CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
EXPERIMENT- 1
AIM: Write a program to insert a new element at end as well as at a given position in an
array.
OBJECTIVE: To understand how to insert an element into an array using the concept of
index.
PREREQUISITES: for loop, Traversing of an array and insertion at beginning of an array.
RESOURCE/ EXPERIMENTAL SET-UP/EQUIPMENT/APPARATUS/TOOLS: Linux OS or Windows 8/10 Operating System C/C++,Turbo C or gcc compiler in linux
THEORY AND APPLICATION:
1) First get the element to be inserted, say x
2) Then get the position at which this element is to be inserted, say pos
3) Then shift the array elements from this position to one position forward, and do this
for all the other elements next to pos.
4) Insert the element x now at the position pos, as this is now empty.
ALGORITHM:
Assume that A is an array with N elements. The maximum numbers of elements it can store
is defined by MAX.
begin
IF N = MAX, return
ELSE
N=N+1
SEEK Location index
For All Elements from A[index] to A[N]
Move to next adjacent location
A[index] = New_Element
End
1
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
SOURCE CODE:
Following is source code of the C++ Program to Insert an element in an array at specific
position. The C++ program is successfully compiled and run(on Codeblocks) on a Windows
system.
#include<iostream>
using namespace std;
int main( )
{ int arr[50], size, insert, i, pos;
cout<<"Enter Array Size : ";
cin>>size;
cout<<"Enter array elements : ";
for(i=0; i<size; i++)
{
cin>>arr[i];
}
cout<<"Enter element to be insert : ";
cin>>insert;
cout<<"At which position (Enter index number) ? ";
cin>>pos;
// now create a space at the required position
for(i=size; i>pos; i--)
{
arr[i]=arr[i-1];
}
arr[pos]=insert;
cout<<"Element inserted successfully..!!\n";
cout<<"Now the new array is : \n";
for(i=0; i<size+1; i++)
{
cout<<arr[i]<<" ";
}
2
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
return 0;
}
EXPERIMENTAL PROCEDURE:
After writing the source code, compile the program by selecting Build option from menu bar
or by pressing Ctrl-F9 keys together. If there are no errors detected in the program & object
file (.obj) has been created successfully, then execute the program by pressing Ctrl-F10 keys
together.
OUTPUT:
(a) Insertion at the end:
(b) Insertion at a given position:
3
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
CONCLUSION:
We have successfully learned how to insert an element in to an array at a given position(at
the end, beginning or at any index value
EXPERIMENT-2
AIM: Write a program to delete an element from a given array whose value is given or
whose position is given.
OBJECTIVE: To understand how to delete an element from an array using the concept of
index and value, both.
PREREQUISITES: for loop and insertion in an array.
RESOURCE/ EXPERIMENTAL SET-UP/EQUIPMENT/APPARATUS/TOOLS: Linux OS or Windows 8/10 Operating System C/C++,Turbo C or gcc compiler in linux
THEORY AND APPLICATION:
Step by step descriptive logic to remove element from array.
1) Move to the specified location which you want to remove in given array.
2) Copy the next element to the current element of array. Which is you need to
perform array[i] = array[i + 1].
3) Repeat above steps till last element of array.
4
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
4) Finally decrement the size of array by one.
a) /* C++ Program - Delete Element(value provided) from Array */
#include<iostream>
using namespace std;
int main()
{
int arr[50], size, i, del, count=0;
cout<<"Enter array size : ";
cin>>size;
cout<<"Enter array elements : ";
for(i=0; i<size; i++)
{
cin>>arr[i];
}
5
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
cout<<"Enter element to be delete : ";
cin>>del;
for(i=0; i<size; i++)
{
if(arr[i]==del)
{
for(int j=i; j<(size-1); j++)
{
arr[j]=arr[j+1];
}
count++;
break;
}
}
if(count==0)
{ cout<<"Element not found..!!";
}
else
{ cout<<"Element deleted successfully..!!\n";
cout<<"Now the new array is :\n";
for(i=0; i<(size-1); i++)
{
cout<<arr[i]<<" "; }
return 0;
}
}
EXPERIMENTAL PROCEDURE:
6
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
After writing the source code, compile the program by selecting Build option from menu bar
or by pressing Ctrl-F9 keys together. If there are no errors detected in the program & object
file (.obj) has been created successfully, then execute the program by pressing Ctrl-F10 keys
together.
