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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. We have discussed infix to postfix conversion. In this post, evaluation of postfix expressions is discussed.
Following is an algorithm for evaluation postfix expressions.

1) Create a stack to store operands (or values).
2) Scan the given expression and do the following for every scanned element. …..

If the element is a number, push it into the stack …..
If the element is an operator, pop operands for the operator from the stack. Evaluate the operator and push the result back to the stack

3) When the expression is ended, the number in the stack is the final answer

Example:

Let the given expression be “2 3 1 * + 9 -“. We scan all elements one by one.

Scan ‘2’, it’s a number, so push it to stack. Stack contains ‘2’
Scan ‘3’, again a number, push it to stack, stack now contains ‘2 3’ (from bottom to top)
Scan ‘1’, again a number, push it to stack, stack now contains ‘2 3 1’
Scan ‘*’, it’s an operator, pop two operands from stack, apply the * operator on operands, we get 3*1 which results in 3. We push the result ‘3’ to stack. The stack now becomes ‘2 3’.
Scan ‘+’, it’s an operator, pop two operands from stack, apply the + operator on operands, we get 3 + 2 which results in 5. We push the result ‘5’ to stack. The stack now becomes ‘5’.
Scan ‘9’, it’s a number, we push it to the stack. The stack now becomes ‘5 9’.
Scan ‘-‘, it’s an operator, pop two operands from stack, apply the – operator on operands, we get 5 – 9 which results in -4. We push the result ‘-4’ to the stack. The stack now becomes ‘-4’.
There are no more elements to scan, we return the top element from the stack (which is the only element left in a stack).

Below is the implementation of the above algorithm.

C++

// C++ program to evaluate value of a postfix expression
#include <iostream>
#include <string.h>

using namespace std;

// Stack type
struct Stack
{
int top;
unsigned capacity;
int* array;
};

// Stack Operations
struct Stack* createStack( unsigned capacity )
{
struct Stack* stack = (struct Stack*) malloc(sizeof(struct Stack));

if (!stack) return NULL;

stack->top = -1;
stack->capacity = capacity;
stack->array = (int*) malloc(stack->capacity * sizeof(int));

if (!stack->array) return NULL;

return stack;
}

int isEmpty(struct Stack* stack)
{
return stack->top == -1 ;
}

char peek(struct Stack* stack)
{
return stack->array[stack->top];
}

char pop(struct Stack* stack)
{
if (!isEmpty(stack))
return stack->array[stack->top--] ;
return '$';
}

void push(struct Stack* stack, char op)
{
stack->array[++stack->top] = op;
}

// The main function that returns value of a given postfix expression
int evaluatePostfix(char* exp)
{
// Create a stack of capacity equal to expression size
struct Stack* stack = createStack(strlen(exp));
int i;

// See if stack was created successfully
if (!stack) return -1;

// Scan all characters one by one
for (i = 0; exp[i]; ++i)
{
// If the scanned character is an operand (number here),
// push it to the stack.
if (isdigit(exp[i]))
push(stack, exp[i] - '0');

// If the scanned character is an operator, pop two
// elements from stack apply the operator
else
{
int val1 = pop(stack);
int val2 = pop(stack);
switch (exp[i])
{
case '+': push(stack, val2 + val1); break;
case '-': push(stack, val2 - val1); break;
case '*': push(stack, val2 * val1); break;
case '/': push(stack, val2/val1); break;
}
}
}
return pop(stack);
}

// Driver program to test above functions
int main()
{
char exp[] = "231*+9-";
cout<<"postfix evaluation: "<< evaluatePostfix(exp);
return 0;
}

C

// C program to evaluate value of a postfix expression
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#include <stdlib.h>

// Stack type
struct Stack
{
int top;
unsigned capacity;
int* array;
};

// Stack Operations
struct Stack* createStack( unsigned capacity )
{
struct Stack* stack = (struct Stack*) malloc(sizeof(struct Stack));

if (!stack) return NULL;

stack->top = -1;
stack->capacity = capacity;
stack->array = (int*) malloc(stack->capacity * sizeof(int));

if (!stack->array) return NULL;

return stack;
}

int isEmpty(struct Stack* stack)
{
return stack->top == -1 ;
}

char peek(struct Stack* stack)
{
return stack->array[stack->top];
}

char pop(struct Stack* stack)
{
if (!isEmpty(stack))
return stack->array[stack->top--] ;
return '$';
}

void push(struct Stack* stack, char op)
{
stack->array[++stack->top] = op;
}

// The main function that returns value of a given postfix expression
int evaluatePostfix(char* exp)
{
// Create a stack of capacity equal to expression size
struct Stack* stack = createStack(strlen(exp));
int i;

