Why Evaluate Postfix Expression Using Stack in DSA Go?

The Big Idea

Discover how a simple stack can turn confusing math expressions into easy calculations!

The Scenario

Imagine you have a math expression written in a strange order, like "23+5*". You want to find the answer, but doing it step-by-step in your head is confusing and slow.

The Problem

Trying to solve this by hand means remembering which numbers to use first and when to multiply or add. It's easy to make mistakes or forget steps, especially with longer expressions.

The Solution

Using a stack, a simple tool that holds numbers temporarily, you can quickly and correctly calculate the answer by following clear rules. The stack helps keep track of numbers and operations in the right order without confusion.

Before vs After

✗ Before

func evaluatePostfix(expression string) int {
    // Manually parse and calculate step by step
    // Hard to track and error-prone
    return 0
}

✓ After

func evaluatePostfix(expression string) int {
    var stack []int
    for _, char := range expression {
        // Push numbers, pop and calculate on operators
    }
    return stack[len(stack)-1]
}

What It Enables

This method lets you quickly and reliably calculate answers from complex math expressions written in postfix form, making computers and calculators work efficiently.

Real Life Example

Calculators and computer programs use this to solve math problems typed without parentheses, so they know exactly what to do first and get the right answer fast.

Key Takeaways

Manual calculation of postfix expressions is confusing and error-prone.

Stacks provide a clear way to track numbers and operations step-by-step.

Using stacks makes evaluating postfix expressions fast and reliable.

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