Infix to Postfix Conversion Using Stack in DSA C - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this infix to postfix conversion?

Given the infix expression A+B*C, what is the resulting postfix expression after conversion using a stack?

DSA C

Input: A+B*C
Output: ?

A AB+C*

B AB*C+

C A+BC*

D ABC*+

💡 Hint

Remember that multiplication (*) has higher precedence than addition (+).

In infix to postfix conversion, operators with higher precedence are placed before lower precedence operators in postfix. So B*C is evaluated first, then added to A.

❓ Predict Output

intermediate

What is the postfix expression for this infix with parentheses?

Convert the infix expression (A+B)*C to postfix using stack-based conversion. What is the output?

DSA C

Input: (A+B)*C
Output: ?

A AB+C*

B ABC+*

C A+BC*

D AB*+C

💡 Hint

Parentheses force the addition to happen before multiplication.

Parentheses mean A+B is evaluated first, so in postfix it becomes AB+, then multiplied by C, so AB+C*.

❓ Predict Output

advanced

What is the postfix output of this complex infix expression?

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

DSA C

Input: A+B*C-D/E
Output: ?

A AB+C*D/E-

B AB+C*DE/-

C ABC*+DE/-

D ABC*+D/E-

💡 Hint

Remember operator precedence: * and / before + and -, and left to right for same precedence.

First B*C and D/E are evaluated, then added and subtracted accordingly. So postfix is ABC*+DE/-.

🔧 Debug

advanced

Identify the error in this infix to postfix conversion snippet

This C code snippet attempts to convert infix to postfix but produces wrong output. What is the main logical error?

DSA C

char stack[100];
int top = -1;
void push(char c) { stack[++top] = c; }
char pop() { return stack[top--]; }

// Infix: A+B*C
// Code pushes operators without checking precedence properly.

// What is the error?

A Operands are pushed onto stack instead of output

B Operators are pushed without popping higher precedence operators first

C Stack overflow is not checked before push

D Pop function returns wrong element

💡 Hint

Check how operator precedence affects when to pop from stack.

The main error is not popping operators with higher or equal precedence before pushing a new operator, which breaks postfix order.

🧠 Conceptual

expert

What is the maximum stack size needed for converting an infix expression of length n?

Given an infix expression of length n (including operands, operators, and parentheses), what is the maximum number of elements that the operator stack can hold during infix to postfix conversion?

A n (all characters could be operators or parentheses)

B n/2 (half the expression length)

C n-1 (one less than expression length)

D Depends on the number of operators only

💡 Hint

Consider the worst case where all characters are operators or parentheses that stay on stack.

In the worst case, all characters except operands could be operators or parentheses pushed onto the stack, so maximum size is n.

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