// See if stack was created successfully
if (!stack) return -1;

// Scan all characters one by one
for (i = 0; exp[i]; ++i)
{
// If the scanned character is an operand (number here),
// push it to the stack.
if (isdigit(exp[i]))
push(stack, exp[i] - '0');

// If the scanned character is an operator, pop two
// elements from stack apply the operator
else
{
int val1 = pop(stack);
int val2 = pop(stack);
switch (exp[i])
{
case '+': push(stack, val2 + val1); break;
case '-': push(stack, val2 - val1); break;
case '*': push(stack, val2 * val1); break;
case '/': push(stack, val2/val1); break;
}
}
}
return pop(stack);
}

// Driver program to test above functions
int main()
{
char exp[] = "231*+9-";
printf ("postfix evaluation: %d", evaluatePostfix(exp));
return 0;
}

Java

// Java program to evaluate value of a postfix expression

import java.util.Stack;

public class Test
{
// Method to evaluate value of a postfix expression
static int evaluatePostfix(String exp)
{
//create a stack
Stack<Integer> stack=new Stack<>();

// Scan all characters one by one
for(int i=0;i<exp.length();i++)
{
char c=exp.charAt(i);

// If the scanned character is an operand (number here),
// push it to the stack.
if(Character.isDigit(c))
stack.push(c - '0');

// If the scanned character is an operator, pop two
// elements from stack apply the operator
else
{
int val1 = stack.pop();
int val2 = stack.pop();

switch(c)
{
case '+':
stack.push(val2+val1);
break;

case '-':
stack.push(val2- val1);
break;

case '/':
stack.push(val2/val1);
break;

case '*':
stack.push(val2*val1);
break;
}
}
}
return stack.pop();
}

// Driver program to test above functions
public static void main(String[] args)
{
String exp="231*+9-";
System.out.println("postfix evaluation: "+evaluatePostfix(exp));
}
}
// Contributed by Sumit Ghosh

Python3

# Python program to evaluate value of a postfix expression

# Class to convert the expression
class Evaluate:

# Constructor to initialize the class variables
def __init__(self, capacity):
self.top = -1
self.capacity = capacity
# This array is used a stack
self.array = []

# check if the stack is empty
def isEmpty(self):
return True if self.top == -1 else False

# Return the value of the top of the stack
def peek(self):
return self.array[-1]

# Pop the element from the stack
def pop(self):
if not self.isEmpty():
self.top -= 1
return self.array.pop()
else:
return "$"

# Push the element to the stack
def push(self, op):
self.top += 1
self.array.append(op)

# The main function that converts given infix expression
# to postfix expression
def evaluatePostfix(self, exp):

# Iterate over the expression for conversion
for i in exp:

# If the scanned character is an operand
# (number here) push it to the stack
if i.isdigit():
self.push(i)

# If the scanned character is an operator,
# pop two elements from stack and apply it.
else:
val1 = self.pop()
val2 = self.pop()
self.push(str(eval(val2 + i + val1)))

return int(self.pop())

# Driver program to test above function
exp = "231*+9-"
obj = Evaluate(len(exp))
print ("postfix evaluation: %d"%(obj.evaluatePostfix(exp)))
# This code is contributed by Nikhil Kumar Singh(nickzuck_007)

C#

// C# program to evaluate value of a postfix expression
using System;
using System.Collections;

namespace GFG
{
class Geek
{
//Main() method
static void Main()
{
Geek e = new Geek();
e.v = ("231*+9-");
e.expression();
Console.WriteLine("postfix evaluation: " + e.answer);
Console.Read();
}

public string v;
//'v' is variable to store the string value

public string answer;
Stack i = new Stack();
//'Stack()' is inbuilt function for namespace 'System.Collections'

public void expression()
//evaluation method
{
int a, b, ans;
for (int j = 0; j < v.Length; j++)
//'v.Length' means length of the string
{
String c = v.Substring(j, 1);
if (c.Equals("*"))
{
String sa = (String)i.Pop();
String sb = (String)i.Pop();
a = Convert.ToInt32(sb);
b = Convert.ToInt32(sa);
ans = a * b;
i.Push(ans.ToString());

