Infix to Postfix Conversion Using Stack in DSA Go - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main purpose of converting an infix expression to postfix?

To make it easier for computers to evaluate expressions without worrying about operator precedence or parentheses.

beginner

What data structure is commonly used to convert infix expressions to postfix?

A stack is used to temporarily hold operators and manage their precedence during conversion.

intermediate

In the infix to postfix conversion, what happens when an operator with higher precedence is encountered?

It is pushed onto the stack because it should be applied before operators with lower precedence.

intermediate

How are parentheses handled during infix to postfix conversion using a stack?

Left parentheses '(' are pushed onto the stack, and when a right parenthesis ')' is found, operators are popped until the matching '(' is removed.

beginner

What is the postfix expression for the infix expression: A + B * C?

The postfix expression is: A B C * +

Which data structure is essential for converting infix to postfix expressions?

A Stack

B Queue

C Array

D Linked List

A stack is used to hold operators and manage precedence during conversion.

What should you do when you encounter a '(' in the infix expression during conversion?

A Pop all operators from the stack

B Push it onto the stack

C Ignore it

D Add it directly to the postfix expression

Left parentheses are pushed onto the stack to mark the start of a sub-expression.

When encountering a ')' during conversion, what is the correct action?

A Add ')' to the postfix expression

B Push ')' onto the stack

C Ignore the ')'

D Pop operators from the stack until '(' is found

Operators are popped until the matching '(' is removed from the stack.

In the expression A + B * C, which operator has higher precedence?

A +

B Both have same precedence

C *

D Depends on position

Multiplication '*' has higher precedence than addition '+'.

What is the postfix form of the infix expression (A + B) * C?

A A B + C *

B A B C * +

C A B + C

D A B C + *

Parentheses change the order so addition happens before multiplication.

Explain step-by-step how to convert the infix expression A + B * C to postfix using a stack.

Think about operator precedence and when to push or pop from the stack.

Describe how parentheses affect the infix to postfix conversion process using a stack.

Focus on how '(' and ')' control the order of operations.

Practice

1. What is the main purpose of using a stack in Infix to Postfix Conversion?

easy

A. To temporarily hold operators and manage their precedence

B. To store the final postfix expression

C. To reverse the infix expression

D. To count the number of operands

Solution

1. Step 1: Understand the role of stack in conversion

   The stack is used to hold operators temporarily while processing the infix expression to respect operator precedence and associativity.

2. Step 2: Identify what is stored in stack

   Operands are directly added to the output, while operators are pushed to the stack to decide their order in postfix.

3. Final Answer:

   To temporarily hold operators and manage their precedence -> Option A

4. Quick Check:

   Stack holds operators for precedence [OK]

Hint: Stack holds operators, output holds operands [OK]

Common Mistakes:

• Thinking stack stores operands
• Confusing stack role with output
• Ignoring operator precedence

2. Which of the following Go code snippets correctly initializes an empty stack for infix to postfix conversion?

easy

A. var stack []rune = []rune{}

B. stack := make([]int, 0)

C. stack := []string{0}

D. var stack []int = nil

Solution

1. Step 1: Identify correct stack type for operators

   Operators are characters, so stack should be a slice of runes (characters) initialized empty.

2. Step 2: Check initialization correctness

   var stack []rune = []rune{} initializes an empty rune slice correctly. stack := make([]int, 0) uses int slice, not suitable. stack := []string{0} has syntax error (cannot use int 0 as string). var stack []int = nil is nil slice, which can cause runtime errors.

3. Final Answer:

   var stack []rune = []rune{} -> Option A

4. Quick Check:

   Empty rune slice for operator stack [OK]

Hint: Use rune slice for operator stack [OK]

Common Mistakes:

• Using int slice for operators
• Initializing with wrong type
• Using nil slice without initialization

3. What is the postfix expression output by the following Go code snippet for input "a+b*c"?

infix := "a+b*c"
// Assume correct infix to postfix conversion function called here
postfix := InfixToPostfix(infix)
fmt.Println(postfix)

medium

A. "a+bc*"

B. "ab+c*"

C. "abc*+"

D. "*abc+"

Solution

1. Step 1: Analyze operator precedence in expression

   Multiplication (*) has higher precedence than addition (+), so 'b*c' is evaluated before adding 'a'.

2. Step 2: Convert infix to postfix step-by-step

   Postfix is formed as 'a' 'b' 'c' '*' '+', which is "abc*+".

3. Final Answer:

   "abc*+" -> Option C

4. Quick Check:

   Multiplication before addition = "abc*+" [OK]

Hint: Multiply before add means * goes before + in postfix [OK]

Common Mistakes:

• Ignoring operator precedence
• Placing + before * in postfix
• Confusing operand order

4. Given this Go function snippet for infix to postfix conversion, what is the bug?

func precedence(op rune) int {
    if op == '+' || op == '-' {
        return 1
    } else if op == '*' || op == '/' {
        return 2
    }
    return 0
}

// InfixToPostfix function uses precedence(op) to compare operators
// but outputs incorrect postfix for input "a+b^c"

medium

A. Precedence function returns 0 for non-operators causing errors

B. Precedence function returns int instead of float

C. Precedence values for '+' and '-' are swapped

D. Precedence function does not handle '^' operator

Solution

1. Step 1: Check if all operators are handled

   The function handles '+', '-', '*', '/' but misses '^' (exponent) operator which is common in infix expressions.

2. Step 2: Understand impact on output

   If input contains '^', missing precedence causes wrong order in postfix output.

3. Final Answer:

   Precedence function does not handle '^' operator -> Option D

4. Quick Check:

   Missing '^' causes wrong postfix [OK]

Hint: Include all operators in precedence function [OK]

Common Mistakes:

• Ignoring missing operators
• Assuming 0 precedence is error
• Confusing precedence values

5. How would you modify the infix to postfix algorithm to correctly handle parentheses in the expression (a+b)*c?

hard

A. Ignore parentheses and treat them as operands

B. Push '(' onto stack and pop operators until '(' when ')' is found

C. Remove all parentheses before conversion

D. Treat '(' as higher precedence operator and never pop it

Solution

1. Step 1: Understand role of parentheses in infix

   Parentheses change normal precedence by grouping expressions to evaluate first.

2. Step 2: Modify stack operations for parentheses

   Push '(' onto stack when encountered. When ')' is found, pop operators until '(' is popped, discarding both parentheses.

3. Final Answer:

   Push '(' onto stack and pop operators until '(' when ')' is found -> Option B

4. Quick Check:

   Parentheses control stack push/pop [OK]

Hint: Push '(' and pop until '(' on ')' [OK]

Common Mistakes:

• Ignoring parentheses in algorithm
• Treating parentheses as operands
• Not popping until '(' on ')'