Infix to Postfix Conversion Using Stack in DSA Python - Execution Trace

Concept Flow - Infix to Postfix Conversion Using Stack

Read next token from infix

↓

Is token operand?

Yes→Add to postfix output

No↓

Is token '(' ?

Yes→Push '(' to stack

No↓

Is token ')' ?

Yes→Pop from stack to output until '('

No↓

Operator token

↓

While stack top has higher or equal precedence

↓

Pop from stack to output

↓

Push current operator to stack

↓

Repeat until all tokens processed

↓

Pop remaining stack to output

↓

Done: Postfix expression ready

The flow reads each token, decides if it's operand, operator, or parenthesis, manages stack accordingly, and builds postfix expression step-by-step.

Execution Sample

DSA Python

infix = "A+B*C"
stack = []
postfix = ""
for token in infix:
    # process token
    pass
# pop remaining stack

Converts infix expression 'A+B*C' to postfix using stack operations.

Execution Table

Step	Token	Operation	Stack State	Postfix Output	Visual State
1	A	Operand: Add to postfix	[]	A	Postfix: A | Stack: empty
2	+	Operator: Stack empty, push '+'	[+]	A	Postfix: A | Stack: +
3	B	Operand: Add to postfix	[+]	AB	Postfix: AB | Stack: +
4	*	Operator: '*' precedence > '+' on stack, push '*'	[+, *]	AB	Postfix: AB | Stack: + *
5	C	Operand: Add to postfix	[+, *]	ABC	Postfix: ABC | Stack: + *
6	End	Pop '*' from stack to postfix	[+]	ABC*	Postfix: ABC* | Stack: +
7	End	Pop '+' from stack to postfix	[]	ABC*+	Postfix: ABC*+ | Stack: empty
8	End	All tokens processed, stack empty	[]	ABC*+	Final Postfix: ABC*+

💡 All tokens processed and stack emptied, postfix expression complete.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	After Step 7	Final
stack	[]	[]	[+]	[+]	[+, *]	[+, *]	[+]	[]	[]
postfix	""	"A"	"A"	"AB"	"AB"	"ABC"	"ABC*"	"ABC*+"	"ABC*+"

Key Moments - 3 Insights

Why do we push '(' directly to the stack without popping?

Because '(' marks the start of a sub-expression; we must keep it to know where to stop popping when we find a ')'. See step where '(' would be pushed and later popped at ')'.

Why do we pop operators from the stack when the incoming operator has lower or equal precedence?

To maintain correct order of operations in postfix, higher or equal precedence operators on stack must be output before pushing the new operator. See step 4 where '*' is pushed because it has higher precedence than '+'.

What happens if the stack is empty when an operator arrives?

We simply push the operator onto the stack as there is nothing to compare precedence with. See step 2 where '+' is pushed onto empty stack.

Visual Quiz - 3 Questions

Look at the execution table, what is the postfix output after processing token 'B' (step 3)?

A A

B AB

C ABC

D ABC*

💡 Hint

Check the 'Postfix Output' column at step 3 in the execution_table.

At which step does the stack first contain two operators?

A Step 2

B Step 3

C Step 4

D Step 5

💡 Hint

Look at the 'Stack State' column and find when it changes from one to two operators.

If the input was 'A*B+C', how would the stack state change at step 2 compared to the current example?

A Stack would have '+' only

B Stack would have '*' only

C Stack would have '+', '*' in that order

D Stack would be empty

💡 Hint

Consider operator precedence and the first operator encountered in the new expression.

Concept Snapshot

Infix to Postfix Conversion Using Stack:
- Read tokens left to right
- Operands go directly to output
- '(' pushed to stack
- ')' pops until '('
- Operators pop stack while top has higher/equal precedence
- Push current operator
- After all tokens, pop remaining stack
- Result is postfix expression

Full Transcript

This visualization shows how to convert an infix expression like 'A+B*C' to postfix using a stack. Each token is read in order. Operands are added directly to the postfix output. Operators are pushed to the stack but only after popping operators with higher or equal precedence from the stack to maintain correct order. Parentheses are handled by pushing '(' and popping until '(' when ')' is found. After processing all tokens, any remaining operators in the stack are popped to the output. The execution table tracks each step, showing the token processed, stack state, and postfix output. The variable tracker shows how the stack and postfix string change after each step. Key moments clarify common confusions about parentheses and operator precedence. The quiz tests understanding of the stack and output states at various steps. This method ensures the postfix expression correctly represents the original infix expression's order of operations.

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