}
else if (c.Equals("/"))
{
String sa = (String)i.Pop();
String sb = (String)i.Pop();
a = Convert.ToInt32(sb);
b = Convert.ToInt32(sa);
ans = a / b;
i.Push(ans.ToString());
}
else if (c.Equals("+"))
{
String sa = (String)i.Pop();
String sb = (String)i.Pop();
a = Convert.ToInt32(sb);
b = Convert.ToInt32(sa);
ans = a + b;
i.Push(ans.ToString());

}
else if (c.Equals("-"))
{
String sa = (String)i.Pop();
String sb = (String)i.Pop();
a = Convert.ToInt32(sb);
b = Convert.ToInt32(sa);
ans = a - b;
i.Push(ans.ToString());

}
else
{
i.Push(v.Substring(j, 1));
}
}
answer = (String)i.Pop();
}
}
}

Javascript

<script>

// Javascript program to evaluate value of a postfix expression

// Method to evaluate value of a postfix expression
function evaluatePostfix(exp)
{
//create a stack
let stack=[];

// Scan all characters one by one
for(let i=0;i<exp.length;i++)
{
let c=exp[i];

// If the scanned character is an operand (number here),
// push it to the stack.
if(! isNaN( parseInt(c) ))
stack.push(c.charCodeAt(0) - '0'.charCodeAt(0));

// If the scanned character is an operator, pop two
// elements from stack apply the operator
else
{
let val1 = stack.pop();
let val2 = stack.pop();

switch(c)
{
case '+':
stack.push(val2+val1);
break;

case '-':
stack.push(val2- val1);
break;

case '/':
stack.push(val2/val1);
break;

case '*':
stack.push(val2*val1);
break;
}
}
}
return stack.pop();
}

// Driver program to test above functions
let exp="231*+9-";
document.write("postfix evaluation: "+evaluatePostfix(exp));

// This code is contributed by avanitrachhadiya2155
</script>

Output

postfix evaluation: -4

Complexity:
Time complexity: O(N) as we need to traverse N times.
Auxiliary Space: O(N) as we are having n elements in stack data structure
There are the following limitations of the above implementation.

It supports only 4 binary operators ‘+’, ‘*’, ‘-‘ and ‘/’. It can be extended for more operators by adding more switch cases.
The allowed operands are only single-digit operands. The program can be extended for multiple digits by adding a separator-like space between all elements (operators and operands) of the given expression.

Below given is the extended program which allows operands to have multiple digits.

C++ 14

// C++ program to evaluate value of a postfix
// expression having multiple digit operands
#include <bits/stdc++.h>
using namespace std;

// Stack type
class Stack
{
public:
int top;
unsigned capacity;
int* array;
};

// Stack Operations
Stack* createStack( unsigned capacity )
{
Stack* stack = new Stack();

if (!stack) return NULL;

stack->top = -1;
stack->capacity = capacity;
stack->array = new int[(stack->capacity * sizeof(int))];

if (!stack->array) return NULL;

return stack;
}

int isEmpty(Stack* stack)
{
return stack->top == -1 ;
}

int peek(Stack* stack)
{
return stack->array[stack->top];
}

int pop(Stack* stack)
{
if (!isEmpty(stack))
return stack->array[stack->top--] ;
return '$';
}

void push(Stack* stack,int op)
{
stack->array[++stack->top] = op;
}

// The main function that returns value
// of a given postfix expression
int evaluatePostfix(char* exp)
{
// Create a stack of capacity equal to expression size
Stack* stack = createStack(strlen(exp));
int i;

// See if stack was created successfully
if (!stack) return -1;

// Scan all characters one by one
for (i = 0; exp[i]; ++i)
{
//if the character is blank space then continue
if(exp[i] == ' ')continue;

// If the scanned character is an
// operand (number here),extract the full number
// Push it to the stack.
else if (isdigit(exp[i]))
{
int num=0;

//extract full number
while(isdigit(exp[i]))
{
num = num * 10 + (int)(exp[i] - '0');
i++;
}
i--;

//push the element in the stack
push(stack,num);
}

// If the scanned character is an operator, pop two
// elements from stack apply the operator
else
{
int val1 = pop(stack);
int val2 = pop(stack);

switch (exp[i])
{
case '+': push(stack, val2 + val1); break;
case '-': push(stack, val2 - val1); break;
case '*': push(stack, val2 * val1); break;
case '/': push(stack, val2/val1); break;