OUTPUT:
b) /* C++ Program - Delete Element(position provided) from Array */
#include <iostream>
using namespace std;
int main()
{
int a[10], size, pos, i, count = 0;
cout << "Enter the size of an array \n";
cin >> size;
cout << "Enter the value in an array \n";
// Take an input array
for (i = 0; i < size; i++) {
cin >> a[i];
}
7
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
//Input position where we delete an element
cout << "Enter the position \n";
cin >> pos;
//Shift element from i+1 to i
for(i = pos-1; i < size; i++) {
a[i] = a[i+1];
}
// Reduce the size of an array
size--;
// Print an array after deleting an element
for(i = 0; i < size; i++) {
cout<<" "<<a[i];
}
return 0;
}
OUTPUT:
CONCLUSION:
We have successfully learned how to delete an element from a given array using its value
and
using its index separately.
8
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
EXPERIMENT -3
AIM: Write a program to find the location of a given element using Linear Search.
OBJECTIVE: To learn how to search the location of a particular element in an array using the
linear search algorithm.
PREREQUISITES: for loop and Traversing of an array.
RESOURCE/ EXPERIMENTAL SET-UP/EQUIPMENT/APPARATUS/TOOLS: Linux OS or Windows 8/10 Operating System C/C++,Turbo C or gcc compiler in linux
THEORY AND APPLICATION:
9
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
Searching is an operation or a technique that helps finds the place of a given element or
value
in the list. Any search is said to be successful or unsuccessful depending upon whether the
element that is being searched is found or not.
Linear Search :
Linear search is a very basic and simple search algorithm.
It traverses the array sequentially to locate the required element.
It searches for an element by comparing it with each element of the array one by one.
So, it is also called as Sequential Search.
Linear Search Algorithm is applied whenNo information is given about the array.
The list of data items is smaller.
Linear search is implemented using following steps:
1) Read the search element from the user.
2) Compare the search element with the first element in the list.
3) If both are matched, then display "Given element is found!!!" and terminate the
function.
4) If both are not matched, then compare search element with the next element in the list.
5) Repeat steps 3 and 4 until search element is compared with last element in the list.
6) If last element in the list also doesn't match, then display "Element is not found!!!" and
terminate the function.
ALGORITHM:
Consider• There is a linear array ‘a’ of size ‘n’.
• Linear search algorithm is being used to search an element ‘item’ in this linear array.
10
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
• If search ends in success, it sets loc to the index of the element otherwise it sets loc to 1.
Then, Linear Search Algorithm is as followsLinear_Search (a , n , item , loc)
for i = 0 to (n - 1) by 1
if (a[i] = item)
set loc = i;
else
set loc = -1;
SOURCE CODE:
#include<iostream>
using namespace std;
int main()
{
int a[20],n,x,i,flag=0;
cout<<"How many elements?";
cin>>n;
cout<<"\n Enter elements of the array \n";
for(i=0;i<n;++i)
cin>>a[i];
cout<<"\n Enter element to search:";
cin>>x;
for(i=0;i<n;++i)
{
11
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
if(a[i]==x)
{
flag=1;
break;
}
}
if(flag)
cout<<"\n Element is found at position "<<i+1;
else
cout<<"\n Element not found";
return 0;
}
EXPERIMENTAL PROCEDUREAfter writing the source code, compile the program by selecting Build option from menu bar
or by pressing Ctrl-F9 keys together. If there are no errors detected in the program & object
file (.obj) has been created successfully, then execute the program by pressing Ctrl-F10 keys
together.
OUTPUT:
12
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
CONCLUSION:
Linear search algorithm has been implemented successfully to find the location of a given
element in an array.
13
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
EXPERIMENT -4
AIM: Write a program to find the location of a given element using Binary Search.
OBJECTIVE: To learn how to search the location of a particular element in an array using the
binary search algorithm.
PREREQUISITES: for loop, Linear search algorithm
RESOURCE/ EXPERIMENTAL SET-UP/EQUIPMENT/APPARATUS/TOOLS: Linux OS or Windows 8/10 Operating System C/C++,Turbo C or gcc compiler in linux
THEORY AND APPLICATION:
Binary search is one of the fastest searching algorithms. It is used for finding the location of
an
element in a linear array. It works on the principle of divide and conquer technique.
