Stack | Set 4 (Evaluation of Postfix Expression)

Difficulty Level : Easy
Last Updated : 14 Jan, 2022

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.
…..a) If the element is a number, push it into the stack
…..b) 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.
1) Scan ‘2’, it’s a number, so push it to stack. Stack contains ‘2’
2) Scan ‘3’, again a number, push it to stack, stack now contains ‘2 3’ (from bottom to top)
3) Scan ‘1’, again a number, push it to stack, stack now contains ‘2 3 1’
4) 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’.
5) 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’.
6) Scan ‘9’, it’s a number, we push it to the stack. The stack now becomes ‘5 9’.
7) 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’.
8) 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

The time complexity of the evaluation algorithm is O(n) where n is a number of characters in the input expression.

There are the following limitations of the above implementation.
1) It supports only 4 binary operators ‘+’, ‘*’, ‘-‘ and ‘/’. It can be extended for more operators by adding more switch cases.
2) 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++

// 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()
 
                # switch statement to perform operation
                switcher ={'+':val2 + val1, '-':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 :

References:
http://www.cs.nthu.edu.tw/~wkhon/ds/ds10/tutorial/tutorial2.pdf
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Stack | Set 4 (Evaluation of Postfix Expression)

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