Evaluate Postfix Expression Using Stack in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a postfix expression?

A postfix expression is a mathematical notation where the operator comes after the operands. For example, instead of writing 3 + 4, we write 3 4 +.

beginner

Why do we use a stack to evaluate postfix expressions?

A stack helps keep track of operands. When an operator appears, we pop the last two operands, apply the operator, and push the result back. This matches the postfix order naturally.

beginner

What happens when you encounter an operand in postfix evaluation?

You push the operand onto the stack to use it later when an operator appears.

intermediate

What is the step-by-step process to evaluate the postfix expression '2 3 1 * + 9 -'?

1. Push 2, push 3, push 1. 2. Encounter '*', pop 1 and 3, multiply (3*1=3), push 3. 3. Encounter '+', pop 3 and 2, add (2+3=5), push 5. 4. Push 9. 5. Encounter '-', pop 9 and 5, subtract (5-9=-4), push -4. Result is -4.

beginner

In C, which data structure is best suited for implementing postfix evaluation and why?

A stack implemented using an array or linked list is best because it allows easy push and pop operations needed for postfix evaluation.

What do you do when you encounter an operator in postfix evaluation?

A Pop two operands, apply operator, push result

B Push operator onto stack

C Ignore operator

D Pop one operand and push operator

In postfix evaluation, when an operator is found, you pop the last two operands, apply the operator, and push the result back.

What is the result of evaluating the postfix expression '4 5 + 2 *'?

A 18

B 14

C 9

D 11

4 + 5 = 9, then 9 * 2 = 18.

Which data structure is primarily used to evaluate postfix expressions?

A Queue

B Linked List

C Stack

D Array

Stack is used because it supports last-in-first-out operations needed for postfix evaluation.

In postfix evaluation, what happens if the expression is invalid (e.g., too many operators)?

A Program runs normally

B Stack overflow occurs

C Result is zero

D Stack underflow occurs

Too many operators cause popping from an empty stack, leading to stack underflow.

What is the first step when evaluating a postfix expression?

A Push operators onto stack

B Push operands onto stack

C Pop operands from stack

D Evaluate expression left to right ignoring stack

Operands are pushed onto the stack as they appear.

Explain how a stack is used to evaluate a postfix expression step-by-step.

Think about what happens when you see numbers and then an operator.

Describe the advantages of using postfix notation and stack evaluation over infix notation.

Consider how postfix removes the need for rules about operator priority.

Practice

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

easy

A. Stack

B. Queue

C. Array

D. Linked List

Solution

1. Step 1: Understand postfix evaluation process

   Postfix expressions are evaluated by scanning from left to right and using a data structure to store operands temporarily.

2. Step 2: Identify the suitable data structure

   A stack is used because it allows pushing operands and popping them when an operator is encountered, following Last-In-First-Out order.

3. Final Answer:

   Stack -> Option A

4. Quick Check:

   Postfix evaluation uses stack = Stack [OK]

Hint: Remember: postfix needs LIFO, so use stack [OK]

Common Mistakes:

• Confusing stack with queue
• Using array without stack operations
• Thinking linked list is primary for postfix

2. Which of the following is the correct syntax to push an integer value 'x' onto a stack named 's' in C?

easy

A. stack_push(x);

B. s.push(x);

C. push(x, s);

D. push(s, x);

Solution

1. Step 1: Understand typical stack push function signature

   In C, stack push usually takes the stack and the value to push as arguments, e.g., push(stack, value).

2. Step 2: Match the correct syntax

   push(s, x); matches the common pattern push(s, x); where 's' is the stack and 'x' is the value.

3. Final Answer:

   push(s, x); -> Option D

4. Quick Check:

   push(stack, value) = push(s, x) [OK]

Hint: Remember: push(stack, value) in C [OK]

Common Mistakes:

• Using object.method() syntax in C
• Swapping argument order
• Using undefined function names

3. What is the result of evaluating the postfix expression "6 2 3 + -" using a stack?

medium

A. 3

B. 1

C. 5

D. -1

Solution

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

   Push 6, push 2, push 3. Encounter '+', pop 3 and 2, add: 2+3=5, push 5. Encounter '-', pop 5 and 6, subtract: 6-5=1.

2. Step 2: Verify final stack value

   After all operations, the stack has one value: 1.

3. Final Answer:

   1 -> Option B

4. Quick Check:

   6 - (2 + 3) = 1 [OK]

Hint: Process operators by popping two operands [OK]

Common Mistakes:

• Subtracting in wrong order (operand2 - operand1)
• Adding instead of subtracting
• Not pushing intermediate results

4. Identify the error in this C code snippet for postfix evaluation:

char* expr = "5 9 8 + 4 6 * * 7 + *";
int i = 0;
while(expr[i] != '\0') {
  if(isdigit(expr[i])) push(stack, expr[i]);
  else { /* operator handling */ }
  i++;
}

medium

A. Pushing character digit instead of integer value

B. Using while loop instead of for loop

C. Missing stack initialization

D. Incorrect operator handling

Solution

1. Step 1: Check what is pushed onto stack

   The code pushes expr[i], which is a character like '5', not the integer 5.

2. Step 2: Explain why this is wrong

   Characters have ASCII codes; pushing '5' pushes 53, not integer 5, causing wrong calculations.

3. Final Answer:

   Pushing character digit instead of integer value -> Option A

4. Quick Check:

   Push integer, not char digit [OK]

Hint: Convert char to int before push: expr[i] - '0' [OK]

Common Mistakes:

• Pushing char instead of int
• Ignoring spaces in expression
• Not handling operators properly

5. Given the postfix expression "4 5 7 2 + - *", what is the final evaluated result using stack evaluation?

hard

A. -24

B. 16

C. -16

D. 24

Solution

1. Step 1: Evaluate inner expression 7 2 +

   Push 4, 5, 7, 2. '+' operator: pop 2 and 7, add 7+2=9, push 9.

2. Step 2: Evaluate next operator '-'

   Next operator '-', pop 9 and 5, subtract 5-9 = -4, push -4.

3. Step 3: Evaluate final operator '*'

   Pop -4 and 4, multiply 4 * -4 = -16, push -16.

4. Final Answer:

   -16 -> Option C

5. Quick Check:

   4 * (5 - (7 + 2)) = -16 [OK]

Hint: Evaluate inner expressions first, then combine [OK]

Common Mistakes:

• Wrong operator order in subtraction
• Not evaluating nested operations correctly
• Mixing up operand order in multiplication