}
}
}
return pop(stack);
}

// Driver code
int main()
{
char exp[] = "100 200 + 2 / 5 * 7 +";
cout << evaluatePostfix(exp);
return 0;
}

// This code is contributed by rathbhupendra

C

// C program to evaluate value of a postfix
// expression having multiple digit operands
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#include <stdlib.h>

// Stack type
struct Stack
{
int top;
unsigned capacity;
int* array;
};

// Stack Operations
struct Stack* createStack( unsigned capacity )
{
struct Stack* stack = (struct Stack*) malloc(sizeof(struct Stack));

if (!stack) return NULL;

stack->top = -1;
stack->capacity = capacity;
stack->array = (int*) malloc(stack->capacity * sizeof(int));

if (!stack->array) return NULL;

return stack;
}

int isEmpty(struct Stack* stack)
{
return stack->top == -1 ;
}

int peek(struct Stack* stack)
{
return stack->array[stack->top];
}

int pop(struct Stack* stack)
{
if (!isEmpty(stack))
return stack->array[stack->top--] ;
return '$';
}

void push(struct Stack* stack,int op)
{
stack->array[++stack->top] = op;
}

// The main function that returns value
// of a given postfix expression
int evaluatePostfix(char* exp)
{
// Create a stack of capacity equal to expression size
struct Stack* stack = createStack(strlen(exp));
int i;

// See if stack was created successfully
if (!stack) return -1;

// Scan all characters one by one
for (i = 0; exp[i]; ++i)
{
//if the character is blank space then continue
if(exp[i]==' ')continue;

// If the scanned character is an
// operand (number here),extract the full number
// Push it to the stack.
else if (isdigit(exp[i]))
{
int num=0;

//extract full number
while(isdigit(exp[i]))
{
num=num*10 + (int)(exp[i]-'0');
i++;
}
i--;

//push the element in the stack
push(stack,num);
}

// If the scanned character is an operator, pop two
// elements from stack apply the operator
else
{
int val1 = pop(stack);
int val2 = pop(stack);

switch (exp[i])
{
case '+': push(stack, val2 + val1); break;
case '-': push(stack, val2 - val1); break;
case '*': push(stack, val2 * val1); break;
case '/': push(stack, val2/val1); break;

}
}
}
return pop(stack);
}

// Driver program to test above functions
int main()
{
char exp[] = "100 200 + 2 / 5 * 7 +";
printf ("%d", evaluatePostfix(exp));
return 0;
}

// This code is contributed by Arnab Kundu

Java

// Java program to evaluate value of a postfix
// expression having multiple digit operands
import java.util.Stack;

class Test1
{
// Method to evaluate value of a postfix expression
static int evaluatePostfix(String exp)
{
//create a stack
Stack<Integer> stack = new Stack<>();

// Scan all characters one by one
for(int i = 0; i < exp.length(); i++)
{
char c = exp.charAt(i);

if(c == ' ')
continue;

// If the scanned character is an operand
// (number here),extract the number
// Push it to the stack.
else if(Character.isDigit(c))
{
int n = 0;

//extract the characters and store it in num
while(Character.isDigit(c))
{
n = n*10 + (int)(c-'0');
i++;
c = exp.charAt(i);
}
i--;

//push the number in stack
stack.push(n);
}

// If the scanned character is an operator, pop two
// elements from stack apply the operator
else
{
int val1 = stack.pop();
int val2 = stack.pop();

switch(c)
{
case '+':
stack.push(val2+val1);
break;

case '-':
stack.push(val2- val1);
break;

case '/':
stack.push(val2/val1);
break;

case '*':
stack.push(val2*val1);
break;
}
}
}
return stack.pop();
}

// Driver program to test above functions
public static void main(String[] args)
{
String exp = "100 200 + 2 / 5 * 7 +";
System.out.println(evaluatePostfix(exp));
}
}

// This code is contributed by Arnab Kundu

Python3

# Python program to evaluate value of a postfix
# expression with integers containing multiple digits

class evalpostfix:
def __init__(self):
self.stack =[]
self.top =-1
def pop(self):
if self.top ==-1:
return
else:
self.top-= 1
return self.stack.pop()
def push(self, i):
self.top+= 1
self.stack.append(i)

def centralfunc(self, ab):
for i in ab:

