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Evaluation of Postfix Expression

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Given a postfix expression, the task is to evaluate the postfix expression.

Postfix expression: The expression of the form “a b operator” (ab+) i.e., when a pair of operands is followed by an operator.

Examples:

Input: str = “2 3 1 * + 9 -“
Output: -4
Explanation: If the expression is converted into an infix expression, it will be 2 + (3 * 1) – 9 = 5 – 9 = -4.

Input: str = “100 200 + 2 / 5 * 7 +”
Output: 757

Evaluation of Postfix Expression using Stack:

To evaluate a postfix expression we can use a stack.

Iterate the expression from left to right and keep on storing the operands into a stack. Once an operator is received, pop the two topmost elements and evaluate them and push the result in the stack again.

Illustration:

Follow the below illustration for a better understanding:

Consider the expression: exp = “2 3 1 * + 9 -“

  • Scan 2, it’s a number, So push it into stack. Stack contains ‘2’.
Push 2 into stack

Push 2 into stack

  • Scan 3, again a number, push it to stack, stack now contains ‘2 3’ (from bottom to top) 
Push 3 into stack

Push 3 into stack

  • Scan 1, again a number, push it to stack, stack now contains ‘2 3 1’ 
Push 1 into stack

Push 1 into stack

  • 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’. 
Evaluate * operator and push result in stack

Evaluate * operator and push result in stack

  • 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’. 
Evaluate + operator and push result in stack

Evaluate + operator and push result in stack

  • Scan 9, it’s a number. So we push it to the stack. The stack now becomes ‘5 9’. 
Push 9 into stack

Push 9 into stack

  • 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’.
Evaluate '-' operator and push result in stack

Evaluate ‘-‘ operator and push result in stack

  • There are no more elements to scan, we return the top element from the stack (which is the only element left in a stack).

So the result becomes -4.

Follow the steps mentioned below to evaluate postfix expression using stack:

  • Create a stack to store operands (or values).
  • Scan the given expression from left to right 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.
  • When the expression is ended, the number in the stack is the final answer.

Below is the implementation of the above approach:

C




// C program to evaluate value of a postfix expression
#include <ctype.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.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 code
int main()
{
    char exp[] = "231*+9-";
   
    // Function call
    printf("postfix evaluation: %d", evaluatePostfix(exp));
    return 0;
}

C++




// C++ program to evaluate value of a postfix expression
#include <bits/stdc++.h>
using namespace std;
 
// The main function that returns value
// of a given postfix expression
int evaluatePostfix(string exp)
{
    // Create a stack of capacity equal to expression size
    stack<int> st;
 
    // Scan all characters one by one
    for (int i = 0; i < exp.size(); ++i) {
         
        // If the scanned character is an operand
        // (number here), push it to the stack.
        if (isdigit(exp[i]))
            st.push(exp[i] - '0');
 
        // If the scanned character is an operator,
        // pop two elements from stack apply the operator
        else {
            int val1 = st.top();
            st.pop();
            int val2 = st.top();
            st.pop();
            switch (exp[i]) {
            case '+':
                st.push(val2 + val1);
                break;
            case '-':
                st.push(val2 - val1);
                break;
            case '*':
                st.push(val2 * val1);
                break;
            case '/':
                st.push(val2 / val1);
                break;
            }
        }
    }
    return st.top();
}
 
// Driver code
int main()
{
    string exp = "231*+9-";
   
    // Function call
    cout << "postfix evaluation: " << 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 code
    public static void main(String[] args)
    {
        String exp = "231*+9-";
       
        // Function call
        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 code
if __name__ == '__main__':
    exp = "231*+9-"
    obj = Evaluate(len(exp))
     
    # Function call
    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();
    }
 
    //'v' is variable to store the string value
    public string v;
 
    public string answer;
    Stack i = new Stack();
 
    // evaluation method
    public void expression()
    {
        int a, b, ans;
        for (int j = 0; j < v.Length; j++)
        {
            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

Time Complexity: O(N) 
Auxiliary Space: O(N)

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.

Postfix evaluation for multi-digit numbers:

The above 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 <ctype.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.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 +";
   
    // Function call
    printf("%d", evaluatePostfix(exp));
    return 0;
}
 
// This code is contributed by Arnab Kundu

C++14




// C++ program to evaluate value of a postfix
// expression having multiple digit operands
#include <bits/stdc++.h>
using namespace std;
 
// 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<int> st;
    int i;
 
    // 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
            st.push(num);
        }
 
        // If the scanned character is an operator, pop two
        // elements from stack apply the operator
        else {
            int val1 = st.top();
            st.pop();
            int val2 = st.top();
            st.pop();
 
            switch (exp[i]) {
            case '+':
                st.push(val2 + val1);
                break;
            case '-':
                st.push(val2 - val1);
                break;
            case '*':
                st.push(val2 * val1);
                break;
            case '/':
                st.push(val2 / val1);
                break;
            }
        }
    }
    return st.top();
}
 
// Driver code
int main()
{
    char exp[] = "100 200 + 2 / 5 * 7 +";
   
    // Function call
    cout << evaluatePostfix(exp);
    return 0;
}
 
// This code is contributed by rathbhupendra

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 +";
       
        // Function call
        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())
 
 
 
# Driver code
if __name__ == '__main__':
    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 +";
       
        // Function call
        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

Time Complexity: O(N) 
Auxiliary Space: O(N)


Last Updated : 27 Mar, 2023
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