Evaluate Postfix Expression Using Stack in DSA C# - Execution Trace

Concept Flow - Evaluate Postfix Expression Using Stack

Read next token from expression

↓

Is token operand?

Yes→Push operand to stack

No↓

Pop two operands from stack

↓

Apply operator on operands

↓

Push result back to stack

↓

More tokens?

Yes→Repeat

No↓

Pop final result from stack

↓

Return result

Process each token; push numbers; on operator pop two numbers, apply operator, push result; final stack top is answer.

Execution Sample

DSA C#

string expr = "231*+9-";
Stack<int> stack = new Stack<int>();
foreach (char token in expr) {
  if (char.IsDigit(token)) stack.Push(token - '0');
  else {
    int b = stack.Pop(); int a = stack.Pop();
    stack.Push(ApplyOp(a, b, token));
  }
}
int result = stack.Pop();

Evaluates postfix expression "231*+9-" step-by-step using a stack.

Execution Table

Step	Operation	Token	Stack Before	Action	Stack After	Visual State
1	Read token	2	[]	Push 2	[2]	2
2	Read token	3	[2]	Push 3	[2,3]	2 -> 3
3	Read token	1	[2,3]	Push 1	[2,3,1]	2 -> 3 -> 1
4	Read token	*	[2,3,1]	Pop 1 and 3, multiply 3*1=3, push 3	[2,3]	2 -> 3
5	Read token	+	[2,3]	Pop 3 and 2, add 2+3=5, push 5	[5]	5
6	Read token	9	[5]	Push 9	[5,9]	5 -> 9
7	Read token	-	[5,9]	Pop 9 and 5, subtract 5-9=-4, push -4	[-4]	-4
8	End		[-4]	Pop final result	[]	Empty stack

💡 All tokens processed; final result popped from stack.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	After 6	After 7	Final
stack	[]	[2]	[2,3]	[2,3,1]	[2,3]	[5]	[5,9]	[-4]	[]
token		2	3	1	*	+	9	-
a (operand1)					3	2		5
b (operand2)					1	3		9

Key Moments - 3 Insights

Why do we pop two operands when we see an operator?

Because postfix operators apply to the two most recent operands on the stack, as shown in steps 4, 5, and 7 in the execution_table where two values are popped before applying the operator.

Why is the first popped operand the second operand in the operation?

The first popped value is the right operand (b), and the second popped is the left operand (a), matching the order in expressions like a - b. This is shown in step 7 where 9 is popped first (b) and 5 second (a) before subtracting.

What happens if the expression is empty or invalid?

The stack would be empty or have insufficient operands to pop when an operator appears, causing errors. The execution_table assumes a valid postfix expression to avoid such cases.

Visual Quiz - 3 Questions

Look at the execution_table at step 4, what operation is performed and what is pushed back to the stack?

A Multiply 3 and 1, push 3

B Add 3 and 1, push 4

C Subtract 3 and 1, push 2

D Divide 3 by 1, push 3

💡 Hint

Check the 'Action' and 'Stack After' columns at step 4 in execution_table.

At which step does the stack first contain only one element?

A Step 3

B Step 5

C Step 6

D Step 7

💡 Hint

Look at the 'Stack After' column to find when stack size is 1.

If the token at step 6 was an operator instead of '9', how would the stack change?

A It would pop two operands and push a result

B It would push the operator as a number

C It would cause an error immediately

D It would ignore the token

💡 Hint

Refer to the concept_flow and execution_table steps for operator handling.

Concept Snapshot

Evaluate Postfix Expression Using Stack:
- Read tokens left to right
- Push numbers to stack
- On operator, pop two operands
- Apply operator, push result
- Final stack top is expression result

Full Transcript

To evaluate a postfix expression, we read each token from left to right. If the token is a number, we push it onto the stack. If the token is an operator, we pop the top two numbers from the stack, apply the operator to them (left operand is second popped, right operand is first popped), then push the result back onto the stack. We repeat this until all tokens are processed. The final value left on the stack is the result of the expression. This process is shown step-by-step in the execution_table, where the stack changes as tokens are processed. Key points include popping two operands for operators and maintaining the correct operand order. The example expression "231*+9-" evaluates to -4 following these steps.

