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.