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 because it helps keep track of operators and their precedence while processing the expression from left to right.

intermediate

What happens when an operator with higher precedence is encountered during infix to postfix conversion?

It is pushed onto the stack to wait until operators with lower precedence are processed, ensuring correct order in the postfix expression.

intermediate

How are parentheses handled during infix to postfix conversion using a stack?

Left parentheses '(' are pushed onto the stack to mark the start of a sub-expression, and when a right parenthesis ')' is found, operators are popped until the matching '(' is removed.

beginner

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

A B C * +

Which data structure is used to convert infix expressions to postfix?

A Queue

B Stack

C Array

D Linked List

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

What should be done when a left parenthesis '(' is encountered in the infix expression?

A Add it directly to the postfix expression

B Pop all operators from the stack

C Push it onto the stack

D Ignore it

Left parentheses are pushed to mark the start of a sub-expression.

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 the postfix expression

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.

What is the postfix form of the infix expression: (A + B) * C?

A A B + C *

B A B C + *

C A B * C +

D A + B C *

Parentheses force addition before multiplication, so postfix is A B + C *.

What is the first step when processing an operand (like A or B) in infix to postfix conversion?

A Push it onto the stack

B Pop operators from the stack

C Ignore it

D Add it directly to the postfix expression

Operands are added directly to the postfix output.

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 operators.

Describe how parentheses affect the infix to postfix conversion process using a stack.

Focus on how '(' and ')' control operator popping.

Practice

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

easy

A. To count the number of operators

B. To temporarily hold operators and manage their precedence

C. To reverse the order of the expression

D. To store operands permanently

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: Identify what is stored in the stack

   Operands are directly added to the output, while operators are pushed to the stack to manage order and precedence.

3. Final Answer:

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

4. Quick Check:

   Stack holds operators = D [OK]

Hint: Stack holds operators to manage precedence [OK]

Common Mistakes:

• Thinking stack stores operands
• Believing stack reverses the entire expression
• Confusing stack role with counting operators

2. Which of the following is the correct syntax to push an operator onto a stack named st in C++?

easy

A. st.push(operator);

B. push(st, operator);

C. st.add(operator);

D. push.operator(st);

Solution

1. Step 1: Recall C++ stack push syntax

   In C++, the standard stack uses the member function push() to add elements.

2. Step 2: Match correct syntax

   The correct syntax is st.push(operator); where st is the stack object.

3. Final Answer:

   st.push(operator); -> Option A

4. Quick Check:

   Stack push method = st.push() [OK]

Hint: Use st.push(element) to add to stack [OK]

Common Mistakes:

• Using non-member functions like push(st, element)
• Using incorrect method names like add()
• Incorrect dot notation like push.operator()

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

medium

A. A+BC*

B. AB+C*

C. ABC*+

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 +, resulting in ABC*+.

3. Final Answer:

   ABC*+ -> Option C

4. Quick Check:

   Postfix of A + B * C = ABC*+ [OK]

Hint: Multiply before add, postfix: operands then operator [OK]

Common Mistakes:

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

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

std::stack<char> st;
std::string infix = "A+B*C";
std::string postfix = "";
for (char ch : infix) {
  if (isalnum(ch))
    postfix += ch;
  else {
    while (!st.empty() && st.top() >= ch) {
      postfix += st.top();
      st.pop();
    }
    st.push(ch);
  }
}
while (!st.empty()) {
  postfix += st.top();
  st.pop();
}

medium

A. Operator precedence comparison is incorrect

B. Operands are not added to postfix

C. Stack is not used for operators

D. Postfix string is not initialized

Solution

1. Step 1: Analyze operator precedence check

   The code compares operators using >= directly on characters, which does not correctly reflect operator precedence.

2. Step 2: Identify correct precedence handling

   Operator precedence should be checked using a function that assigns precedence values, not character comparison.

3. Final Answer:

   Operator precedence comparison is incorrect -> Option A

4. Quick Check:

   Operator precedence needs function, not char compare [OK]

Hint: Use precedence function, not char comparison [OK]

Common Mistakes:

• Comparing operators as characters
• Ignoring precedence rules
• Not popping stack correctly

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

2. Step 2: Convert step-by-step to postfix

   A B + (for A+B), C D - (for C-D), then multiply: AB+CD-*, finally divide by E: 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: Process parentheses first, then operators by precedence [OK]

Common Mistakes:

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