Data Structure Introduction

1. DATA STRUCTURES
Ramanathan G
Department of Computer Science (UG)
KRISTU JAYANTI COLLEGE

2. Data
Data are simply collection of facts and figures. Data are
values or set of values.
Data Item
A data item refers to a single unit of values. Data items
that are divided into sub items are group items; those
that are not are called elementary items.
• For example, a student’s name may be divided into
three sub items – [first name, middle name and last
name] but the ID of a student would normally be
treated as a single item. In the above example ( ID,
Age, Gender, First, Middle, Last, Street, Area ) are
elementary data items, whereas (Name, Address ) are
group data items.

3. In the above example ( ID, Age, Gender, First, Middle,
Last, Street, Area ) are elementary data items, whereas
(Name, Address ) are group data items.

4. Data Structure
Data structure is a method of organizing large amount of
data more efficiently so that any operation on that data
becomes easy.
☀ Every data structure is used to organize the large
amount of data.
☀ Every data structure follows a particular principle
☀ The operations in a data structure should not violate
the basic principle of that data structure.

5. Need of data structure
• It gives different level of organization data.
• It tells how data can be stored and accessed in
its elementary level.
• Provide operation on group of data, such as
adding an item, looking up highest priority
item.
• Provide a means to manage huge amount of
data efficiently.

6. Classification of Data Structure
Data structure
Primitive DS Non-Primitive DS
Integer Float Character Pointer
Float
Integer Float

7. Classification of Data Structure
Non-Primitive DS
Linear List Non-Linear List
Array
Link List Stack
Queue Graph Trees

8. Based on the organizing method of a data structure, data
structures are divided into two types.
• Primitive Data Structures:
If The integers, reals, logical data, character data, pointer
and reference are primitive data structures. Data structures that
normally are directly operated upon by machine-level
instructions are known as primitive data structures.
• Non – Primitive Data Structures:
The data type that are derived from primary data types are
known as non-primitive data type.
The non-primitive data types are used to store the group of
values.
The non-primitive data structures emphasize on structuring of a group of
homogeneous (same type) or heterogeneous (different type) data items.

9. Based on the organizing method of a data structure, data
structures are divided into two types.
• Linear Data Structures: If a data structure is
organizing the data in sequential order, then that data
structure is called as Linear Data Structure.
Example:
Arrays
List (Linked List)
Stack
Queue
• Non - Linear Data Structures: If a data structure is
organizing the data in random order, then that data
structure is called as Non-Linear Data Structure.

10. Based on the organizing method of a data structure, data
structures are divided into two types.
• Linear Data Structures: If a data structure is
organizing the data in sequential order, then that data
structure is called as Linear Data Structure.
Example:
Arrays
List (Linked List)
Stack
Queue
• Non - Linear Data Structures: If a data structure is
organizing the data in random order, then that data
structure is called as Non-Linear Data Structure.

11. Example:
Tree
Graph
Dictionaries
Heaps

12. Differences between primitive and non primitive data
structures
A primitive data structure is generally a basic structure
that is usually built into the language, such as an integer,
a float.
A non-primitive data structure is built out of primitive
data structures linked together in meaningful ways, such
as a or a linked-list, binary search tree, AVL Tree, graph
etc.

13. Homogeneous DS
Homogeneous data structures are those data structures
that contain only similar type of data e.g. like a data
structure containing only integer or float values. The
simplest example of such type of data structures is an
Array.
Non Homogeneous DS
The non-homogeneous data structures are the one in
which the data elements doesn't belong to the same data
type. All the data elements have different data type. For
example: classes, Structure, Union etc

14. Static Data Structure
The memory allocation of elements in this data structure
is done before the program execution (memory size
allocated to data which is static). For Example: Arrays.
Dynamic Data Structure
In the data structure before the usage of the element their
memory allocation is done with the use of D.M.A
function. For example : Linked Lists

15. Operations on Data structures
The most commonly used operation on data structure are
broadly categorized into following types:
Create: Creation of data.
It reserves memory for the program elements.
In a programming language, this operation can be
performed by the variable declaration statement.
For example, int x=10;
This causes memory to be allocated for variable ‘x’ and it
allows integer value 10 to be stored.

