DATA STRUCTURE CLASS 12 COMPUTER SCIENCE

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Unit-II
Data Structure
Arrays, Stacks, Queues And Linked List Chapter: 06
In Computer Science, a data structure is a particular way of storing and organizing data in a
computer so that it can be used efficiently. Different kinds of data structures are suited to different
kinds of applications, and some are highly specialized to specific tasks.
Simple Data Structure: These data structures are normally built from primitive data types like
integers, floats, characters. For example arrays and structure.
Compound Data Structure: simple data structures can be combined in various ways to form
more complex structure called compound structures. Linked Lists, Stack, Queues and Trees are
examples of compound data structure.
Searching methods in array
Linear Search: In this method each Binary Search Method
element of the array is compared with the Binary search algorithm is applicable for
number to be searched in linear order (from already sorted array only. In this algorithm,
first to last). And where the number is to search for the given item from the sorted
matched the position is displayed. array (in ascending order), the item is
#include<iostream.h> compared with the middle element of the array.
#include<conio.h> If the middle element is equal to the item then
void main() index of the middle element is returned,
{ otherwise, if item is less than the middle item
int lsearch(int[],int,int); then the item is present in first half segment of
int a[50],item,n,index; the array (i.e. between 0 to middle-1), so the
clrscr(); next iteration will continue for first half only, if
cout<<"n Enter size of array"; the item is larger than the middle element then
cin>>n; the item is present in second half of the array
cout<<"n Enter array elements"; (i.e. between middle+1 to size-1), so the next
for(int i=0;i<n;i++) iteration will continue for second half segment
cin>>a[i]; of the array only. The same process continues
cout<<"Enter the item to be searched"; until either the item is found (search
cin>>item; successful) or the segment is reduced to the
index=lsearch(a,n,item); single element and still the item is not found
if(index= = -1) (search unsuccessful).
cout<<"n Element not found";
else #include<iostream.h>
cout<<"n Element found at position #include<conio.h>
"<<index+1;
getch(); void main()
} {
int bsearch(int[],int,int);
int lsearch(int a[],int size,int item) int a[50], item, n, index;
{ clrscr();
int found=0; cout<<"n Enter total elements";
for(int i=0;i<size;i++) cin>>n;
{ cout<<"n Enter array elements in sorted
if(a[i]==item) form:";
{ for(int i=0;i<n;i++)
return i; cin>>a[i];

