (identifiers) Punctuation : ; : , ‘ “ [ ] { } ( ) Operators: =, +, -, *, /, <>, <, >, >=, !=, &&, ||, +

+, --

Simple C++Program

/*---- Hello World C Example ("hello.c") -------------------------------------*/

/* ANSI C Headers */

#include <iostream.h>

/* Main Program starts here */

void main( )

{

int i = 0;

/* End of declarations ... */

for ( i = 0; i < 10; i++ )

{

cout<<“Hello World”<<endl<< i ); /* print to standard

output */

}

}

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Include headers if you need to use functions in these files

Comment :/* .. */

Declare all your variables first

Control Statement

Selection Iteration Jump

If For Break

Switch While Continue

………… Do- while Return

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Eg:- to calculate the average of n number

/*Calculate the average of n numbers*/

#include<iostream.h>

void main(){

int n, count=1;

float x, average,sum=0;

cout<<"Enter the limit”<<endl; /*initialize and read in a value for

n*/

cin>>n;

while(count<=n) /*Read in the numbers*/

{

cout<<"x= “;

cin>>x;

sum+=x;

++count;

}

/*calculate the average and display result*/

average=sum/n;

cout<<“The average is ”<<average;

getch(); }

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While

Syntax -:

While (Expression ) { Statement (s )

Increment counter }

Do – while

Syntax-:

Do {

statement(s)Counter}While(expression ) ;

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Functions

A function is a self contained program segment that carries

out some specific,well-defined task.

C regards main() as function

Functions should be defined separately before or after main.

A function will process information that is passed to it from the

calling program and return a single value

Each function contains:

A function heading (function name), followed by optional

list of arguments enclosed in parentheses.

A list of argument declarations

A compound statement enclosed within a pair of braces

{ }19

Functions Cont..

Function Definition: returntype fn_name(type1 arg1,type2 arg2, …..type

n,arg n)

{ localvariables  

functioncode }

Example: int maximum(int x, int y)

{ int z;

z=(x>=y) ? x:y;

return(z);}

Calling A function:

function-name(arg1,arg2,….arg n);

Function Prototype: returntype fn_name(type1 arg1,type2 arg2, …..type

n,arg n);

C ++ Program illustrating Function

/*Program to calculate the area of a circle*/

#include <iostream.h>

const float PI= 3.14;

float areacircle( float radius) ; /* function prototype*/

main() {

float radius, area;

cout<<"Enter value of radius“<<endl;

cin>>radius;

area=areacircle(radius); /* call function */

cout<<“Area= “<<area ;

getch();

}

float areacircle(float r) { /* definition of function */

a= PI*r*r;

return(a);

}20

Assignment -1-

Write algorithm for the following

sum of n numbers between given range ( Using while )

sum of n numbers between given range ( Using Do…

while )

count even& odd numbers in given range( Using For )

count even & odd numbers in given range( Using while )

count even & odd numbers in given range(Using Do..

while)

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