16. Select: Accessing of data with in a data structure.
Example: printf(“%d”,a[5]);
The array element a[5] is selected for printing.
Update: - change data or modify the data in a data
structure
For example,
int x=3; // declaration and initialization of x
.
.
x=10; // Assignment statement
Here, initially value 3 is assigned to x. Later value 10 is
assigned to x. This modifies the value of x from 3 to 10.
Consider x=x+5; This expression x=x+5
modifies 10, to the new value 15.

17. DESTROY
This operation is used to destroy the data structure.
In C programming, destroy operation, can be done using
the function free(). This helps in efficient use of memory
and prevents memory wastage.

18. 1. Traversing- It is the process of accessing or visiting
each element exactly once to perform some operations
on it..
2. Searching- It is used to find out the location of the data
item if it exists in the given collection of data items.
3. Inserting- It is used to add a new data item in the given
collection of data items.
4. Deleting- It is used to delete an existing data item from
the given collection of data items.
5. Sorting- It is used to arrange the data items in some
order i.e. in ascending or descending order in case of
numerical data and in dictionary order in case of
alphanumeric data.
6. Merging- It is used to combine the data items of two
sorted files into single file in the sorted form.

19. Pointers:
• Pointers in C language is a variable that stores/points
the address of another variable. A Pointer in C is used
to allocate memory dynamically i.e. at run time. The
pointer variable might be belonging to any of the data
type such as int, float, char, double, short etc.
Syntax :
data_type *var_name;
Example : int *p; char *p;
• Where, * is used to denote that “p” is pointer variable
and not a normal variable.

20. Normal variable stores the value whereas pointer variable
stores the address of the variable.
The content of the C pointer always be a whole number
i.e. address.
& symbol is used to get the address of the variable.
* symbol is used to get the value of the variable that the
pointer is pointing to.
Accessing the address of a variable:
Any variable when declared and initialized is associated
with the following:
The memory location or address of the variable
The name of the variable
Value stored in the variable

21. Consider the statement int n=20;

22. #include <stdio.h>
int main()
{
int *ptr, q;
q = 50;
/* address of q is assigned to ptr */
ptr = &q;
/* display q's value using ptr variable */
printf("%d", *ptr);
return 0;
}

23. Recursion
It is a function that calls itself during execution.
It enables the function to repeat itself several times to
solve a given problem.
The various types of recursion are
* Direct Recursion:
A recursive function that invokes itself is said to have
direct recursion.
* Indirect Recursion :
A function which contains a call to another function
which in turn call another function and so on, and
eventually calls the first function

24. For example:
int fact(int n)
{
if(n==0) return 1;
return n*fact(n-1); Direct Recursion
}
Indirect Recursion
void f1() void f2() void f3()
{ { {
- - -
f2(); f3(); f1();
} } }

25. GCD or Greatest Common Divisor is also known as Highest
Common Factor(HCF). It is the largest number that can divide
each of the number exactly.
The GCD of two positive integers x and y is defined recursively as
follows.
Euclid’s Algorithm
x if(y==0)
GCD ( x, y) GCD( y, x) if (y>x)
GCD (y, x % y) otherwise
Where x % y is x modulo y, the remainder of dividing x by y

26. Algorithm
Step1: Start
Step2: Accept two numbers a and b
Step3: Call the function res=gcd(a,b)
Step4: Print res
Step5: Stop
Algorithm for gcd(a,b)
Step1: If a==b
return (a)
else
if(a>b)
return(gcd(a-b,b)
else
return (gcd(a,b-a)
End if