found=1;
break;
}
}
if(found==0)
return -1;
}
cout<<"Enter the item to be searched";
cin>>item;
index=bsearch(a, n, item);
if(index= = -1)
cout<<"n Element not found";
else
cout<<"n Element found at position
"<<index+1;
getch();
}
int bsearch(int a[], int size, int item)
{
int beg, med, last;
beg=0,found=0;
last=size-1;
int mid=(last+beg)/2;
while(beg<=last)
{
mid=(beg+last)/2;
if(item= =a[mid])
{
return mid;
found=1;
}
else if(item>a[mid])
beg=mid+1;
else
last=mid-1;
}
if(found==0)
return -1;
}
Sorting operation in the array
Sorting means to arrange the array elements in Ascending order or in Descending order. There are
various methods to do this but for the ease sake Bubble sort method is displayed here.
#include<iostream.h>
#include<conio.h>
void bubblesort (int[],int);
void main()
{
int a[50],n;
clrscr();
cout<<"nHow many elements do you want to create array with? ";
cin>>n;
cout<<"nEnter array elementsn";
for(int i=0;i<n;i++)
cin>>a[i];
bubblesort(a,n);
cout<<"nnThe sorted array is as shown belown";
for(i=0;i<n;i++)
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cout<<a[i]<<"n";
getch();
}
void bubblesort(int a[],int n) //Function to perform bubble sort
{
int temp;
for(int i=0;i<n-1;i++)
{
for(int j=0;j<n-i-1;j++)
if(a[j]>a[j+1])
{
temp=a[j];
a[j]=a[j+1];
a[j+1]=temp;
}
}
}
Some Questions Based on Array
Q1. Write a function in C++ which accepts an integer array and its size as arguments/parameters and
reverses the array
example : if the array is 1,2,3,4,5 then rearrange the array as 5,4,3,2,1
Ans : void reverse(int arr[ ], int n)
{
int temp;
for(int i=0,j=n-1; i<=j; i++,j--)
{
temp= arr[i];
arr[i] = arr[j];
arr[j] = temp;
}
}
Q2. Write a function in C++ which accepts an integer array and its size as arguments/parameters and
exchange the array in the given manner
example : if the array is 1,2,3,4,5,6,7,8,9,10 then rearrange the array as2,1,4,3,6,5,8,7,10,9
Ans : void change(int arr[ ], int n)
{
int temp;
for(int i=0; i<n; i=i+2)
{
temp= arr[i];
arr[i] = arr[i+1];
arr[i+1] = temp;
}
}
Q3 Write a function in C++ to merge the contents of two sorted arrays A & B into third array C.
Assuming array A is sorted in ascending order, B is sorted in descending order, the resultant array is
required to be in ascending order.
Q 4 Write a function in C++ which accepts an integer array and its size as arguments and assign the
elements into a two dimensional array of integers in the following format
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If the array is 1,2,3,4,5,6
The resultant 2D array is
1 2 3 4 5 6
0 1 2 3 4 5
0 0 1 2 3 4
0 0 0 1 2 3
0 0 0 0 1 2
0 0 0 0 0 1
if the array is 1,2,3
The resultant 2D array is
1 2 3
0 1 2
0 0 1
Question based on Two dimensional Array
Q1. Write a function in C++ that will accept a 2-D array and its row and column size as argument
and find sum of rows and columns
Ans : void rowcolsum(int A[ ][ ],int N, int M)
{
for (int i=0;i<N;i++)
{
int SumR=0;
for (int j=0;j<M;j++)
SumR+=A[i][j];
cout<<SumR<<endl;
}
for (int i=0;i<N;i++)
{
int SumC=0;
for (int j=0;j<M;j++)
SumC+=A[j][i];
cout<<SumC<<endl;
}
}
Q2. Write a function in C++ to find the sum of both left and right diagonal elements from a two
dimensional array (matrix).
Ans : void DiagSum(int A[ ][ ], int N)
{
int SumD1=0,SumD2=0;
for (int I=0;I<N;I++)
{
SumD1+=A[I][I];
SumD2+=A[N-I-1][I];
}
}
Address Calculation in Two Dimensional Array
Two dimensional array can be arranged in two manner
1. Row Major Order
2. Column Major Order
To find the address of a particular row and column the formula in Row Major Order is
Address of A[row][column]=B +w*(n(row)+column)
Where
B= Base address of the array
w= Word size
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n= total no of columns in the array
To find the address of a particular row and column the formula in Column Major Order is
Address of A[row][column]=B +w*(n(Column)+row)
Where
B= Base address of the array
w= Word size
n= total no of rows in the array
Q1. An array x[30][10] is stored in the memory with each element requiring 4 bytes of storage. If the
base address of x is 4500, find out memory locations of x[12][8] if the content is stored along the
row.
Ans: Here the array is stored in Row Major Order so
B=4500
W= 4
N= 10
As per the formula
Address of A[row][column]=B +w*(n(row)+column)
=4500+4*(10(12)+8)
=4500+4*(128)
=4500+512
=5012
Q 2. An array P[20][30] is stored in the memory along the column with each of the element
occupying 4 bytes, find out the Base Address of the array, if an element P[2][20] is stored at the
memory location 5000.
Ans : Given, W=4, N=20, M=30, Loc(P[2][20])=5000
Column Major Formula:
Loc(P[I][J]) =Base(P)+W*(N*J+I)
Loc(P[2][20]) =Base(P)+4*(20*20+2)
Base(P) =5000 4*(400+2)
=5000 1608
=3392
Q3. An array S[40][30] is stored in the memory along the row with each of the element occupying 2
bytes, find out the memory location for the element S[20][10], if an element S[15][5] is stored at the
memory location 5500.
Ans. Given, W=2, N=40, M=30, Loc(S[15][5])=5500
Row Major Formula:
Loc(S[I][J]) =Base(S)+W*(M*I+J)
Loc(S[15][5]) =Base(S)+2*(30*15+5)
5500 =Base(S) + 2*(450+5)
Base(S) =5500 910 = 4590
Loc(S[20][10]) =4590+2*(30*20+10)
=4590+2*(600+10)
=4590+1220 = 5810

STACKS, QUEUES AND LINKED LIST
Stack
In computer science, a stack is a Last in, First out (LIFO) data structure. It simply means that an
element that is inserted at the end will be deleted first. To Manage a stack all the insertion and
deletion takes place from one posi
One of the common uses of stack is in function call.
Operations on the Stack
There are two fundamental operations
Push
Pop
Push means to insert an element
Pop means to delete an element
Queue
In computer science, a Queue is a First in, First out (FIFO) data structure. It simply means that an
element that is inserted at the beginning will be deleted first. To Manage a queue all the insertion and
Every element is inserted from the rear position and deleted from the front position in the queue.
Linked List
A linked list is a data structure consisting of a group of nodes which together represent a sequence.
Under the simplest form, each node is composed of a data and a reference (in other words, a link) to
the next node in the sequence; more complex variants add additional links. This structure allows for
efficient insertion or removal of elements from any position in thesequence.
Here in the figure is an example of a linked list whose nodes contain two fields: an integer value and
a link to the next node. The last node is linked to a terminator used to signify the end of thelist.
Linked lists are among the simplest and most common data structures. They can be used to
implement several other common abstract data types, stacks, queues etc though it is not uncommon to
implement the other data structures directly without using a list as the basis of implementation.
The principal benefit of a linked list over an array is that the list elements can easily be inserted or
removed without reallocation or reorganization of the entire structure because the data items need not
be stored contiguously in memory or on disk. Linked lists allow insertion and removal of nodes at
any point in the list, and can do so with a constant number of operations if the link previous to the
link being added or removed is maintained during list traversal.
Linked list are dynamic structure where memory allocation takes place at run time.
Operation on a linked list
There are three basic operations on a linked list
Insertion
Deletion
Traversal
Inserting a node or element into Linked list :
Inserting an element into linked list contains 3 types .
1. Insertion at beginning of the Linked list
2. Insertion after/before any element of the linked list
3. Insertion at the end of the linked list
Deleting a node from the Linked list.
A node can be deleted in 3 ways similar to Insertion.
1. Deleting a Node from the beginning of the Linked List
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DATA STRUCTURE CLASS 12 COMPUTER SCIENCE

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DATA STRUCTURE CLASS 12 COMPUTER SCIENCE