Binary Search Algorithm can be applied only on Sorted arrays. So, the elements must be
arranged inEither ascending order if the elements are numbers.
Or dictionary order if the elements are strings.
To apply binary search on an unsorted array:
First, sort the array using some sorting technique.
Then, use binary search algorithm.
Consider-
14
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
There is a linear array ‘a’ of size ‘n’.
Binary search algorithm is being used to search an element ‘item’ in this linear array.
If search ends in success, it sets loc to the index of the element otherwise it sets loc to 1.
Variables beg and end keeps track of the index of the first and last element of the array
or sub array in which the element is being searched at that instant.
Variable mid keeps track of the index of the middle element of that array or sub array
in which the element is being searched at that instant.
Binary search algorithm searches an element by comparing it with the middle most element
of the array. Then, following three cases are possibleCase-01:
If the element being searched is found to be the middle most element, its index is returned.
Case-02:
If the element being searched is found to be greater than the middle most element, then its
search is further continued in the right sub array of the middle most element.
Case-03:
If the element being searched is found to be smaller than the middle most element, then its
search is further continued in the left sub array of the middle most element.
This iteration keeps on repeating on the sub arrays until the desired element is found
OR size of the sub array reduces to zero.
ALGORITHM:
BinarySearch(DATA,BEG,END,LOC,MID,ITEM)
DATA is a sorted array with lower bound LB & upper bound UB, and ITEM is given item of
information to be searched. The variables BEG, END and MID denote, respectively, the
15
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
beginning, the end and the middle locations of an array. This algorithm finds the location
LOC
of ITEM in DATA or sets LOC to NULL.
1) Set BEG:= LB,END:=UB and MID:=INT((BEG+END)/2).
2) Repeat steps 3 & 4 while BEG≤END and DATA[MID]≠ITEM.
3) If ITEM <DATA[MID],then:
Set END:=MID-1
else
Set BEG:=MID+1
4) Set MID:=INT((BEG+END)/2).
5) If DATA[MID]=ITEM, then
Set LOC:=MID
else
Set LOC:=NULL
6) Exit.
SOURCE CODE:
#include <iostream>
using namespace std;
int main( )
{ int count, i, arr[20], num, first, last, mid;
cout<<"how many elements would you like to enter?:";
cin>>count;
for (i=0; i<count; i++)
{
cout<<"enter number "<<(i+1)<<": ";
cin>>arr[i];
16
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
}
cout<<"enter the number that you want to search:";
cin>>num;
first = 0;
last = count-1;
mid = (first+last)/2;
while (first <= last)
{
if(arr[mid] < num)
{
first = mid + 1;
}
else if(arr[mid] == num)
{
cout<<num<<" found in the array at the location "<<mid+1<<"\n";
break;
}
else
{ last = mid - 1;
}
mid = (first + last)/2;
}
if(first > last)
{
cout<<num<<" not found in the array";
}
return 0;
17
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
}
EXPERIMENTAL PROCEDURE:
After writing the source code, compile the program by selecting Build option from menu bar
or by pressing Ctrl-F9 keys together. If there are no errors detected in the program & object
file (.obj) has been created successfully, then execute the program by pressing Ctrl-F10 keys
together.
OUTPUT:
CONCLUSION:
Binary search algorithm has been successfully implemented to find location of a given
element on a sorted array.
18
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
EXPERIMENT -5
AIM: Write a program to implement push and pop operations on a stack using linear
array.
OBJECTIVE: To understand & perform insertion(PUSH) & deletion(POP) operations in a
stack using an array.
PREREQUISITES: for loop and array traversal.
RESOURCE/ EXPERIMENTAL SET-UP/EQUIPMENT/APPARATUS/TOOLS: Linux OS or Windows 8/10 Operating System C/C++,Turbo C or gcc compiler in linux
THEORY AND APPLICATION:
A stack is an Abstract Data Type (ADT), commonly used in most programming languages. It
is named stack as it behaves like a real-world stack, for example – a deck of cards or a pile of
plates, etc. Stack ADT allows all data operations at one end only. At any given time, we can
only access the top element of a stack.
This feature makes it LIFO data structure. LIFO stands for Last-in-first-out. Here, the element
which is placed (inserted or added) last, is accessed first. In stack terminology, insertion
operation is called PUSH operation and removal operation is called POP operation. The
19
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
following diagram depicts a stack and its operations –
PUSH OPERATION:
The process of putting a new data element onto stack is known as a Push Operation. Push
operation involves a series of steps −
Step 1 − Checks if the stack is full.
