Evaluate Postfix Expression Using Stack in DSA Python - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Evaluate Postfix Expression Output

What is the output of the following Python code that evaluates a postfix expression using a stack?

DSA Python

def evaluate_postfix(expression):
    stack = []
    for char in expression:
        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(int(a / b))
    return stack.pop()

result = evaluate_postfix("231*+9-")
print(result)

A -4

B 7

C 8

D 2

💡 Hint

Trace the stack operations step-by-step for each character in the expression.

The postfix expression "231*+9-" is evaluated as follows: push 2, push 3, push 1, multiply top two (3*1=3), stack becomes [2,3], add top two (2+3=5), stack becomes [5], push 9, subtract top two (5-9=-4), final result is -4.

🧠 Conceptual

intermediate

Stack Usage in Postfix Evaluation

Why is a stack the best data structure to evaluate postfix expressions?

A Because it stores all operands in sorted order automatically.

B Because it uses less memory than other data structures.

C Because it can store operators and operands separately.

D Because it allows easy access to the last two operands needed for each operator.

💡 Hint

Think about how postfix expressions are evaluated step-by-step.

A stack allows pushing operands and popping the last two operands when an operator is encountered, which matches the postfix evaluation process perfectly.

🔧 Debug

advanced

Identify the Error in Postfix Evaluation Code

What error will the following code raise when evaluating the postfix expression "82/"? ```python def evaluate_postfix(expression): stack = [] for char in expression: 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("82/")) ```

A No error, output is 4

B IndexError

C TypeError

D ZeroDivisionError

💡 Hint

Check the division operation and the stack contents carefully.

The expression "82/" means 8 divided by 2, which is 4. The code uses integer division (//), which works correctly here. No error occurs.

❓ Predict Output

advanced

Output of Postfix Evaluation with Multi-digit Numbers

What will be the output of this code that attempts to evaluate a postfix expression with multi-digit numbers separated by spaces?

DSA Python

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

print(evaluate_postfix("12 3 4 * + 6 -"))

A SyntaxError

B 18

C 14

D 24

💡 Hint

Evaluate the expression step-by-step: 3*4=12, 12+12=24, 24-6=18.

The expression "12 3 4 * + 6 -" evaluates as: push 12, push 3, push 4, multiply top two (3*4=12), stack: [12,12], add top two (12+12=24), stack: [24], push 6, subtract top two (24-6=18), final result 18.

🧠 Conceptual

expert

Handling Division in Postfix Evaluation

In postfix evaluation, why might using integer division (//) instead of float division (/) cause issues in some cases?

A Because integer division converts operands to strings before dividing.

B Because integer division raises an error when dividing by zero.

C Because integer division truncates the result, losing decimal precision which may be needed.

D Because integer division always rounds up the result.

💡 Hint

Think about the difference between truncating and keeping decimals.

Integer division truncates the decimal part, which can lead to incorrect results if the exact decimal value is important in the expression evaluation.

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