Practice

1. What is the main data structure used to evaluate a postfix expression?

easy

A. Array

B. Queue

C. Stack

D. Linked List

Solution

1. Step 1: Understand postfix evaluation process

   Postfix expressions are evaluated by pushing operands onto a stack and popping them when an operator is encountered. The stack allows last-in, first-out access which is perfect for postfix evaluation.

2. Final Answer:

   Stack -> Option C

3. Quick Check:

   Postfix evaluation uses stack [OK]

Hint: Postfix needs last-in-first-out structure: stack [OK]

Common Mistakes:

• Confusing stack with queue
• Using array without stack logic
• Thinking linked list is primary structure

2. Which of the following C# code snippets correctly pushes an integer operand onto a stack named stack?

easy

A. stack.Push(operand);

B. stack.Add(operand);

C. stack.Insert(operand);

D. stack.Enqueue(operand);

Solution

1. Step 1: Recall C# Stack.Push method

   In C#, the method to add an element to a stack is Push. Enqueue is for queues; Add and Insert are not stack methods.

2. Final Answer:

   stack.Push(operand); -> Option A

3. Quick Check:

   Use Push() to add to stack [OK]

Hint: Use Push() to add items to stack in C# [OK]

Common Mistakes:

• Using Enqueue which is for queues
• Using Add or Insert which are not stack methods
• Confusing stack with list methods

3. What is the output of the following C# code that evaluates the postfix expression "23+5*"?

string expr = "23+5*";
Stack<int> stack = new Stack<int>();
foreach (char c in expr)
{
    if (char.IsDigit(c))
        stack.Push(c - '0');
    else
    {
        int b = stack.Pop();
        int a = stack.Pop();
        if (c == '+') stack.Push(a + b);
        else if (c == '*') stack.Push(a * b);
    }
}
Console.WriteLine(stack.Pop());

medium

A. 25

B. 15

C. 10

D. Error

Solution

1. Step 1: Trace code execution

   Push 2, push 3; '+' pops b=3, a=2, push 5. Push 5; '*' pops b=5, a=5, push 25. Final pop prints 25.

2. Final Answer:

   25 -> Option A

3. Quick Check:

   (2+3)*5 = 25 [OK]

Hint: Calculate stepwise: operands pushed, operators pop two values [OK]

Common Mistakes:

• Mixing operand order when popping
• Confusing '+' and '*' operations
• Forgetting to convert char digits to int

4. Identify the error in the following C# code snippet that evaluates a postfix expression:

string expr = "82/";
Stack<int> stack = new Stack<int>();
foreach (char c in expr)
{
    if (char.IsDigit(c))
        stack.Push(c - '0');
    else
    {
        int a = stack.Pop();
        int b = stack.Pop();
        if (c == '/') stack.Push(b / a);
    }
}
Console.WriteLine(stack.Pop());

medium

A. Stack is not initialized

B. Operands are popped in wrong order

C. Division operator is not handled

D. Digits are not converted to integers

Solution

1. Step 1: Trace popping and computation for division

   Push 8, push 2 (top=2). For '/', b=Pop()=2 (right), a=Pop()=8 (left), but pushes b/a=2/8=0 instead of a/b=8/2=4. Operands popped correctly but used/applied in wrong order for non-commutative division.

2. Final Answer:

   Operands are popped in wrong order -> Option B

3. Quick Check:

   Pop right first (b), left second (a), compute a / b [OK]

Hint: Pop second operand first, then first operand for correct order [OK]

Common Mistakes:

• Swapping operand order causing wrong division
• Not handling division operator
• Forgetting to convert char to int

5. Given the postfix expression "6523+8*+3+*", what is the final result after evaluation using a stack?

hard

A. 2880

B. Incorrect expression

C. None (runtime error)

D. 288

Solution

1. Step 1: Evaluate postfix step-by-step

   Push 6,5,2,3; '+' pops 3&2 push 5 (stack:6,5,5); push 8; '*' pops 8&5 push 40 (6,5,40); '+' pops 40&5 push 45 (6,45); push 3 (6,45,3); '+' pops 3&45 push 48 (6,48); '*' pops 48&6 push 288.

2. Final Answer:

   288 -> Option D

3. Quick Check:

   Stepwise postfix evaluation = 288 [OK]

Hint: Evaluate postfix stepwise, push operands, apply operators [OK]

Common Mistakes:

• Misordering operands during pop
• Skipping steps in complex expressions
• Confusing operator precedence in postfix