Step 2 − If the stack is full, produces an error and exit.
Step 3 − If the stack is not full, increments top to point next empty space.
Step 4 − Adds data element to the stack location, where top is pointing.
Step 5 − Returns success.
ALGORITHM FOR PUSH OPERATION:
A simple algorithm for Push operation can be derived as follows –
PUSH(STACK,TOP,MAXSTK,ITEM)
1) If TOP=MAXSTK, then PRINT: “OVERFLOW” and return.
2) Set TOP:= TOP + 1
3) Set STACK[TOP]:= ITEM
4) Return
POP OPERATION:
Accessing the content while removing it from the stack, is known as a Pop Operation. In an
array implementation of pop() operation, the data element is not actually removed,
instead top is decremented to a lower position in the stack to point to the next value. A Pop
operation may involve the following steps −
Step 1 − Checks if the stack is empty.
Step 2 − If the stack is empty, produces an error and exit.
Step 3 − If the stack is not empty, accesses the data element at which top is pointing.
Step 4 − Decreases the value of top by 1.
20
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
Step 5 − Returns success.
ALGORITHM FOR POP OPERATION:
A simple algorithm for Pop operation can be derived as follows –
POP(STACK,TOP,ITEM)
1) If TOP=0,then PRINT: “UNDERFLOW” and return.
2) Set ITEM:= STACK[TOP]
3) Set TOP:= TOP - 1
4) Return
SOURCE CODE:
#include <iostream>
using namespace std;
int stack[20], n = 20, top = -1;
void push(int val) {
if(top >= n-1)
cout<<"stack overflow"<<endl;
else { top++;
stack[top] = val;
}
}
void pop()
{
if(top <= -1)
cout<<"stack underflow"<<endl;
else {
cout<<"the popped element is "<< stack[top] <<endl;
21
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
top--;
}
}
void display() {
if(top>= 0) {
cout<<"stack elements are:";
for(int i = top; i>= 0; i--)
cout<<stack[i]<<" ";
cout<<endl;
} else
cout<<"stack is empty";
}
int main()
{
int ch, val;
cout<<"1) push in stack"<<endl;
cout<<"2) pop from stack"<<endl;
cout<<"3) display stack"<<endl;
cout<<"4) exit"<<endl;
do {
cout<<"enter choice: "<<endl;
cin>>ch;
switch(ch) {
case 1: {
cout<<"enter value to be pushed:"<<endl;
cin>>val;
push(val);
22
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
break;
}
case 2: { pop();
break;}
case 3: { display();
break;
}
case 4: {
cout<<"exit"<<endl;
break;
}
default: {
cout<<"invalid choice"<<endl;
}
}
}while(ch!=4);
return 0;
}
EXPERIMENTAL PROCEDURE:
After writing the source code, compile the program by selecting Build option from menu bar
or by pressing Ctrl-F9 keys together. If there are no errors detected in the program & object
file (.obj) has been created successfully, then execute the program by pressing Ctrl-F10 keys
together.
OUTPUT:
23
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
CONCLUSION: PUSH & POP operations have been successfully implemented in stack ADT using
array.
EXPERIMENT-6
AIM: Write a program to convert an infix expression to a postfix expression using
stacks.
OBJECTIVE: To understand the process of conversion of infix expression to postfix
expression as an application of stacks
PREREQUISITES: Infix, Prefix & Postfix Expressions.
RESOURCE/ EXPERIMENTAL SET-UP/EQUIPMENT/APPARATUS/TOOLS: 24
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
Linux OS or Windows 8/10 Operating System C/C++,Turbo C or gcc compiler in linux
THEORY AND APPLICATION:
INFIX notations are not as simple as they seem specially while evaluating them. To evaluate
an infix expression we need to consider operators’ priority and associative property.
e.g. Expression 3+5*4 evaluate to 32 i.e. (3+5)*4 OR to 23 i.e. 3+(5*4).
To solve this, problem precedence or priority of the operators was defined. Operator
precedence governs evaluation order. An operator with higher precedence is applied before
an operator with lower precedence
Postfix and prefix expression forms do not rely on operator priorities, a tie breaker, or
delimiters. Both prefix and postfix notations have an advantage over infix that while
evaluating an expression in prefix or postfix form, we need not consider the priority and
associative property (order of brackets).
e.g. x/y*z becomes */xyz in prefix and xy/z* in postfix.
