Course Name: DATA STRUCTURESCourse Code: 10B11CI211Course Credits: 4 (3-1-2)Session: Jan – Jun 2013

Data Structures Team:

Course Coordinator: Deepak, Nitin and Hemraj

WHAT THE COURSE IS ABOUT

• Data structures is concerned with the representation and manipulation of data.

• All programs manipulate data.• So, all programs represent data in some way.• Data manipulation requires an algorithm.• We shall study ways to represent data and

algorithms to manipulate these representations.• The study of data structures is fundamental to

Computer Science & Engineering.

PREREQUISITE

• C• Enumerated data type, void data type• typedef statement• Control statements• Use of memory by a program• Specification of pointers• Memory management functions• Problems with pointers• Various aspects of user defined functions

WHAT IS DATA STRUCTURE

“A Conceptual and concrete way to organize data for efficient storage and manipulation”

WHAT IS DATA STRUCTURE

A data structure is a logical and mathematical model of a particular organization of data.

The choice of particular data structure depends upon following consideration:

1.It must be able to represent the inherent relationship of data in the real world.

2.It must be simple enough so that it can process efficiently as and when necessary

OVERVIEW OF DATA STRUCTURE

• Basic Terms related to data organization

• Data type

• Meaning of data structure

• Factor that influence the choice of data structure

• Different data structure

• Various operation performed on data structure

BASIC TERMS RELATED TO DATA ORGANIZATION

• Data:Values or set of values.Eg. Observation of experiment, marks obtained by student.• Data item:A data item refers to a single unit of values.Eg. Roll no. name etc.• Entity:That has certain attribute or properties which may be

assigned values.Eg. Student is an entity

BASIC TERMS RELATED TO DATA ORGANIZATION

• Entity set:Collection of similar entity.Eg. Student of a class• Record:Collection of related data items.Eg. Rollno, Dob, gender, class of a particular student.• File:Collection of related record.Eg. A file containing records of all students in a class

BASIC TERMS RELATED TO DATA ORGANIZATION

• Key:

A key is a data item in a record that takes unique values and can be used to distinguish a record from other records.

• Information:

Meaningful data, coveys some meaning and hence can be used for decision making

DATA TYPE

A data type is a collection of values and a set of operation that act on those values

Classification of data type:

1. Primitive data type

2. Abstract data type

3. Polymorphic data type

PRIMITIVE DATA TYPE

• That is predefined. It is also known as built in data type.

Eg. C have built in data type int, long int, float, double, char.

ABSTRACT DATA TYPE

• In computing, an abstract data type (ADT) is a specification of a set of data and the set of operations that can be performed on the data. Such a data type is abstract in the sense that it is independent of various concrete implementations.

• The main contribution of the abstract data type theory is that it – (1) formalizes a definition of type (which was only intuitively

hinted on procedural programming) – (2) on the basis of the information hiding principle and – (3) in a way that such formalization can be explicitly

represented in programming language notations and semantics. This important advance in computer science theory (motivated by software engineering challenges in procedural programming) led to the emergence of languages and methodological principles of object-oriented programming.

POLYMORPHIC DATA TYPE• Very often in programs, a generic operation must be

performed on data of different types. For example, in our bubble sort algorithm for the payroll records, when elements were found out of order in the id[] array, we needed to swap the integer elements in that array as well as the float elements in the hrs[] and rate[] arrays. If we decided to implement this swapping operation as a function, we would need to write two functions: one to swap integers, and another to swap floating point values; even though the algorithm for swapping is the same in both cases.

• The C language provides a mechanism which allows us to write a single swapping function which can be used on any data type. This mechanism is called a polymorphic data type, i.e. a data type which can be transformed to any distinct data type as required..

THE STUDY OF DATA STRUCTURE INCLUDE:

• Logical description of data structure

• Implementation of data structure

• Quantative analysis of data structure, this include amount of memory, processing time

TYPES OF DATA STRUCTURES

1. Linear data structure

2. Non linear data structure

LINEAR DATA STRUCTURE

A data structure whose elements form a sequence, and every element in the structures has a unique predecessor and unique successor.

Eg. Array, linked list, stack and queues.

NON LINEAR DATA STRUCTURE

A data structure whose elements do not form a sequence, and there is no predecessor and unique successor.

Eg. Trees, graphs

ARRAYS

Collection of homogenous data elements.

