Check if Number is Power of Two in DSA Javascript - 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 an 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 works because powers of two have only one '1' bit in binary.

advanced

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

Because subtracting 1 from a power of two flips the only '1' bit and all bits after it, so ANDing with original clears all bits, resulting in zero.

beginner

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

function isPowerOfTwo(n) { return n > 0 && (n & (n - 1)) === 0; }

beginner

Can zero or negative numbers be powers of two?

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

Which of these numbers is a power of two?

A 22

B 18

C 20

D 16

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

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

A If n is prime

B If n is even

C If n is a power of two

D If n is negative

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

What should be true about n before applying (n & (n - 1)) === 0 to check power of two?

A n must be zero

B n must be positive

C n must be negative

D n can be any integer

Only positive numbers can be powers of two.

Which of these is NOT a power of two?

A 3

B 2

C 1

D 8

3 is not a power of two.

What is the binary representation of a power of two?

A Only one '1' bit and rest '0's

B All bits are '1'

C Alternating '1' and '0' bits

D Only '0' bits

Powers of two have exactly one '1' bit in binary.

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 JavaScript function to check if a number is a power of two and explain each step.

Start with checking if number is positive, then use bitwise trick.

Practice

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

easy

A. It is any even number greater than zero.

B. It is any number divisible by 3.

C. It can be written as 2 raised to an integer exponent (e.g., 2^3 = 8).

D. It is a number that ends with digit 2.

Solution

1. Step 1: Understand the definition of power of two

   A power of two is a number that can be expressed as 2 raised to some integer exponent, like 2^0=1, 2^1=2, 2^2=4, etc.

2. Step 2: Compare options with the definition

   Only It can be written as 2 raised to an integer exponent (e.g., 2^3 = 8). correctly describes this. Options A, C, and D do not match the definition.

3. Final Answer:

   It can be written as 2 raised to an integer exponent (e.g., 2^3 = 8). -> Option C

4. Quick Check:

   Power of two = 2^n [OK]

Hint: Power of two means 2 multiplied by itself n times [OK]

Common Mistakes:

• Thinking all even numbers are powers of two
• Confusing divisibility by 3 with powers of two
• Assuming number ending with 2 is power of two

2. Which JavaScript expression correctly checks if a number n is a power of two using bitwise operations?

easy

A. n & (n - 1) === 0

B. n | (n - 1) === 0

C. n ^ (n - 1) === 0

D. n & (n + 1) === 0

Solution

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

   A number that is a power of two has only one bit set. The expression n & (n - 1) clears the lowest set bit. If the result is zero, it means only one bit was set.

2. Step 2: Analyze each option

   n & (n - 1) === 0 uses the correct expression. Options B, C, and D use incorrect bitwise operators or operands.

3. Final Answer:

   n & (n - 1) === 0 -> Option A

4. Quick Check:

   Bitwise AND with n-1 equals zero means power of two [OK]

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

Common Mistakes:

• Using OR or XOR instead of AND
• Using n + 1 instead of n - 1
• Not comparing result to zero

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

function isPowerOfTwo(n) {
  return n > 0 && (n & (n - 1)) === 0;
}
console.log(isPowerOfTwo(16));
console.log(isPowerOfTwo(18));

medium

A. false\nfalse

B. false\ntrue

C. true\ntrue

D. true\nfalse

Solution

1. Step 1: Evaluate isPowerOfTwo(16)

   16 in binary is 10000. 16 & 15 (01111) = 0, so returns true.

2. Step 2: Evaluate isPowerOfTwo(18)

   18 in binary is 10010. 18 & 17 (10001) = 16 (not zero), so returns false.

3. Final Answer:

   true\nfalse -> Option D

4. Quick Check:

   16 is power of two: true, 18 is not: false [OK]

Hint: Check bitwise AND with n-1 for zero to confirm power of two [OK]

Common Mistakes:

• Assuming all even numbers return true
• Forgetting to check n > 0
• Misunderstanding bitwise AND result

4. Find the error in this JavaScript function that checks if a number is a power of two:

function checkPower(n) {
  return (n & n - 1) === 0;
}

medium

A. Using bitwise OR instead of AND

B. Not checking if n is positive

C. Missing parentheses around (n & (n - 1))

D. Using subtraction instead of addition

Solution

1. Step 1: Test with edge case n=0

   0 & (0 - 1) = 0 & (-1) = 0 === 0 returns true, but 0 is not a power of two.

2. Step 2: Analyze options

   The function lacks n > 0 check. Not checking if n is positive identifies this. No OR used (B wrong), parentheses not required due to operator precedence (C wrong), subtraction is correct (D wrong).

3. Final Answer:

   Not checking if n is positive -> Option B

4. Quick Check:

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

Hint: Include n > 0 check for power of two validation [OK]

Common Mistakes:

• Ignoring operator precedence
• Not checking if number is positive
• Using wrong bitwise operators

5. You want to filter an array nums to keep only numbers that are powers of two. Which code snippet correctly does this in JavaScript?

hard

A. nums.filter(n => n > 0 && (n & (n - 1)) === 0)

B. nums.filter(n => n % 2 === 0)

C. nums.filter(n => n & (n + 1) === 0)

D. nums.filter(n => n > 0 && (n | (n - 1)) === 0)

Solution

1. Step 1: Understand filtering condition for power of two

   We need to keep numbers greater than zero where n & (n - 1) === 0 is true.

2. Step 2: Evaluate each filter condition

   nums.filter(n => n > 0 && (n & (n - 1)) === 0) correctly uses this condition. nums.filter(n => n % 2 === 0) filters even numbers, which is incorrect. Options C and D use wrong bitwise operations.

3. Final Answer:

   nums.filter(n => n > 0 && (n & (n - 1)) === 0) -> Option A

4. Quick Check:

   Filter with bitwise AND and n > 0 [OK]

Hint: Filter with n > 0 and n & (n-1) === 0 to find powers of two [OK]

Common Mistakes:

• Filtering only even numbers
• Using wrong bitwise operators
• Not checking for positive numbers