Introduction

Infix to Postfix conversion means converting a mathematical expression from infix notation into postfix notation.

Infix notation:

A + B

Postfix notation:

AB+

In infix notation:

  • operators are written between operands

In postfix notation:

  • operators are written after operands

Example:

Input: A+B*C
Output: ABC*+

Explanation:

Multiplication has higher precedence than addition.

So:

  • B*C is evaluated first
  • then addition is performed

Constraints

Expression contains:Operands:
A-Z, a-z, 0-9

Operators:
+, -, *, /, ^

Parentheses:
( )

Approach 1 : Brute Force (Manual Operator Handling)

Explanations:

Explanation:

The idea is to manually process operands and operators separately.

Steps:

  1. Traverse the expression.
  2. Add operands directly into output.
  3. Store operators separately.
  4. Append operators later.

This approach is simple but does not correctly handle:

  • precedence
  • associativity
  • nested brackets

So it is not suitable for complex expressions.

Dry Run

Input:
A+B*C

Traversal:
A → operand

Output:
A

+ → operator
B → operand

Output:
AB

* → operator
C → operand

Output:
ABC

Append operators:
ABC*+

Final Output:
ABC*+

Practice :


Complexity Analysis

Time Complexity:- O(n)Explanation :
Expression is traversed once.

Space Complexity:- O(n)
Explanation :
Extra operator storage is used.


Approach 2 : Optimal Solution(Using Stack)

Explanations:

Explanation:

This is the most optimized and interview-preferred solution.

The idea is to use a stack for handling:

  • operators
  • precedence
  • parentheses

Rules:

  1. Operand → directly add to output
  2. '(' → push into stack
  3. ')' → pop until '('
  4. Higher precedence operators remain on stack
  5. Lower precedence operators pop existing operators

This correctly handles complex mathematical expressions.

Dry Run

Input:
A+B*C

Initial:
Stack = []

Output = ""

Step 1:
A → operand

Output:
A

Step 2:
+ → push into stack

Stack:
[+]

Step 3:
B → operand

Output:
AB

Step 4:
* → higher precedence than +

Stack:
[+, *]

Step 5:
C → operand

Output:
ABC

Pop stack:
*
+

Final Output:
ABC*+

Practice :


Complexity Analysis

Time Complexity:- O(n)Explanation :
Each character is processed only once.

Space Complexity:- O(n)
Explanation :
Stack stores operators and parentheses.

Why This Problem is Important

This problem builds the foundation for:

  • Expression parsing
  • Compiler design
  • Stack applications
  • Operator precedence handling
  • Mathematical expression evaluation

Real-World Applications

Infix to Postfix conversion is used in:

  • Compilers
  • Calculators
  • Programming language parsers
  • SQL parsers
  • Mathematical evaluation engines

Common Beginner Mistakes

  • Incorrect precedence comparison
  • Forgetting parentheses handling
  • Popping operators incorrectly
  • Ignoring associativity rules
  • Not clearing remaining stack operators

Interview Tip

Interviewers often expect:

  • use of Stack Data Structure
  • correct precedence handling
  • parentheses management
  • O(n) solution

Always explain why postfix notation simplifies expression evaluation.

Related Questions

  • Prefix to Infix
  • Evaluate Postfix Expression
  • Basic Calculator
  • Valid Parentheses
  • Expression Tree Evaluation

Final Takeaway

The Infix to Postfix problem is one of the most important stack-based expression handling problems.

It teaches:

  • operator precedence
  • stack processing
  • parsing logic
  • expression conversion

Understanding this problem builds a strong foundation for:

  • compiler design
  • expression evaluation
  • advanced stack interview problems.