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 postfix expression produced by the standard stack-based conversion algorithm?

DSA C#

string infix = "A+B*C";
string postfix = ConvertInfixToPostfix(infix);
Console.WriteLine(postfix);

// Assume ConvertInfixToPostfix implements the standard algorithm with precedence: * > +

A ABC*+

B AB+C*

C A+BC*

D AB*C+

💡 Hint

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

In infix to postfix conversion, operators with higher precedence are placed after their operands first. Here, B*C is evaluated before adding A, so postfix is ABC*+.

❓ Predict Output

intermediate

Output of infix to postfix for expression with parentheses

What is the postfix expression for the infix expression (A+B)*C using the stack method?

DSA C#

string infix = "(A+B)*C";
string postfix = ConvertInfixToPostfix(infix);
Console.WriteLine(postfix);

A AB*+C

B ABC+*

C AB+C*

D A+BC*

💡 Hint

Parentheses change the order of operations, so evaluate inside them first.

Parentheses force A+B to be evaluated first, so postfix is AB+ then multiplied by C, resulting in AB+C*.

🔧 Debug

advanced

Identify the error in this infix to postfix code snippet

What error will this C# code produce when converting infix to postfix?

string infix = "A+B";
Stack stack = new Stack();
string postfix = "";
foreach (char ch in infix)
{
    if (char.IsLetter(ch))
        postfix += ch;
    else
        stack.Push(ch);
}
while (stack.Count > 0)
    postfix += stack.Pop();
Console.WriteLine(postfix);

A Output: AB+

B Output: A+B

C Output: AB

D Output: BA+

💡 Hint

Think about the order operators are popped from the stack.

The code pushes operators without checking precedence or popping before pushing, so the operator order is reversed, producing BA+ instead of AB+.

🧠 Conceptual

advanced

Which operator has the highest precedence in infix to postfix conversion?

In the standard infix to postfix conversion using a stack, which operator among these has the highest precedence?

A *

B -

C +

D (

💡 Hint

Think about multiplication vs addition and subtraction.

Multiplication (*) has higher precedence than addition (+) and subtraction (-). Parentheses are handled separately and are not operators in precedence comparison.

🚀 Application

expert

Final postfix expression after multiple operations and parentheses

What is the postfix expression for the infix expression A+(B*C-(D/E^F)*G)*H using the standard stack-based infix to postfix conversion?

A +*H-*G/^FED*CBA

B ABC*DEF^/G*-H*+

C BC*DEF^/G*-H*+

D ABC*DEF^/G*-H*

💡 Hint

Remember operator precedence: ^ > * / > + - and parentheses change order.

The postfix expression is ABC*DEF^/G*-H*+ after correctly applying operator precedence and parentheses.

Practice

1. What is the main purpose of using a stack in Infix to Postfix Conversion?

easy

A. To temporarily hold operators and manage their precedence

B. To store the final postfix expression

C. To reverse the infix expression

D. To count the number of operands

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 tasks

   The postfix expression is built separately, and the stack is not used to store operands or reverse the expression.

3. Final Answer:

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

4. Quick Check:

   Stack holds operators = A [OK]

Hint: Stack holds operators to manage precedence [OK]

Common Mistakes:

• Thinking stack stores operands
• Confusing stack with output storage
• Assuming stack reverses expression

2. Which of the following C# code snippets correctly pushes an operator onto a stack named operatorStack?

easy

A. operatorStack.Push('+');

B. operatorStack.Add('+');

C. operatorStack.Insert('+');

D. operatorStack.Append('+');

Solution

1. Step 1: Recall stack method to add elements

   In C#, the method to add an element to a stack is Push().

2. Step 2: Verify other methods are invalid for Stack

   Add(), Insert(), and Append() are not valid methods for the Stack class.

3. Final Answer:

   operatorStack.Push('+'); -> Option A

4. Quick Check:

   Stack push method = Push() [OK]

Hint: Use Push() to add elements to stack [OK]

Common Mistakes:

• Using Add() instead of Push()
• Confusing List methods with Stack methods
• Trying to use Append() on Stack

3. What is the postfix expression output for the infix expression A + B * C using standard operator precedence?

medium

A. *ABC+

B. AB+C*

C. ABC*+

D. A+BC*

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 * then A +, resulting in ABC*+.

3. Final Answer:

   ABC*+ -> Option C

4. Quick Check:

   Multiplication before addition = ABC*+ [OK]

Hint: Multiply before add in postfix [OK]

Common Mistakes:

• Ignoring operator precedence
• Placing operators before operands
• Confusing postfix order

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

Stack<char> stack = new Stack<char>();
string infix = "A+B*C";
string postfix = "";
foreach (char ch in infix)
{
  if (char.IsLetter(ch))
    postfix += ch;
  else
    stack.Push(ch);
}
while (stack.Count > 0)
  postfix += stack.Pop();
Console.WriteLine(postfix);

medium

A. Operands are not added to postfix

B. Operators are pushed without checking precedence

C. Stack is not initialized

D. Postfix string is not printed

Solution

1. Step 1: Analyze operator handling in code

   The code pushes operators directly onto the stack without checking precedence or popping higher precedence operators first.

2. Step 2: Understand impact on postfix output

   This causes incorrect postfix order because operator precedence is ignored.

3. Final Answer:

   Operators are pushed without checking precedence -> Option B

4. Quick Check:

   Missing precedence check = B [OK]

Hint: Always check operator precedence before pushing [OK]

Common Mistakes:

• Ignoring operator precedence rules
• Assuming stack auto-sorts operators
• Not popping operators when needed

5. Convert the infix expression (A+B)*(C-D)/E to postfix using stack-based conversion. 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, then multiply results, then divide by E.

2. Step 2: Convert stepwise to postfix

   A+B becomes AB+, C-D becomes CD-, then multiply: AB+CD-*, then divide by E: AB+CD-*E/.

3. Final Answer:

   AB+CD-*E/ -> Option D

4. Quick Check:

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

Hint: Process parentheses first, then operators by precedence [OK]

Common Mistakes:

• Ignoring parentheses order
• Mixing operator precedence
• Placing division before multiplication