Both prefix and postfix notations make expression evaluation a lot easier. So it is easier to
evaluate expressions that are in these forms.
ALGORITHM :
Given an expression in the infix form.
Create and initialize a stack to hold operators.
Print operands as they arrive.
If the stack is empty or contains a left parenthesis on top, push the incoming operator
onto the stack.
If the incoming symbol is a left parenthesis, push it on the stack.
If the incoming symbol is a right parenthesis, pop the stack and print the operators
until you see a left parenthesis. Discard the pair of parentheses.
If the incoming symbol has higher precedence than the top of the stack, push it on the
stack.
25
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
If the incoming symbol has equal precedence with the top of the stack, use
association. If the association is left to right, pop and print the top of the stack and
then push the incoming operator. If the association is right to left, push the incoming
operator.
If the incoming symbol has lower precedence than the symbol on the top of the stack,
pop the stack and print the top operator. Then test the incoming operator against the
new top of stack.
At the end of the expression, pop and print all operators on the stack. (No parentheses
should remain.)
SOURCE CODE:
#include<iostream>
#include<stack>
using namespace std;
void Postfix(char *exp)
{ stack <char> s;
char output[50],t;
for(int i=0;exp[i]!='\0';i++)
{ char ch = exp[i];
switch(ch)
{
case '^':
case '-':
case '+':
case '/':
case '*': s.push(ch);
break;
26
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
case ')': t=s.top();
s.pop();
cout<<t;
break;
}
if (isalpha(ch))
cout<<ch;
}
}
int main( )
{
char exp[ ] = "a+b*(c^d-e)^(f+g*h)-i";
cout<<”\n CONVERTED POSTFIX EXPRESSION=”;
Postfix(exp);
return 0;
}
EXPERIMENTAL PROCEDURE:
After writing the source code, compile the program by selecting Build option from menu bar
or by pressing Ctrl-F9 keys together. If there are no errors detected in the program & object
file (.obj) has been created successfully, then execute the program by pressing Ctrl-F10 keys
together.
OUTPUT:
27
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
CONCLUSION:
The given infix expression has been successfully converted into postfix expression using
stack.
EXPERIMENT-7
AIM: Write a program to evaluate a postfix expression using stacks.
28
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
OBJECTIVE: To understand the process of evaluation of postfix expression as an application
of stacks.
PREREQUISITES: Infix, Prefix & Postfix Expressions.
RESOURCE/ EXPERIMENTAL SET-UP/EQUIPMENT/APPARATUS/TOOLS: Linux OS or Windows 8/10 Operating System C/C++,Turbo C or gcc compiler in linux
THEORY AND APPLICATION:
The Postfix notation is used to represent algebraic expressions. The expressions written in
postfix form are evaluated faster compared to infix notation as parenthesis are not required
in postfix. The compiler finds it convenient to evaluate an expression in its postfix form.
Postfix form include elimination of parentheses which signify priority of evaluation and the
elimination of the need to observe rules of hierarchy, precedence and associativity during
evaluation of the expression.
Evaluation rule of a Postfix Expression:
1) While reading the expression from left to right, push the element in the stack if it is an
operand.
2) Pop the two operands from the stack, if the element is an operator and then evaluate it.
3) Push back the result of the evaluation. Repeat it till the end of the expression.
ALGORITHM:
1) Add “)” to postfix expression.
