Evaluate Postfix Expression Using Stack in DSA Python - Build from Scratch

Evaluate Postfix Expression Using Stack

📖 Scenario: You are building a simple calculator that reads a postfix expression and calculates the result. Postfix expressions have operators after their operands, like 23+ which means 2 + 3.Using a stack helps to solve this easily by pushing numbers and applying operators step-by-step.

🎯 Goal: Build a program that uses a stack to evaluate a postfix expression and prints the final result.

📋 What You'll Learn

Create a stack as a list

Use a loop to process each character in the postfix expression

Push numbers onto the stack

Pop two numbers when an operator is found and apply the operator

Push the result back to the stack

Print the final result from the stack

💡 Why This Matters

🌍 Real World

Postfix expressions are used in calculators and computer programs to simplify expression evaluation without parentheses.

💼 Career

Understanding stack-based expression evaluation is important for programming, compiler design, and technical interviews.

1

Create the postfix expression string

Create a variable called postfix_expr and set it to the string '231*+9-' which represents the postfix expression.

DSA Python

# Create the postfix expression string
# Your code here

Hint

Postfix expressions are strings like '231*+9-'. Just assign it to postfix_expr.

2

Create an empty stack list

Create an empty list called stack to use as the stack for evaluation.

DSA Python

postfix_expr = '231*+'
# Create an empty list called stack
# Your code here

Hint

Use stack = [] to create an empty list for the stack.

3

Process each character and evaluate using stack

Write a for loop using char to go through each character in postfix_expr. Inside the loop, if char is a digit, convert it to int and append it to stack. If char is an operator (+, -, *, /), pop the top two numbers from stack, apply the operator, and push the result back to stack. Use if and elif to check operators.

DSA Python

postfix_expr = '231*+9-'
stack = []
# Loop through each character in postfix_expr
# Your code here

Hint

Use char.isdigit() to check digits. Use stack.pop() to get last two numbers. Apply operator and push result back.

4

Print the final result from the stack

Print the last remaining value in stack which is the result of the postfix expression evaluation.

DSA Python

postfix_expr = '231*+9-'
stack = []
for char in postfix_expr:
    if char.isdigit():
        stack.append(int(char))
    elif char == '+':
        b = stack.pop()
        a = stack.pop()
        stack.append(a + b)
    elif char == '-':
        b = stack.pop()
        a = stack.pop()
        stack.append(a - b)
    elif char == '*':
        b = stack.pop()
        a = stack.pop()
        stack.append(a * b)
    elif char == '/':
        b = stack.pop()
        a = stack.pop()
        stack.append(a // b)
# Print the final result
# Your code here

Hint

The final result is the last item in the stack. Use print(stack[-1]).

Practice

1. What does evaluating a postfix expression using a stack mainly involve?

easy

A. Using recursion to evaluate the expression

B. Converting the postfix expression to infix before evaluation

C. Pushing operands onto the stack and popping two operands for each operator to apply the operation

D. Ignoring operators and only summing operands

Solution

1. Step 1: Understand postfix evaluation process

   In postfix evaluation, operands are pushed onto a stack. When an operator is encountered, two operands are popped, the operation is applied, and the result is pushed back.

2. Step 2: Identify correct method

   Pushing operands onto the stack and popping two operands for each operator to apply the operation correctly describes this stack-based process. Other options describe unrelated or incorrect methods.

3. Final Answer:

   Pushing operands onto the stack and popping two operands for each operator to apply the operation -> Option C

4. Quick Check:

   Postfix evaluation uses stack push/pop [OK]

Hint: Remember: push operands, pop two for operator, push result [OK]

Common Mistakes:

• Thinking postfix needs conversion to infix first
• Trying to evaluate from left to right without stack
• Ignoring the order of operands when popping

2. Which of the following Python code snippets correctly pushes operands and evaluates a postfix expression using a stack?

easy

A. stack.append(int(char)) when char is digit; pop two, apply operator, push result

B. stack.push(char) for operands; pop one operand for operator

C. Use stack.pop() to push operands; stack.append() to pop

D. Directly evaluate expression without stack

Solution

1. Step 1: Check correct stack operations

   In Python, list's append() adds elements (push), pop() removes last element (pop). For postfix, push operands as integers, pop two for operator.

