Check if Number is Power of Two in DSA Go - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does it mean for a number to be a power of two?

A number is a power of two if it can be written as 2 raised to some integer exponent, like 1, 2, 4, 8, 16, etc.

intermediate

How can you check if a number is a power of two using bitwise operations?

If a number n is a power of two, then n & (n-1) equals 0. This means only one bit is set in n.

intermediate

Why does the expression n & (n-1) == 0 work for powers of two?

Because powers of two have only one '1' bit. Subtracting 1 flips that bit and all bits after it, so ANDing clears the number to zero.

beginner

What is a simple Go function to check if a number is a power of two?

func isPowerOfTwo(n int) bool { return n > 0 && (n&(n-1)) == 0 }

beginner

Can zero or negative numbers be powers of two?

No, powers of two are positive integers only. Zero and negative numbers are not powers of two.

Which of these numbers is a power of two?

A 16

B 18

C 20

D 22

16 is 2 raised to the 4th power, so it is a power of two.

What does the expression n & (n-1) == 0 check for?

A If n is zero

B If n is even

C If n is a power of two

D If n is odd

This expression is true only when n is a power of two.

What should be true about n for the check n > 0 && (n & (n-1)) == 0 to work correctly?

A n must be positive

B n can be any integer

C n must be negative

D n must be zero

The number must be positive because powers of two are positive integers.

What is the output of isPowerOfTwo(0) in the Go function?

A undefined

B true

C error

D false

Zero is not a power of two, so the function returns false.

Which bitwise operator is used in the power of two check?

A | (OR)

B & (AND)

C ^ (XOR)

D ~ (NOT)

The AND operator (&) is used to check if only one bit is set.

Explain how to check if a number is a power of two using bitwise operations.

Think about how subtracting 1 changes the bits of a power of two.

Write a simple Go function to determine if a number is a power of two and explain each step.

Use n > 0 && (n & (n-1)) == 0 in your function.

Practice

1. Which of the following statements correctly describes a number that is a power of two?

easy

A. It has exactly one bit set to 1 in its binary form.

B. It is always an odd number.

C. It is divisible by 3.

D. It has all bits set to 1 in its binary form.

Solution

1. Step 1: Understand binary representation of powers of two

   A power of two in binary has exactly one '1' bit and the rest are '0's. For example, 4 is 100 in binary.

2. Step 2: Analyze the options

   The statement "It has exactly one bit set to 1 in its binary form" matches the binary property of powers of two. The other options do not: powers of two (except 1) are even, not divisible by 3, and do not have all bits set to 1.

3. Final Answer:

   It has exactly one bit set to 1 in its binary form. -> Option A

4. Quick Check:

   Power of two = one '1' bit [OK]

Hint: Power of two has only one '1' bit in binary [OK]

Common Mistakes:

• Thinking powers of two are always odd
• Confusing powers of two with numbers divisible by 3
• Assuming all bits are set to 1

2. Which of the following Go code snippets correctly checks if an integer n is a power of two?

easy

A. if n & (n + 1) == 0 { /* power of two */ }

B. if n | (n - 1) == 0 { /* power of two */ }

C. if n & (n - 1) == 0 { /* power of two */ }

D. if n ^ (n - 1) == 0 { /* power of two */ }

Solution

1. Step 1: Understand bitwise check for power of two

   The expression n & (n - 1) == 0 is true only if n is a power of two (and n > 0).

2. Step 2: Analyze each option

   The snippet if n & (n - 1) == 0 { /* power of two */ } uses the correct bitwise AND operation. The others use incorrect bitwise operations that do not correctly check for power of two.

3. Final Answer:

   if n & (n - 1) == 0 { /* power of two */ } -> Option C

4. Quick Check:

   Use n & (n-1) == 0 to check power of two [OK]

Hint: Use n & (n-1) == 0 to check power of two [OK]

Common Mistakes:

• Using bitwise OR instead of AND
• Using n + 1 instead of n - 1
• Using XOR which does not work here

3. What is the output of the following Go code?

package main
import "fmt"
func main() {
    n := 16
    if n > 0 && (n & (n - 1)) == 0 {
        fmt.Println("Power of Two")
    } else {
        fmt.Println("Not Power of Two")
    }
}

medium

A. Runtime Error

B. Power of Two

C. Compilation Error

D. Not Power of Two

Solution

1. Step 1: Evaluate the condition for n = 16

   16 in binary is 10000. 16 - 1 = 15 (binary 01111). Bitwise AND: 10000 & 01111 = 0.

2. Step 2: Check the if condition

   Since n > 0 and bitwise AND is 0, the condition is true, so it prints "Power of Two".

3. Final Answer:

   Power of Two -> Option B

4. Quick Check:

   16 & 15 == 0 means power of two [OK]

Hint: Check if n & (n-1) == 0 and n > 0 [OK]

Common Mistakes:

• Ignoring n > 0 check
• Misunderstanding bitwise AND result
• Assuming all even numbers are powers of two

4. The following Go code is intended to check if n is a power of two. What is the error?

func isPowerOfTwo(n int) bool {
    return n & (n - 1) == 0
}

medium

A. The function should return an integer, not bool.

B. The bitwise AND operator is used incorrectly.

C. The parentheses around n - 1 are unnecessary and cause error.

D. It does not handle the case when n is zero or negative.

Solution

1. Step 1: Understand the function logic

   The expression n & (n - 1) == 0 returns true for powers of two and also for zero.

2. Step 2: Identify missing check

   Zero and negative numbers are not powers of two, but this function returns true for zero. It lacks a check for n > 0.

3. Final Answer:

   It does not handle the case when n is zero or negative. -> Option D

4. Quick Check:

   Check n > 0 before bitwise test [OK]

Hint: Always check n > 0 before bitwise power of two test [OK]

Common Mistakes:

• Not checking for n > 0
• Misusing bitwise operators
• Assuming parentheses cause error

5. You want to write a Go function that returns true if a number n is a power of two, but also handles zero and negative inputs correctly. Which of the following implementations is correct?

hard

A. func isPowerOfTwo(n int) bool {
return n > 0 && (n & (n - 1)) == 0
}

B. func isPowerOfTwo(n int) bool {
return n >= 0 && (n | (n - 1)) == 0
}

C. func isPowerOfTwo(n int) bool {
return n != 0 && (n & (n + 1)) == 0
}

D. func isPowerOfTwo(n int) bool {
return (n & (n - 1)) == 1
}

Solution

1. Step 1: Check for positive input

   The function must ensure n is greater than zero to exclude zero and negatives.

2. Step 2: Use correct bitwise condition

   The condition (n & (n - 1)) == 0 correctly identifies powers of two.

3. Step 3: Analyze options

   The implementation func isPowerOfTwo(n int) bool { return n > 0 && (n & (n - 1)) == 0 } correctly combines both checks. The others use incorrect operators or conditions.

4. Final Answer:

   func isPowerOfTwo(n int) bool { return n > 0 && (n & (n - 1)) == 0 } -> Option A

5. Quick Check:

   Check n > 0 and n & (n-1) == 0 [OK]

Hint: Check n > 0 and n & (n-1) == 0 for power of two [OK]

Common Mistakes:

• Using bitwise OR instead of AND
• Not checking n > 0
• Using wrong bitwise expressions