Infix to Postfix Conversion Using Stack in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main purpose of converting an infix expression to postfix?

To make it easier for computers to evaluate expressions without worrying about operator precedence or parentheses.

beginner

What data structure is commonly used to convert infix expressions to postfix?

A stack is used to temporarily hold operators and manage their precedence during conversion.

intermediate

In the infix to postfix conversion, what happens when an operator with higher or equal precedence is encountered on the stack compared to the current operator?

Operators with higher or equal precedence on the stack are popped and added to the postfix expression before pushing the current operator.

intermediate

Why do we push '(' onto the stack during infix to postfix conversion?

Because '(' marks the start of a sub-expression and helps to control when operators inside parentheses are popped.

beginner

What is the postfix expression for the infix expression: A + B * C?

The postfix expression is: A B C * +

Which data structure is essential for converting infix to postfix expressions?

A Stack

B Queue

C Linked List

D Array

Stack is used to hold operators and manage precedence during conversion.

What should you do when you encounter a ')' in the infix expression during conversion?

A Push it onto the stack

B Ignore it

C Pop operators from the stack until '(' is found

D Add it directly to the postfix expression

Pop operators until '(' is found to close the sub-expression.

In infix to postfix conversion, which operator has the highest precedence?

A +

B -

C (

D *

Multiplication (*) has higher precedence than addition (+) and subtraction (-).

What happens to remaining operators in the stack after processing the entire infix expression?

A They are added to the postfix expression

B They are discarded

C They remain in the stack

D They are reversed

Remaining operators are popped and added to the postfix expression.

Which of the following is a valid postfix expression for infix: (A + B) * C?

A A B * C +

B A B + C *

C A + B C *

D A B C + *

Postfix for (A + B) * C is A B + C *.

Explain step-by-step how to convert the infix expression 'A + B * C' to postfix using a stack.

Think about operator precedence and when to push or pop from the stack.

Describe how parentheses affect the infix to postfix conversion process.

Consider how '(' and ')' help manage order of operations.

Practice

1. What is the main purpose of using a stack in converting an infix expression to postfix?

easy

A. To reverse the order of operands

B. To temporarily hold operators and manage their precedence

C. To store operands permanently

D. To count the number of operators

Solution

1. Step 1: Understand the role of stack in infix to postfix

   The stack is used to hold operators temporarily while processing the expression to respect operator precedence and associativity.

2. Step 2: Clarify what the stack does not do

   The stack does not store operands permanently or reverse operands; it only manages operators.

3. Final Answer:

   To temporarily hold operators and manage their precedence -> Option B

4. Quick Check:

   Stack manages operators [OK]

Hint: Stack holds operators, not operands, during conversion [OK]

Common Mistakes:

• Thinking stack stores operands
• Confusing stack role with reversing expression
• Ignoring operator precedence handling

2. Which of the following is the correct way to push an operator onto a stack in Python?

easy

A. stack.append(operator)

B. stack.push(operator)

C. stack.insert(operator)

D. stack.add(operator)

Solution

1. Step 1: Recall Python list methods for stack operations

   In Python, a list is used as a stack and the method to add an element on top is append().

2. Step 2: Identify incorrect methods

   push() and add() are not valid list methods; insert() inserts at a specific index, not top of stack.

3. Final Answer:

   stack.append(operator) -> Option A

4. Quick Check:

   Use append() to push on stack [OK]

Hint: Use append() to push items on Python list stack [OK]

Common Mistakes:

• Using push() which is not a Python list method
• Using add() which is for sets, not lists
• Using insert() incorrectly for stack push

3. What is the postfix expression for the infix expression A + B * C?

medium

A. ABC*+

B. AB+C*

C. A+BC*

D. *ABC+

Solution

1. Step 1: Apply operator precedence rules

   Multiplication (*) has higher precedence than addition (+), so B * C is evaluated first.

2. Step 2: Convert to postfix respecting precedence

   Postfix places operands first, then operator: B C * for multiplication, then A and + last, so expression is A B C * +.

3. Final Answer:

   ABC*+ -> Option A

4. Quick Check:

   Multiplication before addition = ABC*+ [OK]

Hint: Multiply before add; postfix puts operator after operands [OK]

Common Mistakes:

• Ignoring operator precedence
• Placing operators before operands
• Mixing operand order

4. Given the following code snippet for infix to postfix conversion, what is the error?

def precedence(op):
    if op == '+' or op == '-':
        return 1
    if op == '*' or op == '/':
        return 2
    return 0

stack = []
postfix = ''
expr = 'A+B*C'

for char in expr:
    if char.isalpha():
        postfix += char
    else:
        while stack and precedence(stack[-1]) >= precedence(char):
            postfix += stack.pop()
        stack.append(char)

while stack:
    postfix += stack.pop()

print(postfix)

medium

A. The precedence function returns 0 for unknown operators, causing errors

B. The postfix string is not updated with operands

C. The stack is not initialized properly

D. The code does not handle parentheses in the expression

Solution

1. Step 1: Analyze code handling of operators and operands

   The code correctly appends operands and manages operator precedence using the stack.

2. Step 2: Check for missing features

   The code does not check or handle parentheses, which are common in infix expressions and affect precedence.

3. Final Answer:

   The code does not handle parentheses in the expression -> Option D

4. Quick Check:

   Missing parentheses handling [OK]

Hint: Remember to handle parentheses explicitly in infix to postfix [OK]

Common Mistakes:

• Assuming precedence 0 causes errors (it just means lowest)
• Ignoring parentheses handling
• Thinking stack initialization is wrong

5. Convert the infix expression (A+B)*(C-D)/E to postfix notation using stack. What is the correct postfix expression?

hard

A. AB+CD-E*/

B. AB+CD-E/*

C. AB+CD-*E/

D. AB+CD*-E/

Solution

1. Step 1: Handle parentheses and operator precedence

   Parentheses force A+B and C-D to be evaluated first, so their postfix forms are AB+ and CD- respectively.

2. Step 2: Apply multiplication and division in order

   After parentheses, multiply the two results: AB+ CD- * then divide by E: AB+CD-* E /.

3. Final Answer:

   AB+CD-*E/ -> Option C

4. Quick Check:

   Parentheses first, then * and / = AB+CD-*E/ [OK]

Hint: Convert inside parentheses first, then apply * and / left to right [OK]

Common Mistakes:

• Ignoring parentheses order
• Mixing operator order for * and /
• Placing operators before operands