2) Read postfix expression Left to Right until ) encountered
3) If operand is encountered, push it onto Stack
[End If]
4) If operator is encountered, Pop two elements
i) A -> Top element
29
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
ii) B-> Next to Top element
iii) Evaluate B operator A
push B operator A onto Stack
5) Set result = pop
6) END
SOURCE CODE:
#include <iostream>
#include <stack>
using namespace std;
// Function to evaluate given postfix expression
int postfixEval(string exp)
{
// create an empty stack
stack<int> stack;
// traverse the given expression
for (int i = 0; i < exp.length(); i++)
{
// if current char is an operand, push it to the stack
if (exp[i] >= '0' && exp[i] <= '9') {
stack.push(exp[i] - '0');
}
// if current char is an operator
else
{
// pop top two elements from the stack
int x = stack.top();
stack.pop()
30
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
int y = stack.top();
stack.pop();
// evaluate the expression x op y, and push the
// result back to the stack
if (exp[i] == '+')
stack.push(y + x);
else if (exp[i] == '-')
stack.push(y - x);
else if (exp[i] == '*')
stack.push(y * x);
else if (exp[i] == '/')
stack.push(y / x);
}
}
// At this point, the stack is left with only one element
// i.e. expression result
return stack.top();
}
int main()
{ char exp[20];
char *e;
cout<< "\n enter postfix Expression: =";
cin>> exp;
e = exp;
cout << postfixEval(e);
return 0;
}
31
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
EXPERIMENTAL PROCEDURE:
After writing the source code, compile the program by selecting Build option from menu bar
or by pressing Ctrl-F9 keys together. If there are no errors detected in the program & object
file (.obj) has been created successfully, then execute the program by pressing Ctrl-F10 keys
together.
OUTPUT:
CONCLUSION:
Postfix expression has been successfully implemented using stacks.
32
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
EXPERIMENT-8
AIM: Write a recursive function for Tower of Hanoi problem.
OBJECTIVE: To learn how to write recursive programs for complex iterative problems
PREREQUISITES: Concept and Usage of recursion using stacks
RESOURCE/ EXPERIMENTAL SET-UP/EQUIPMENT/APPARATUS/TOOLS: Linux OS or Windows 8/10 Operating System C/C++,Turbo C or gcc compiler in linux
THEORY AND APPLICATION:
Tower of Hanoi, is a mathematical puzzle which consists of three towers (pegs) and more
than one rings is as depicted –
These rings are of different sizes and stacked upon in an ascending order, i.e. the smaller
one
sits over the larger one. There are other variations of the puzzle where the number of disks
increase, but the tower count remains the same.
Rules:
The mission is to move all the disks to some another tower without violating the sequence
of
arrangement. A few rules to be followed for Tower of Hanoi are −
33
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
* Only one disk can be moved among the towers at any given time.
* Only the "top" disk can be removed.
* No large disk can sit over a small disk.
ALGORITHM:
A recursive algorithm for Tower of Hanoi can be driven as follows −
START
Procedure Hanoi(disk, source, dest, aux)
IF disk == 1, THEN
move disk from source to dest
ELSE
Hanoi(disk - 1, source, aux, dest) // Step 1
move disk from source to dest // Step 2
Hanoi(disk - 1, aux, dest, source) // Step 3
END IF
END Procedure
STOP
A skeletal recursive procedure (Outline) for the solution of the problem for N number of
disks
is as follows:
1. Move the top N-1 disks from peg A to peg B (using C as an auxiliarypeg)
2. Move the bottom disk from peg A to peg C
3. Move N-1 disks from Peg B to Peg C (using Peg A as an auxiliary peg)
4.
SOURCE CODE:
#include <iostream>
34
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
using namespace std;
void toh(int ,char,char,char);
int main()
{ char a,b,c;
int x;
a='A'; //Start disc
b='B'; //Auxillary disc
c='C'; //End Disc
cout<<"Enter No. of discs:";
cin>>x;
toh(x,a,c,b);
return 0;
}
void toh(int x,char a ,char c,char b)
{
if(x==1)
{ cout<<"Move the disc 1 from "<<a<<" to "<<c<<endl; //only disc remaining
x=x-1;
}
else
{
toh(x-1,a,b,c) ; //Moving n-1 poles to auxillary pole
cout<<"Move the disc "<<x<<" from"<<a<<" to "<<c<<endl;
toh(x-1,b,c,a); // Move n-1 poles to destination
}
}
EXPERIMENTAL PROCEDURE:
35
Roll no. 1915037
Name – ANIKET THAKUR
CGC,FACULTY OF ENGINEERING
JHANJERI, MOHALI – 140307
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
After writing the source code, compile the program by selecting Build option from menu bar
or by pressing Ctrl-F9 keys together. If there are no errors detected in the program & object
file (.obj) has been created successfully, then execute the program by pressing Ctrl-F10 keys
together.
OUTPUT:
CONCLUSION:
Recursive solution to puzzle problem “Tower of Hanoi” has been studied & implemented
successfully using stacks.
36
Roll no. 1915037
Name – ANIKET THAKUR