27. //Program to find GCD of two numbers using recursion.
#include<stdio.h>
void main()
{
int a,b,res;
clrscr();
printf("nGreatest Common Divisorn");
printf("Enter the value for a : ");
scanf("%d",&a);
printf("Enter the value for b : ");
scanf("%d",&b);
res=gcd(a,b);
printf("The Greatest Common Divisor of %d and %d is
%d",a,b,res);
getch(); }

28. int gcd(int a,int b)
{
if(a==b)
{
return(a);
}
else
{
if(a>b)
return(gcd(a-b,b));
else
return(gcd(a,b-a));
}
}

29. GCD (20, 12) a=20 b=12
If (20>12)
return(gcd(20-12,12)
Gcd (8,12)
If (8>12) return no
Else return (gcd(8,12-8)
Gcd (8,4)
If(8>4)
return gcd(8-4,4)
Gcd (4,4)
If (4==4)
Return (4)

30. Algorithm
Step1: Start
Step2: Accept two numbers n and r
Step3: If n<r
Print “Invalid input”
Else
result=fact(n)/(fact(r)*fact(n-r))
Print result
End if
Stop

31. Algorithm for Fact(x)
Step1: If x=0
return 1
Else
return x*fact(x-1)
End if

32. //Program to find Binomial Coefficient
#include<stdio.h>
void main()
{
int n,r;
int fact(int);
clrscr();
printf("nEnter the value for n:");
scanf("%d",&n);
printf("nEnter the value for r:");
scanf("%d",&r);
if(n<r)
printf("Invalid Inputn");

33. else
printf("nBinomial Coefficient nCr is
%d",fact(n)/(fact(n-r)*fact(r)));
getch();
}
int fact(int x)
{
if(x==0||x==1)
return 1;
else
return(x*(fact(x-1)));
}

34. If(x==0 ||x=1) return 1
Return(4*fact(4-1))
(4*fact(3))
(4*(3*fact(3-1))
(4*3*(2*fact(2))
4*3*2*fact(2-1))
4*3*2*fact(1))
4*3*2*1

35. Direct Computation Method
• Fibonacci numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
where each number is the sum of the preceding
two.
• Recursive definition:
– F(0) = 0;
– F(1) = 1;
– F(number) = F(number-1)+ F(number-
2);

36. /*Program to print the Fibonacci sequence*/
#include <stdio.h>
int fib(int n);
void main()
{
int i,n;
printf("nEnter a numbern");
scanf("%d",&n);
printf(“Fibonacci sequence:n”);
for(i=0;i<n;i++)
printf("%d t",fib(i));
}

37. /*Program to print the Fibonacci sequence*/
/*fibonnacci function*/
int fib(int n)
{
if((n==0)||(n==1))
return(n);
else
return(fib(n-1)+fib(n-2));
}

39. Trace a Fibonacci Number
fib(0):
0 == 0 ? Yes.
fib(0) = 0;
return fib(0);
fib(2) = 1 + 0 = 1;
return fib(2);
fib(3) = 1 + fib(1)
fib(1):
1 == 0 ? No; 1 == 1? Yes
fib(1) = 1;
return fib(1);
fib(3) = 1 + 1 = 2;
return fib(3)

40. Trace a Fibonacci Number
fib(2):
2 == 0 ? No; 2 == 1? No.
fib(2) = fib(1) + fib(0)
fib(1):
1== 0 ? No; 1 == 1? Yes.
fib(1) = 1;
return fib(1);
fib(0):
0 == 0 ? Yes.
fib(0) = 0;
return fib(0);
fib(2) = 1 + 0 = 1;
return fib(2);
fib(4) = fib(3) + fib(2)
= 2 + 1 = 3;
return fib(4);

41. TOWER OF HANOI

47. ++-

57. Memory allocation is the process of setting aside sections
of memory in a program to be used to store variables, and
instances of structures and classes.
Memory allocation has two core types;
Static Memory Allocation: The program is allocated
memory at compile time.
Static memory allocation means we reserve a certain amount
of memory by default, inside our program to use for
variables. It is fixed in size. It need not grow or shrink in
size.
The standard method of creating an array of 10 integers on
the stack is:
int arr[10];
This means 10 memory locations are allocated to hold 10
integers. Memory is said to be allocated statically.

