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

Recall & Review

beginner

What is a postfix expression?

A postfix expression is a way of writing math where the operator comes after the numbers. For example, instead of writing 3 + 4, we write 3 4 +.

beginner

Why do we use a stack to evaluate postfix expressions?

We use a stack because it helps us keep track of numbers and apply operators in the right order. When we see a number, we push it on the stack. When we see an operator, we pop numbers, calculate, and push the result back.

beginner

What happens when you encounter an operator in a postfix expression during evaluation?

You pop the last two numbers from the stack, apply the operator to them, and push the result back onto the stack.

intermediate

Show the step-by-step stack changes when evaluating the postfix expression: 2 3 1 * + 9 -

Start with empty stack [] Push 2: [2] Push 3: [2, 3] Push 1: [2, 3, 1] Operator *: pop 1 and 3, multiply 3*1=3, push 3: [2, 3] Operator +: pop 3 and 2, add 2+3=5, push 5: [5] Push 9: [5, 9] Operator -: pop 9 and 5, subtract 5-9=-4, push -4: [-4] Final result: -4

beginner

Write the general algorithm to evaluate a postfix expression using a stack.

1. Create an empty stack. 2. For each token in the postfix expression: - If it is a number, push it onto the stack. - If it is an operator, pop two numbers from the stack, apply the operator, and push the result back. 3. After processing all tokens, the stack will have one number, which is the result.

What is the first step when evaluating a postfix expression using a stack?

A Push numbers onto the stack

B Pop numbers from the stack

C Apply operators immediately

D Convert postfix to infix

We push numbers onto the stack as we read them before applying operators.

In postfix evaluation, when you see an operator, what do you do?

A Pop one number and apply operator

B Push it onto the stack

C Ignore it

D Pop two numbers, apply operator, push result

Operators cause popping two numbers, applying the operator, then pushing the result.

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

A 14

B 18

C 9

D 11

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

Which data structure is best suited for evaluating postfix expressions?

A Queue

B Array

C Stack

D Linked List

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

What is the final step after processing all tokens in a postfix expression?

A The stack has one number which is the result

B The stack is empty

C The stack has multiple numbers

D The stack has operators

After evaluation, the stack contains one number which is the final result.

Explain how to evaluate a postfix expression using a stack with an example.

Think about reading tokens one by one and using the stack to store intermediate results.

Describe why a stack is the right data structure for postfix expression evaluation.

Consider how operators need the most recent numbers to calculate.

Practice

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

easy

A. Linked List

B. Queue

C. Stack

D. Array

Solution

1. Step 1: Understand postfix evaluation process

   Postfix expressions are evaluated using a stack to hold operands until an operator is encountered.

2. Step 2: Identify the correct data structure

   The stack allows pushing operands and popping them for operations, which fits postfix evaluation perfectly.

3. Final Answer:

   Stack -> Option C

4. Quick Check:

   Postfix evaluation uses stack = Stack [OK]

Hint: Postfix uses stack to hold operands until operators appear [OK]

Common Mistakes:

• Choosing queue instead of stack
• Using array without stack operations
• Confusing with infix evaluation

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

easy

A. stack.push(element);

B. stack.add(element);

C. stack.insert(element);

D. stack.enqueue(element);

Solution

1. Step 1: Recall JavaScript stack operations

   JavaScript arrays use push() to add elements to the end, simulating stack push.

2. Step 2: Match correct method

   push() is the standard method; add(), insert(), enqueue() are incorrect for stack push.

3. Final Answer:

   stack.push(element); -> Option A

4. Quick Check:

   Push uses push() method = stack.push(element); [OK]

Hint: Use push() to add elements to stack in JavaScript [OK]

Common Mistakes:

• Using add() or insert() which don't exist
• Confusing enqueue() with queue operation
• Using pop() instead of push()

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

function evaluatePostfix(expr) {
  const stack = [];
  for (const ch of expr) {
    if (!isNaN(ch)) {
      stack.push(Number(ch));
    } else {
      const b = stack.pop();
      const a = stack.pop();
      if (ch === '+') stack.push(a + b);
      else if (ch === '*') stack.push(a * b);
    }
  }
  return stack.pop();
}
console.log(evaluatePostfix("23+5*"));

medium

A. 25

B. 15

C. 10

D. Error

Solution

1. Step 1: Evaluate postfix expression "23+5*" step-by-step

   Push 2, push 3, then '+' operator: pop 3 and 2, add = 5, push 5. Push 5, then '*' operator: pop 5 and 5, multiply = 25, push 25.

2. Step 2: Final stack value

   Only one value 25 remains, which is returned and printed.

3. Final Answer:

   25 -> Option A

4. Quick Check:

   2+3=5, 5*5=25 = 25 [OK]

Hint: Calculate stepwise: operands pushed, operators pop two and push result [OK]

Common Mistakes:

• Mixing operand order in subtraction/division
• Forgetting to convert char to number
• Confusing operator precedence

4. Identify the error in the following postfix evaluation code snippet:

function evalPostfix(expr) {
  const stack = [];
  for (const ch of expr) {
    if (ch >= '0' && ch <= '9') {
      stack.push(ch);
    } else {
      const b = stack.pop();
      const a = stack.pop();
      if (ch === '+') stack.push(a + b);
      else if (ch === '-') stack.push(a - b);
    }
  }
  return stack.pop();
}

medium

A. Stack pop order is reversed

B. Operands are pushed as strings, not numbers

C. Missing handling for multiplication operator

D. Loop does not iterate over expression

Solution

1. Step 1: Check how operands are pushed

   The code pushes characters directly without converting to numbers, so operands are strings.

2. Step 2: Effect of pushing strings on arithmetic

   Adding strings with '+' concatenates instead of numeric addition, causing wrong results.

3. Final Answer:

   Operands are pushed as strings, not numbers -> Option B

4. Quick Check:

   Push operands as numbers, not strings = Operands are pushed as strings, not numbers [OK]

Hint: Convert chars to numbers before pushing to stack [OK]

Common Mistakes:

• Pushing chars without Number()
• Ignoring operator cases
• Assuming pop order is wrong

5. Given the postfix expression "82/3-4*", what is the correct evaluation result using a stack-based approach?

hard

A. 6

B. 0

C. 8

D. 4

Solution

1. Step 1: Evaluate "82/3-4*" step-by-step

   Push 8, push 2, '/' operator: 8 / 2 = 4, push 4. Push 3, '-' operator: 4 - 3 = 1, push 1. Push 4, '*' operator: 1 * 4 = 4, push 4.

2. Step 2: Final stack value

   Only one value 4 remains, but check carefully: The last '*' uses 1 and 4, result 4.

3. Step 3: Re-check calculation

   Actually, after '-' operation, stack has 1. Then push 4, then '*': 1 * 4 = 4.

4. Final Answer:

   4 -> Option D

5. Quick Check:

   8/2=4, 4-3=1, 1*4=4 = 4 [OK]

Hint: Evaluate stepwise: divide, subtract, then multiply [OK]

Common Mistakes:

• Mixing operand order in division
• Skipping operator precedence
• Incorrect stack pop sequence