Infix to Postfix Conversion Using Stack in DSA Python - Build from Scratch

Infix to Postfix Conversion Using Stack

📖 Scenario: You are building a simple calculator that converts expressions written in the usual way (like 3 + 4) into a form easier for computers to calculate (postfix notation).This helps computers solve math problems step-by-step without confusion about order.

🎯 Goal: Build a program that takes a math expression in infix form (like (A+B)*C) and converts it to postfix form (like AB+C*) using a stack.This shows how stacks help manage order of operations in math.

📋 What You'll Learn

Create a stack using a list to hold operators

Define operator precedence using a dictionary

Write a function to convert infix expression to postfix

Print the postfix expression after conversion

💡 Why This Matters

🌍 Real World

This technique is used in calculators and compilers to process and evaluate math expressions correctly.

💼 Career

Understanding stacks and expression parsing is important for software developers working on interpreters, compilers, and calculators.

1

Create the operator precedence dictionary

Create a dictionary called precedence with these exact entries: '+' with value 1, '-' with value 1, '*' with value 2, and '/' with value 2.

DSA Python

# Create the operator precedence dictionary
# Your code here

Hint

Use curly braces {} to create the dictionary and put operators as keys with their precedence numbers as values.

2

Create an empty stack list

Create an empty list called stack to be used as a stack for operators.

DSA Python

precedence = {'+': 1, '-': 1, '*': 2, '/': 2}
# Create an empty list called stack
# Your code here

Hint

Use square brackets [] to create an empty list.

3

Write the function to convert infix to postfix

Write a function called infix_to_postfix that takes a string expression and returns the postfix string. Use the stack list and precedence dictionary. Use variables postfix as an empty string and iterate over each character char in expression. Push operators to stack and pop them based on precedence. Append operands directly to postfix. Handle parentheses by pushing '(' and popping until '(' when ')' is found. After the loop, pop all remaining operators from stack to postfix. Return postfix.

DSA Python

precedence = {'+': 1, '-': 1, '*': 2, '/': 2}
stack = []
# Write the infix_to_postfix function below
# Your code here

Hint

Use char.isalnum() to check if character is a letter or number (operand). Use stack.append() to push and stack.pop() to pop. Compare precedence using the dictionary.

4

Print the postfix expression for a sample input

Call the function infix_to_postfix with the exact string '(A+B)*C' and print the result.

DSA Python

precedence = {'+': 1, '-': 1, '*': 2, '/': 2}
stack = []

def infix_to_postfix(expression):
    postfix = ''
    for char in expression:
        if char.isalnum():
            postfix += char
        elif char == '(':  
            stack.append(char)
        elif char == ')':
            while stack and stack[-1] != '(':  
                postfix += stack.pop()
            stack.pop()  # Remove '('
        else:
            while stack and stack[-1] != '(' and precedence[stack[-1]] >= precedence[char]:
                postfix += stack.pop()
            stack.append(char)
    while stack:
        postfix += stack.pop()
    return postfix

# Call the function with '(A+B)*C' and print the result
# Your code here

Hint

Use print(infix_to_postfix('(A+B)*C')) exactly to show the postfix expression.

Practice

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

easy

A. To reverse the order of operands

B. To temporarily hold operators and manage their precedence

C. To store operands permanently

D. To count the number of operators

Solution

1. Step 1: Understand the role of stack in infix to postfix

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

2. Step 2: Clarify what the stack does not do

   The stack does not store operands permanently or reverse operands; it only manages operators.

3. Final Answer:

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

4. Quick Check:

   Stack manages operators [OK]

Hint: Stack holds operators, not operands, during conversion [OK]

Common Mistakes:

• Thinking stack stores operands
• Confusing stack role with reversing expression
• Ignoring operator precedence handling

2. Which of the following is the correct way to push an operator onto a stack in Python?

easy

A. stack.append(operator)

B. stack.push(operator)

C. stack.insert(operator)

D. stack.add(operator)

Solution

1. Step 1: Recall Python list methods for stack operations

   In Python, a list is used as a stack and the method to add an element on top is append().

2. Step 2: Identify incorrect methods

   push() and add() are not valid list methods; insert() inserts at a specific index, not top of stack.

3. Final Answer:

   stack.append(operator) -> Option A

4. Quick Check:

   Use append() to push on stack [OK]

Hint: Use append() to push items on Python list stack [OK]

Common Mistakes:

• Using push() which is not a Python list method
• Using add() which is for sets, not lists
• Using insert() incorrectly for stack push

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 respecting precedence

   Postfix places operands first, then operator: B C * for multiplication, then A and + last, so expression is A B C * +.

3. Final Answer:

   ABC*+ -> Option A

4. Quick Check:

   Multiplication before addition = 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?

def precedence(op):
    if op == '+' or op == '-':
        return 1
    if op == '*' or op == '/':
        return 2
    return 0

stack = []
postfix = ''
expr = 'A+B*C'

for char in expr:
    if char.isalpha():
        postfix += char
    else:
        while stack and precedence(stack[-1]) >= precedence(char):
            postfix += stack.pop()
        stack.append(char)

while stack:
    postfix += stack.pop()

print(postfix)

medium

A. The precedence function returns 0 for unknown operators, causing errors

B. The postfix string is not updated with operands

C. The stack is not initialized properly

D. The code does not handle parentheses in the expression

Solution

1. Step 1: Analyze code handling of operators and operands

   The code correctly appends operands and manages operator precedence using the stack.

2. Step 2: Check for missing features

   The code does not check or handle parentheses, which are common in infix expressions and affect precedence.

3. Final Answer:

   The code does not handle parentheses in the expression -> Option D

4. Quick Check:

   Missing parentheses handling [OK]

Hint: Remember to handle parentheses explicitly in infix to postfix [OK]

Common Mistakes:

• Assuming precedence 0 causes errors (it just means lowest)
• Ignoring parentheses handling
• Thinking stack initialization is wrong

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: Handle parentheses and operator precedence

   Parentheses force A+B and C-D to be evaluated first, so their postfix forms are AB+ and CD- respectively.

2. Step 2: Apply multiplication and division in order

   After parentheses, multiply the two results: AB+ CD- * then divide by E: AB+CD-* E /.

3. Final Answer:

   AB+CD-*E/ -> Option C

4. Quick Check:

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

Hint: Convert inside parentheses first, then apply * and / left to right [OK]

Common Mistakes:

• Ignoring parentheses order
• Mixing operator order for * and /
• Placing operators before operands