Arrays can be:

1. One dimensional

2. Two dimensional

3. Multi dimensional

LINKED LIST

• Linked list – Linear collection of self-referential class objects,

called nodes– Connected by pointer links– Accessed via a pointer to the first node of the list– Subsequent nodes are accessed via the link-pointer

member of the current node– Link pointer in the last node is set to null to mark the

list’s end• Use a linked list instead of an array when

– You have an unpredictable number of data elements– Your list needs to be sorted quickly

The Linked List data structure

[0] [1] [2]array

A B CArray

linked

A B CLinked list

Linked lists are unbounded(maximum number of items limited only by memory)

node

LINKED LIST

• Types of linked lists:– Singly linked list

• Begins with a pointer to the first node• Terminates with a null pointer• Only traversed in one direction

– Circular, singly linked• Pointer in the last node points back to the first node

– Doubly linked list• Two “start pointers” – first element and last element• Each node has a forward pointer and a backward pointer• Allows traversals both forwards and backwards

– Circular, doubly linked list• Forward pointer of the last node points to the first node and

backward pointer of the first node points to the last node

LINKED LISTS (VARIATIONS)

• Basic elements:– Head– Node

• Simplest form: Linear-Singly-linked

headA

data pointer

node

A

Head

B C

LINKED LISTS (VARIATIONS)

• Circular-linked Lists

– The last node points to the first node of the list

• Strengths– Able to traverse the list starting from any point– Allow quick access to first and last records through

a single pointer

• Weakness– A bit complicated during insertion, needs careful

setting of pointer for empty or one-node list

A

Head

B C

LINKED LISTS (VARIATIONS)• Doubly-linked Lists

– Each inner node points to BOTH successor and the predecessor

• Strengths– Able to traverse the list in any direction– Can insert or delete a node very quickly given only that

node’s address

• Weakness– Requires extra memory and handling for additional

pointers

A

Head

B C

LINKED LISTS (VARIATIONS)

• Putting together…Circular-doubly-linked lists!

A

Head

B C

STACK

• Stack – New nodes can be added and removed only at the top– Similar to a pile of dishes– Last-in, first-out (LIFO) – Bottom of stack indicated by a link member to NULL– Constrained version of a linked list

• push– Adds a new node to the top of the stack

• pop– Removes a node from the top – Stores the popped value – Returns true if pop was successful

DATA STRUCTURES -- STACKS

• A stack is a list in which insertion and deletion take place at the same end– This end is called top– The other end is called bottom

QUEUES

• Queue– Similar to a supermarket checkout line– First-in, first-out (FIFO) – Nodes are removed only from the head – Nodes are inserted only at the tail

• Insert and remove operations – Enqueue (insert) and dequeue (remove)

The Queue Operations

• A queue is like a line of people waiting for a bank teller. The queue has a front and a rear.

$ $

FrontRear

TREES

• Tree nodes contain two or more links– All other data structures we have discussed

only contain one

• Binary trees– All nodes contain two links

• None, one, or both of which may be NULL

– The root node is the first node in a tree. – Each link in the root node refers to a child– A node with no children is called a leaf node

TREE TERMINOLOGY

There is a uniquepath from the rootto each node.

Root is a level 0, childis at level(parent) + 1.

Depth/height of a treeis the length of the longest path.

level 0

1

2

3

4

BINARY TREE• Each node has two successors

– one called the left child– one called the right child– left child and/or right child may be empty

A binary tree is either - empty or - consists of a root and two binary trees, one called the left subtree and one called the right subtree

GRAPHSG = (V, E)

a vertex may have: 0 or more predecessors 0 or more successors

abstract containers

hierarchical (1 to many)

graph (many to many)first ith last

sequence/linear (1 to 1)

set

HEAPS

Heap is a binary tree that satisfy the following property:

• Shape property• Order propertyShape property states that heap is complete or

nearly complete binary tree.Order property states that:1. Either the element at any node is smallest of

all of its children, called min heap2. Element at any node is largest of all of its

children, called max heap.

HASH TABLES

• There are many application that require a dynamic structure that support only insert, search and delete operations. These operations are commonly known as dictionary operations. A hash table is an effective data structure for implementing dictionaries.

COMMON OPERATIONS ON DATA STRUCTURE

1. Traversal:-Accessing each element exactly once in order to process it.

2. Searching:-Finding the location of a given element.

3. Insertion:-Adding the new element to the structure.

4. Deletion:-Removing a existing element from the structure.

5. Sorting:-Arranging the elements in logical order.

6. Merging:-Combining the elements of two similar sorted structures into a single structure.

ENUMERATED DATA TYPE

• Variable of enumerated data type enhance the readability of the program.

enum boolean {false, true};Here boolean is called tag name for the user

defined data type. Then we can declare variable of this type as follows:

enum boolean flag;Then we can assign value false or true to variable

flag, and also we can compare the value of flag with these values.

void DATA TYPE• This is also known as empty data type, is useful in many situation;1. Void functionname(int x, int y)

{}

Functionname() does not return any value.2. Int functionname(void)

{}

Functionname() does not take any rgument.3. Void main()

{void *ptr;int x=5;ptr=&x;printf(“value pointed to pointer is now %d”,*(int*)ptr);

}Void pointer cannot be directly dereferenced without type casting. This

is because the compiler cannot determie the size of the value the pointer points to.

