Evaluate Postfix Expression Using Stack in DSA Go - 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 a number in a postfix expression during evaluation?

You push the number 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
2. Push 3
3. Push 1
4. '*' operator: pop 1 and 3, multiply (3*1=3), push 3
5. '+' operator: pop 3 and 2, add (2+3=5), push 5
6. Push 9
7. '-' operator: pop 9 and 5, subtract (5-9=-4), push -4
Result is -4.

intermediate

What error can occur if the postfix expression is invalid during evaluation?

If there are not enough operands for an operator, popping from the stack will fail, causing an error. Also, leftover operands after evaluation mean the expression was invalid.

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

A Ignore operator

B Pop two operands, apply operator, push result

C Push operator onto stack

D Pop one operand and push operator

Operators require two operands, so we pop two values, apply the operator, then push the result back.

What data structure is best suited for evaluating postfix expressions?

A Queue

B Array

C Linked List

D Stack

Stack works best because it follows last-in-first-out order, matching postfix evaluation needs.

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

A 18

B 14

C 9

D 11

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

If the postfix expression is '7 2 - 3 /', what is the final result?

A 1

B 2

C 5

D 3

7 - 2 = 5, then 5 / 3 = 1 (integer division).

What happens if there are leftover operands in the stack after evaluating a postfix expression?

A Result is sum of leftovers

B Expression is valid

C Expression is invalid

D Ignore leftovers

Leftover operands mean operators were missing, so the expression is invalid.

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

Think about how you handle numbers and operators step by step.

What errors can occur during postfix expression evaluation and how can you detect them?

Consider what happens if the stack is empty when you need operands.

Practice

1. What is the main purpose of using a stack to evaluate a postfix expression?

easy

A. To count the number of operators

B. To store operands and apply operators in correct order

C. To convert postfix to infix expression

D. To reverse the postfix expression

Solution

1. Step 1: Understand postfix evaluation process

   In postfix, operands come before operators. A stack helps store operands until an operator appears.

2. Step 2: Role of stack in evaluation

   When an operator is found, the top two operands are popped from the stack, the operation is performed, and the result is pushed back.

3. Final Answer:

   To store operands and apply operators in correct order -> Option B

4. Quick Check:

   Stack stores operands for operator application [OK]

Hint: Stack holds operands until operators appear [OK]

Common Mistakes:

• Thinking stack reverses the expression
• Confusing postfix with infix conversion
• Ignoring the order of operations

2. Which of the following Go code snippets correctly pushes an integer onto a stack represented by a slice?

easy

A. stack.add(value)

B. stack.push(value)

C. stack.insert(value)

D. stack = append(stack, value)

Solution

1. Step 1: Understand Go slice operations

   In Go, slices use append() to add elements at the end.

2. Step 2: Identify correct push operation

   stack = append(stack, value) correctly adds value to the stack slice.

3. Final Answer:

   stack = append(stack, value) -> Option D

4. Quick Check:

   Use append() to push in Go slices [OK]

Hint: Use append() to add elements to slice stack [OK]

Common Mistakes:

• Using non-existent push() method on slice
• Confusing slice with other data structures
• Trying to use insert() which is not a Go slice method

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

func evaluatePostfix(expr string) int {
    stack := []int{}
    for _, ch := range expr {
        if ch >= '0' && ch <= '9' {
            stack = append(stack, int(ch-'0'))
        } else {
            b := stack[len(stack)-1]
            stack = stack[:len(stack)-1]
            a := stack[len(stack)-1]
            stack = stack[:len(stack)-1]
            switch ch {
            case '+':
                stack = append(stack, a+b)
            case '*':
                stack = append(stack, a*b)
            }
        }
    }
    return stack[0]
}

fmt.Println(evaluatePostfix("23+5*"))

medium

A. 25

B. 15

C. 10

D. Error

Solution

1. Step 1: Evaluate "23+" part

   Push 2, push 3, then '+' pops 3 and 2, adds to 5, pushes 5.

2. Step 2: Evaluate remaining "5*" part

   Push 5, then '*' pops 5 and 5, multiplies to 25, pushes 25.

3. Final Answer:

   25 -> Option A

4. Quick Check:

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

Hint: Calculate stepwise: operands first, then operator [OK]

Common Mistakes:

• Mixing operand order during pop
• Confusing '+' and '*' precedence
• Forgetting to push intermediate results

4. The following Go code attempts to evaluate a postfix expression but produces a runtime error. What is the error?

func evaluatePostfix(expr string) int {
    stack := []int{}
    for _, ch := range expr {
        if ch >= '0' && ch <= '9' {
            stack = append(stack, int(ch-'0'))
        } else {
            a := stack[len(stack)-1]
            stack = stack[:len(stack)-1]
            b := stack[len(stack)-1]
            stack = stack[:len(stack)-1]
            switch ch {
            case '+':
                stack = append(stack, a+b)
            case '*':
                stack = append(stack, a*b)
            }
        }
    }
    return stack[0]
}

What causes the error?

medium

A. Stack underflow due to popping before checking stack size

B. Operands are popped in wrong order causing wrong calculation

C. Invalid type conversion from rune to int

D. Missing case for '-' operator

Solution

1. Step 1: Analyze stack pop operations

   The code pops two operands without checking if stack has enough elements, risking empty slice access.

2. Step 2: Identify runtime error cause

   If expression is invalid or incomplete, popping causes stack underflow and runtime panic.

3. Final Answer:

   Stack underflow due to popping before checking stack size -> Option A

4. Quick Check:

   Always check stack size before popping [OK]

Hint: Check stack length before popping operands [OK]

Common Mistakes:

• Assuming stack always has enough operands
• Swapping operand pop order but no error
• Ignoring runtime panic messages

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

hard

A. 8

B. 2

C. 4

D. 6

Solution

1. Step 1: Evaluate "82/" part

   Push 8, push 2, '/' pops 2 and 8, divides 8/2 = 4, push 4.

2. Step 2: Evaluate "3-" part

   Push 3, '-' pops 3 and 4, subtracts 4-3 = 1, push 1.

3. Step 3: Evaluate "4*" part

   Push 4, '*' pops 4 and 1, multiplies 1*4 = 4, push 4.

4. Final Answer:

   4 -> Option C

5. Quick Check:

   (8/2 - 3) * 4 = 4 [OK]

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

Common Mistakes:

• Incorrect operand order in division or subtraction
• Forgetting operator precedence in postfix
• Mixing up intermediate stack values