# if the component of the list is an integer
try:
self.push(int(i))
# if the component of the list is not an integer,
# it must be an operator. Using ValueError, we can
# evaluate components of the list other than type int
except ValueError:
val1 = self.pop()
val2 = self.pop()
if i == '/':
self.push(val2 / val1)
else:
# switch statement to perform operation
switcher ={'+':val2 + val1, '-':val2-val1, '*':val2 * val1, '^':val2**val1}
self.push(switcher.get(i))
return int(self.pop())

str ='100 200 + 2 / 5 * 7 +'

# splitting the given string to obtain
# integers and operators into a list
strconv = str.split(' ')
obj = evalpostfix()
print(obj.centralfunc(strconv))

# This code is contributed by Amarnath Reddy

C#

// C# program to evaluate value of a postfix
// expression having multiple digit operands
using System;
using System.Collections.Generic;

class GFG
{
// Method to evaluate value of
// a postfix expression
public static int evaluatePostfix(string exp)
{
// create a stack
Stack<int> stack = new Stack<int>();

// Scan all characters one by one
for (int i = 0; i < exp.Length; i++)
{
char c = exp[i];

if (c == ' ')
{
continue;
}

// If the scanned character is an
// operand (number here),extract
// the number. Push it to the stack.
else if (char.IsDigit(c))
{
int n = 0;

// extract the characters and
// store it in num
while (char.IsDigit(c))
{
n = n * 10 + (int)(c - '0');
i++;
c = exp[i];
}
i--;

// push the number in stack
stack.Push(n);
}

// If the scanned character is
// an operator, pop two elements
// from stack apply the operator
else
{
int val1 = stack.Pop();
int val2 = stack.Pop();

switch (c)
{
case '+':
stack.Push(val2 + val1);
break;

case '-':
stack.Push(val2 - val1);
break;

case '/':
stack.Push(val2 / val1);
break;

case '*':
stack.Push(val2 * val1);
break;
}
}
}
return stack.Pop();
}

// Driver Code
public static void Main(string[] args)
{
string exp = "100 200 + 2 / 5 * 7 +";
Console.WriteLine(evaluatePostfix(exp));
}
}

// This code is contributed by Shrikant13

Javascript

<script>
// Javascript program to evaluate value of a postfix
// expression having multiple digit operands

// Method to evaluate value of
// a postfix expression
function evaluatePostfix(exp)
{
// create a stack
let stack = [];

// Scan all characters one by one
for (let i = 0; i < exp.length; i++)
{
let c = exp[i];

if (c == ' ')
{
continue;
}

// If the scanned character is an
// operand (number here),extract
// the number. Push it to the stack.
else if (c >= '0' && c <= '9')
{
let n = 0;

// extract the characters and
// store it in num
while (c >= '0' && c <= '9')
{
n = n * 10 + (c - '0');
i++;
c = exp[i];
}
i--;

// push the number in stack
stack.push(n);
}

// If the scanned character is
// an operator, pop two elements
// from stack apply the operator
else
{
let val1 = stack.pop();
let val2 = stack.pop();

switch (c)
{
case '+':
stack.push(val2 + val1);
break;

case '-':
stack.push(val2 - val1);
break;

case '/':
stack.push(parseInt(val2 / val1, 10));
break;

case '*':
stack.push(val2 * val1);
break;
}
}
}
return stack.pop();
}

let exp = "100 200 + 2 / 5 * 7 +";
document.write(evaluatePostfix(exp));

// This code is contributed by decode2207.
</script>

Output

757
Complexity :
Time complexity : O(N) as we need to traverse N times.
Auxiliary Space : O(N) as we are having n elements in stack data structure

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The importance of Evaluation of Postfix Expression cannot be overstated, especially for Class 8 aspirants. This document holds the key to success in the Class 8 exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

Evaluation of Postfix Expression Notes

Evaluation of Postfix Expression Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to Evaluation of Postfix Expression. It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, Evaluation of Postfix Expression Notes on EduRev are your ultimate resource for success.

Evaluation of Postfix Expression Class 8 Questions

The "Evaluation of Postfix Expression Class 8 Questions" guide is a valuable resource for all aspiring students preparing for the Class 8 exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study Evaluation of Postfix Expression on the App

Students of Class 8 can study Evaluation of Postfix Expression alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the Evaluation of Postfix Expression, students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of Evaluation of Postfix Expression is prepared as per the latest Class 8 syllabus.

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