REDEFINING DATA TYPES

• Using typedef statement we can make it possible to declare variables of user defined data types as with built in data types by redefining the user defined data type and giving our own name.

typedef enum{false, true} boolean;

The word boolean becomes name of the new defined data type.

boolean flag;

CONTROL STATEMENTS

1. Decision making statements• if statement• if-else statement• switch statement2. Looping Statements• for statement• while statement• do while statement3. Jumping statements• brake statement• continue statement• goto statement

MEMORY USE IN C

STACK

HEAP

BSS

CONST

DATA

TEXT

High Memory

Low Memory

Initialized and un initialized local variable

Memory allocated with malloc(). Calloc(), and realloc() functions

Un initialized static variable

Read only variable

Initialized & un initialized global variables & initialized static variables

Program code

POINTER

• Pointer is a variable which contains reference of another variable

Address of x value of x

px x

Pointerpx=&x

DECLARATION OF POINTER• “*” is used to declare and dereference the

pointers.data type *ptvar;

int *ip; /*declare ip to be pointer to an integer*/ *ip=5;/* assign 5 to the integer pointer to which ip

points*/

address 5

ip

POINTER OPERATOR

• Two operators:

&-----address of

*------at address in

X=8 let x be at 100 (x at 100)

Ip=&x ip contains 100 (ip at 200)

a=*ip contains 8 (a at 250)

8

100

8

ASSIGNMENT IN POINTER

GivenInt x;Double y;Int *a,*b;double *c;

a=&x; /* a now points to x*/b=a; /*b now points to the same variable as a

points */c=&y; /* c points to y */

POINTER TO A POINTER

• Variable that hold an address of a another variable that in turn holds an address of another variable, this type of variable is know as pointer to pointer.

• Pointer to pointer will be declared as

**ptr;

DYNAMIC MEMORY MANAGEMENT

Memory management functions

Function name

Description

malloc Allocate memory from heap

calloc Allocate memory from heap and initializes the allocated memory to zeros

realloc Readjusts the existing block and copies the contents to new location

free Deallocates block allocated by malloc, calloc and realloc fuctions

DYNAMIC MEMORY ALLOCATION

• Dynamic memory allocation– Obtain and release memory during execution

• malloc– Takes number of bytes to allocate

• Use sizeof to determine the size of an object– Returns pointer of type void *

• A void * pointer may be assigned to any pointer• If no memory available, returns NULL

– ExamplenewPtr = malloc( sizeof( struct node ) );

• free– Deallocates memory allocated by malloc– Takes a pointer as an argument– free ( newPtr );

calloc()

The calloc() function dynamically allocates memory and automatically initializes the memory to zeroes. Example

newPtr = calloc( 5,sizeof( struct node ) );

realloc()

The realloc() function changes the size of previously dynamically allocated memory with malloc(),calloc() or realloc function() functions.

The prototype of realloc() function is Void *realloc(void *block,size_t size);It takes two arguments, first argumant is

pointer to the original object and second argument is new size of the object.

free()

The free() function deallocates a memory block previously allocated with malloc(), calloc(), or realloc() functions. Prototype for free function is

void free(void *block);

It takes one argument that specify the pointer to the allocated block.

DEBUGGING POINTERS

The pointer can be the source of mysterious and catastrophic program bugs. Common bugs related to related to pointer and memory management is

1. Dangling pointer

2. Null pointer assignment

3. Memory leak

4. Allocation failure

STRUCTURES

A structure is a collection of data elements, called fields which may be of different type.

Individual elements of a structure variable are accessed using dot operator (.), if a pointer is used to point to a structure variable , then arrow operator (->) is used.

STRUCTURE

Example of complex data structures and the corresponding self referential structure to represent these data structure.

Next pointer field

Information field

head

1200 1201 1202 X

STRUCTURE

typedef struct nodetype{

int info;

struct nodetype *next;

} node;

node * head;

Recursion

Divide-and-conquer

What is recursion?

Recursive functions

Nature of recursion

Nature of recursion

Types of Recursion• Direct Recursion• Indirect Recursion

Iteration vs. recursion

Recursion: sum()

Recursion: sum()

How does recursion work?

How does recursion work?

How does recursion work?

RecursionRecursive functions

– Functions that call themselves

– Can only solve a base case

– Divide a problem up into• What it can do• What it cannot do

– What it cannot do resembles original problem– The function launches a new copy of itself (recursion

step) to solve what it cannot do

– Eventually base case gets solved• Gets plugged in, works its way up and

solves whole problem

RecursionExample: factorials–5! = 5 * 4 * 3 * 2 * 1

–Notice that•5! = 5 * 4!•4! = 4 * 3! ...