2. Step 2: Match with options

   stack.append(int(char)) when char is digit; pop two, apply operator, push result correctly uses stack.append(int(char)) for digits and pops two operands for operators. Others misuse push/pop or skip stack.

3. Final Answer:

   stack.append(int(char)) when char is digit; pop two, apply operator, push result -> Option A

4. Quick Check:

   Use append to push, pop to remove [OK]

Hint: Use append() to push and pop() to remove from stack [OK]

Common Mistakes:

• Using stack.push() which is not a Python list method
• Popping only one operand for operator
• Not converting char to int before pushing

3. What is the output of the following Python code that evaluates the postfix expression '231*+9-'?

def evaluate_postfix(expr):
    stack = []
    for char in expr:
        if char.isdigit():
            stack.append(int(char))
        else:
            b = stack.pop()
            a = stack.pop()
            if char == '+':
                stack.append(a + b)
            elif char == '-':
                stack.append(a - b)
            elif char == '*':
                stack.append(a * b)
            elif char == '/':
                stack.append(a // b)
    return stack.pop()

print(evaluate_postfix('231*+9-'))

medium

A. -4

B. -2

C. -3

D. 4

Solution

1. Step 1: Evaluate expression step-by-step

   Expression: '2 3 1 * + 9 -' - Push 2, 3, 1 - '*' operator: pop 1 and 3, multiply 3*1=3, push 3 - '+' operator: pop 3 and 2, add 2+3=5, push 5 - Push 9 - '-' operator: pop 9 and 5, subtract 5-9=-4, push -4

2. Step 2: Final result

   Pop final value from stack: -4

3. Final Answer:

   -4 -> Option A

4. Quick Check:

   Postfix '231*+9-' = -4 [OK]

Hint: Evaluate stepwise: push digits, apply operators on last two [OK]

Common Mistakes:

• Mixing operand order when popping (a, b vs b, a)
• Using float division instead of integer division
• Misreading the expression order

4. The following code is intended to evaluate a postfix expression but throws an error. What is the error and how to fix it?

def eval_postfix(expr):
    stack = []
    for char in expr:
        if char.isdigit():
            stack.append(char)
        else:
            a = stack.pop()
            b = stack.pop()
            if char == '+':
                stack.append(a + b)
            elif char == '-':
                stack.append(a - b)
    return stack.pop()

print(eval_postfix('23+'))

medium

A. SyntaxError due to missing colon; fix by adding colon after if

B. TypeError due to adding strings; fix by converting char to int before pushing

C. IndexError due to popping from empty stack; fix by checking stack size

D. No error; output is '5'

Solution

1. Step 1: Identify error cause

   The code pushes characters as strings onto stack. When popping, it tries to add strings, causing TypeError.

2. Step 2: Fix by converting to int

   Convert char to int before pushing: stack.append(int(char)) to allow arithmetic operations.

3. Final Answer:

   TypeError due to adding strings; fix by converting char to int before pushing -> Option B

4. Quick Check:

   Push integers, not strings, to avoid TypeError [OK]

Hint: Always convert digit chars to int before pushing [OK]

Common Mistakes:

• Pushing strings instead of integers
• Swapping operand order when popping
• Ignoring operator cases other than '+' and '-'

5. Given the postfix expression '56+82/-', what is the result after evaluating it using a stack? Show the step-by-step evaluation.

hard

A. 5

B. 1

C. 9

D. 7

Solution

1. Step 1: Evaluate postfix expression stepwise

   Expression: '5 6 + 8 2 / -' - Push 5, 6 - '+' operator: pop 6 and 5, add 5+6=11, push 11 - Push 8, 2 - '/' operator: pop 2 and 8, integer divide 8//2=4, push 4 - '-' operator: pop 4 and 11, subtract 11-4=7, push 7

2. Step 2: Final result

   Pop final value from stack: 7

3. Final Answer:

   7 -> Option D

4. Quick Check:

   Postfix '56+82/-' = 7 [OK]

Hint: Process operators on last two stack values in order [OK]

Common Mistakes:

• Dividing operands in wrong order (2/8 instead of 8/2)
• Using float division instead of integer division
• Mixing operand order when subtracting