58. • Dynamic Memory Allocation: The programs are allocated
with memory at run time. Dynamic memory allocation
allows your program to obtain more memory space while
running, or to release it if it's not required.
In simple terms, Dynamic memory allocation allows you
to manually handle memory space for your program.

59. malloc()
The name malloc stands for "memory allocation".
The function malloc() reserves a block of memory of specified
size and return a pointer of type void which can be casted into
pointer of any form.
Syntax of malloc()
ptr = (cast-type*) malloc(byte-size)
Here, ptr is pointer of cast-type. The malloc() function returns a
pointer to an area of memory with size of byte size. If the space
is insufficient, allocation fails and returns NULL pointer.
ptr = (int*) malloc(100 * sizeof(int));
This statement will allocate either 200 or 400 according to size
of int 2 or 4 bytes respectively and the pointer points to the
address of first byte of memory.

60. C calloc()
The name calloc stands for "contiguous allocation".
The only difference between malloc() and calloc() is that,
malloc() allocates single block of memory whereas calloc()
allocates multiple blocks of memory each of same size and
sets all bytes to zero.
Syntax of calloc()
ptr = (cast-type*)calloc(n, element-size);
This statement will allocate contiguous space in memory for
an array of n elements.
For example:
ptr = (float*) calloc(25, sizeof(float));This statement
allocates contiguous space in memory for an array of 25
elements each of size of float, i.e, 4 bytes.

61. free()
Dynamically allocated memory created with either calloc()
or malloc() doesn't get freed on its own. You must
explicitly use free() to release the space.
syntax of free()
free(ptr);
This statement frees the space allocated in the memory
pointed by ptr.
realloc()
If the previously allocated memory is insufficient or more
than required, you can change the previously allocated
memory size using realloc().
Syntax of realloc()
ptr = realloc(ptr, newsize);

62. #include<stdio.h>
#include<string.h>
#include<stdlib.h>
int main()
{
char *mem_alloc; /* memory allocated dynamically */
mem_alloc = malloc( 15 * sizeof(char) );
if(mem_alloc== NULL )
{
printf("Couldn't able to allocate requested memoryn");
}
else
{ strcpy( mem_alloc,"w3schools.in"); }
printf("Dynamically allocated memory content : %sn", mem_alloc );
free(mem_alloc); }

63. #include<stdio.h>
#include<string.h>
#include<stdlib.h>
int main()
{
char *mem_alloc;
mem_alloc = calloc( 15, sizeof(char));/*memory allocated dynamically*/
if( mem_alloc== NULL )
{ printf("Couldn't able to allocate requested memoryn"); }
else
{ strcpy( mem_alloc,"w3schools.in");
}
printf("Dynamically allocated memory content : %sn", mem_alloc );
free(mem_alloc);
}

64. #include <stdio.h>
#include <string.h>
#include <stdlib.h>
int main()
{
char *mem_allocation; /*memory is allocated dynamically */
mem_allocation = malloc( 20 * sizeof(char) );
if( mem_allocation == NULL )
{
printf("Couldn't able to allocate requested memoryn");
}
else
{ strcpy( mem_allocation,"fresh2refresh.com"); }
printf("Dynamically allocated memory content : "
"%sn", mem_allocation );

65. mem_allocation=realloc(mem_allocation,100*sizeof(char));
if( mem_allocation == NULL )
{
printf("Couldn't able to allocate requested memoryn");
}
else
{
strcpy( mem_allocation,"space is extended upto "
"100 characters");
}
printf("Resized memory : %sn", mem_allocation );
free(mem_allocation);
}