–Can compute factorials recursively

–Solve base case (1! = 0! = 1) then plug in•2! = 2 * 1! = 2 * 1 = 2;•3! = 3 * 2! = 3 * 2 = 6;

Recursion

5!

(a) Sequence of recursive calls. (b) Values returned from each recursive call.

Final value = 120

5! = 5 * 24 = 120 is returned

4! = 4 * 6 = 24 is returned

2! = 2 * 1 = 2 is returned

3! = 3 * 2 = 6 is returned

1 returned

5 * 4!

1

4 * 3!

3 * 2!

2 * 1!

5!

5 * 4!

1

4 * 3!

3 * 2!

2 * 1!

1

2 Recursive factorial function */

3 #include <stdio.h>

4

5 long factorial( long number ); /* function prototype */

6

7 /* function main begins program execution */

8 int main()

9 {

10 int i; /* counter */

11

12 /* loop 10 times. During each iteration, calculate

13 factorial( i ) and display result */

14 for ( i = 1; i <= 10; i++ ) {

15 printf( "%2d! = %ld\n", i, factorial( i ) );

16 } /* end for */

17

18 return 0; /* indicates successful termination */

19

20 } /* end main */

21

1! = 1 2! = 2 3! = 6 4! = 24 5! = 120 6! = 720 7! = 5040 8! = 40320 9! = 36288010! = 3628800

22 /* recursive definition of function factorial */

23 long factorial( long number )

24 {

25 /* base case */

26 if ( number <= 1 ) {

27 return 1;

28 } /* end if */

29 else { /* recursive step */

30 return ( number * factorial( number - 1 ) );

31 } /* end else */

32

33 } /* end function factorial */

Example Using Recursion: The Fibonacci Series

Fibonacci series: 0, 1, 1, 2, 3, 5, 8...– Each number is the sum of the previous two – Can be solved recursively:

• fib( n ) = fib( n - 1 ) + fib( n – 2 )

– Code for the fibonacci functionlong fibonacci( long n ){if (n == 0 || n == 1) // base case

return n;else

return fibonacci( n - 1) + fibonacci( n – 2 );}

 

Example Using Recursion: The Fibonacci Series

f( 3 )

f( 1 )f( 2 )

f( 1 ) f( 0 ) return 1

return 1 return 0

return +

+return 

1

2 Recursive fibonacci function */

3 #include <stdio.h>

4

5 long fibonacci( long n ); /* function prototype */

6

7 /* function main begins program execution */

8 int main()

9 {

10 long result; /* fibonacci value */

11 long number; /* number input by user */

12

13 /* obtain integer from user */

14 printf( "Enter an integer: " );

15 scanf( "%ld", &number );

16

17 /* calculate fibonacci value for number input by user */

18 result = fibonacci( number );

19

20 /* display result */

21 printf( "Fibonacci( %ld ) = %ld\n", number, result );

22

23 return 0; /* indicates successful termination */

24

25 } /* end main */

26

Enter an integer: 0Fibonacci( 0 ) = 0

Enter an integer: 1Fibonacci( 1 ) = 1

Enter an integer: 2Fibonacci( 2 ) = 1

Enter an integer: 3Fibonacci( 3 ) = 2

Enter an integer: 4Fibonacci( 4 ) = 3

27 /* Recursive definition of function fibonacci */

28 long fibonacci( long n )

29 {

30 /* base case */

31 if ( n == 0 || n == 1 ) {

32 return n;

33 } /* end if */

34 else { /* recursive step */

35 return fibonacci( n - 1 ) + fibonacci( n - 2 );

36 } /* end else */

37

38 } /* end function fibonacci */

Enter an integer: 5Fibonacci( 5 ) = 5

Enter an integer: 6Fibonacci( 6 ) = 8

Enter an integer: 10Fibonacci( 10 ) = 55

Enter an integer: 20Fibonacci( 20 ) = 6765

Enter an integer: 30Fibonacci( 30 ) = 832040

Enter an integer: 35Fibonacci( 35 ) = 9227465

Recursion vs. Iteration• Repetition

– Iteration: explicit loop– Recursion: repeated function calls

• Termination– Iteration: loop condition fails– Recursion: base case recognized

• Both can have infinite loops

• Balance – Choice between performance (iteration) and

good software engineering (recursion)

GCD

else{

r=x%y;return (recgcd(y,r));

}

Output:Enter the two number 5 8G.C.D. of the 5 and 8 is 1

Problems on recursion• Factorial• Fibonacci number generation• Fibonacci series generation• Reversing an integer number• Calculating power of a number• Prime Number checking• Generating prime number series• Calculating GCD of two numbers• Generating table of a number