Infix to Postfix Conversion Using Stack in DSA C - 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

In the context of infix to postfix conversion, what data structure is primarily used and why?

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

beginner

What does the precedence of operators mean in infix to postfix conversion?

Precedence defines the order in which operators are applied; higher precedence operators are applied before lower precedence ones.

intermediate

Explain what happens when a closing parenthesis ')' is encountered during infix to postfix conversion.

Operators are popped from the stack and added to the postfix expression until an opening parenthesis '(' is found, which is then discarded.

beginner

Why are operands added directly to the postfix expression during conversion?

Because operands do not affect operator precedence and should appear in the output in the same order as in the infix expression.

Which data structure is used to hold operators during infix to postfix conversion?

A Stack

B Queue

C Array

D Linked List

A stack is used because it allows easy access to the last operator inserted, which is needed to manage precedence.

What should be done when an operand is encountered in the infix expression?

A Push it onto the stack

B Add it directly to the postfix expression

C Ignore it

D Pop operators from the stack

Operands are added directly to the postfix expression as they appear.

When an operator with lower precedence is encountered, what happens to operators on the stack with higher or equal precedence?

A They are popped and added to postfix

B They remain on the stack

C They are discarded

D They are pushed again

Operators with higher or equal precedence are popped to maintain correct order in postfix.

What is the role of parentheses in infix to postfix conversion?

A They are added to postfix expression

B They are converted to operators

C They change operator precedence temporarily

D They are ignored

Parentheses temporarily change precedence by grouping expressions.

At the end of the infix expression, what should be done with remaining operators in the stack?

A Discard them

B Ignore them

C Push more operators

D Pop and add them to postfix expression

All remaining operators must be popped and added to the postfix expression to complete conversion.

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

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

Explain why a stack is the best data structure for infix to postfix conversion.

Consider how operators are processed in reverse order of arrival.

Practice

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

easy

A. To temporarily hold operators and manage precedence

B. To store operands permanently

C. To reverse the order of operands

D. To count the number of operators

Solution

1. Step 1: Understand the role of stack in conversion

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

2. Step 2: Differentiate stack usage from other data structures

   Operands are directly added to the postfix output, while operators are pushed to the stack to ensure correct order in the postfix expression.

3. Final Answer:

   To temporarily hold operators and manage precedence -> Option A

4. Quick Check:

   Stack holds operators = A [OK]

Hint: Stack holds operators to manage order and precedence [OK]

Common Mistakes:

• Thinking stack stores operands
• Assuming stack reverses operands
• Believing stack counts operators

2. Which of the following is the correct way to check if the stack is empty in C during infix to postfix conversion?

easy

A. if (stack == NULL)

B. if (top == -1)

C. if (stack->top == 0)

D. if (stack.size == 0)

Solution

1. Step 1: Understand stack implementation in C

   In array-based stack, 'top' is the index of the last pushed element. When empty, top is -1.

2. Step 2: Identify correct empty condition

   Checking if top == -1 correctly indicates the stack is empty.

3. Final Answer:

   if (top == -1) -> Option B

4. Quick Check:

   top == -1 means empty stack [OK]

Hint: Empty stack means top index is -1 [OK]

Common Mistakes:

• Checking stack pointer NULL instead of top
• Using top == 0 which means one element present
• Using struct size field incorrectly

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

   Postfix places operands first, then operator: B C * then A + gives ABC*+

3. Final Answer:

   ABC*+ -> Option A

4. Quick Check:

   Infix A + (B * C) = 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?

if (isOperator(ch)) {
  while (!isEmpty(stack) && precedence(peek(stack)) >= precedence(ch)) {
    postfix[j++] = pop(stack);
  }
  push(stack, ch);
}

medium

A. The pop operation should not be inside the while loop

B. The push operation should be outside the if block

C. The condition should use > instead of >= for precedence comparison

D. The isEmpty function is called incorrectly

Solution

1. Step 1: Understand operator precedence handling

   For correct associativity, when precedence is equal and operator is right-associative (like '^'), we should not pop.

2. Step 2: Identify correct comparison operator

   Using >= causes popping on equal precedence, which breaks right-associativity. Using > fixes this.

3. Final Answer:

   The condition should use > instead of >= for precedence comparison -> Option C

4. Quick Check:

   Use > to handle associativity correctly [OK]

Hint: Use >, not >=, to handle right-associative operators [OK]

Common Mistakes:

• Using >= causes wrong operator order
• Pushing outside operator check
• Misusing isEmpty function

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: Convert each parenthesis group to postfix

   (A + B) becomes AB+ and (C - D) becomes CD-.

2. Step 2: Combine with multiplication and division

   Expression becomes (AB+) * (CD-) / E. Multiplication and division are left associative, so postfix is AB+ CD- * E /.

3. Final Answer:

   AB+CD-*E/ -> Option D

4. Quick Check:

   Postfix of (A+B)*(C-D)/E = AB+CD-*E/ [OK]

Hint: Convert parentheses first, then apply operators left to right [OK]

Common Mistakes:

• Ignoring parentheses grouping
• Mixing operator order
• Misplacing division operator