Check if Number is Power of Two in DSA Java - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this code snippet?

Consider the following Java method that checks if a number is a power of two. What will be printed when calling isPowerOfTwo(16)?

DSA Java

public class PowerCheck {
    public static boolean isPowerOfTwo(int n) {
        return n > 0 && (n & (n - 1)) == 0;
    }
    public static void main(String[] args) {
        System.out.println(isPowerOfTwo(16));
    }
}

A Runtime exception

B false

C Compilation error

D true

💡 Hint

Think about how binary AND works for powers of two.

The method returns true if n is greater than zero and n & (n-1) equals zero. For 16 (binary 10000), 16 & 15 (01111) is 0, so it returns true.

❓ Predict Output

intermediate

What is the output when input is zero?

What will the following Java code print when calling isPowerOfTwo(0)?

DSA Java

public class PowerCheck {
    public static boolean isPowerOfTwo(int n) {
        return n > 0 && (n & (n - 1)) == 0;
    }
    public static void main(String[] args) {
        System.out.println(isPowerOfTwo(0));
    }
}

A Runtime exception

B false

C Compilation error

D true

💡 Hint

Zero is not a power of two.

Since n is 0, n > 0 is false, so the method returns false.

❓ Predict Output

advanced

What is the output of this code with negative input?

What will be printed when calling isPowerOfTwo(-8) with the following code?

DSA Java

public class PowerCheck {
    public static boolean isPowerOfTwo(int n) {
        return n > 0 && (n & (n - 1)) == 0;
    }
    public static void main(String[] args) {
        System.out.println(isPowerOfTwo(-8));
    }
}

A false

B true

C Compilation error

D Runtime exception

💡 Hint

Negative numbers are not powers of two in this context.

The method checks if n is greater than zero. Since -8 is less than zero, it returns false.

🔧 Debug

advanced

What will this code print?

What will this Java code print when compiled and run?

DSA Java

public class PowerCheck {
    public static boolean isPowerOfTwo(int n) {
        return n > 0 & (n & (n - 1)) == 0;
    }
    public static void main(String[] args) {
        System.out.println(isPowerOfTwo(4));
    }
}

A Compilation error

B Prints false

C Prints true

D Runtime exception

💡 Hint

Check the difference between & and && operators in Java.

The code compiles and prints true. Operator precedence parses it as (n > 0) & ((n & (n - 1)) == 0). Relational > has higher precedence than ==, which is higher than bitwise &. For n=4, both sides evaluate to true, and boolean & boolean is true (non-short-circuit logical AND).

🧠 Conceptual

expert

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

Choose the best explanation for why the expression (n & (n - 1)) == 0 is used to check if n is a power of two.

A Because powers of two have only one bit set, and subtracting 1 flips all bits after that bit, so ANDing results in zero.

B Because powers of two are always even numbers, and this expression checks if n is even.

C Because subtracting 1 from n always results in zero for powers of two.

D Because this expression counts the number of set bits in n and returns true if it is one.

💡 Hint

Think about binary representation of powers of two and what happens when you subtract 1.

A power of two in binary has exactly one bit set to 1. Subtracting 1 flips that bit and all bits after it. ANDing n and n-1 clears the lowest set bit. If the result is zero, n had only one set bit, so it is a power of two.

Practice

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

easy

A. It is divisible by 3.

B. It is always an odd number.

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

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, e.g., 4 is 100.

2. Step 2: Check other options

   Odd numbers and divisibility by 3 do not define powers of two. Having all bits set to 1 is not a power of two.

3. Final Answer:

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

4. Quick Check:

   Power of two = single 1 bit [OK]

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

Common Mistakes:

• Thinking all odd numbers are powers of two
• Confusing powers of two with numbers having all bits set
• Assuming divisibility by 3 means power of two

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

easy

A. return (n | (n - 1)) == 0;

B. return (n & (n - 1)) == 0;

C. return (n & (n + 1)) == 0;

D. return (n ^ (n - 1)) == 0;

Solution

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

   The expression n & (n - 1) clears the lowest set bit. For powers of two, this results in zero.

2. Step 2: Analyze other options

   Options A, C, and D use incorrect bitwise operations that do not correctly check power of two.

3. Final Answer:

   return (n & (n - 1)) == 0; -> Option B

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 OR or XOR instead of AND in bitwise check
• Checking n & (n + 1) which is incorrect
• Not considering zero or negative numbers

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

int n = 16;
boolean result = (n & (n - 1)) == 0;
System.out.println(result);

medium

A. true

B. Compilation error

C. false

D. Runtime exception

Solution

1. Step 1: Calculate n & (n - 1) for n = 16

   16 in binary is 10000, 15 is 01111. Bitwise AND is 00000 (0).

2. Step 2: Compare result to zero

   Since 16 & 15 == 0, the expression is true, so result is true.

3. Final Answer:

   true -> Option A

4. Quick Check:

   16 is power of two, so output is true [OK]

Hint: If n & (n-1) == 0, print true [OK]

Common Mistakes:

• Confusing bitwise AND with OR
• Expecting false for powers of two
• Ignoring parentheses in expression

4. The following Java method is intended to check if a number is a power of two. What is the error?

public static boolean isPowerOfTwo(int n) {
    return (n & n - 1) == 0;
}

medium

A. Method does not handle negative numbers.

B. Using bitwise OR instead of AND.

C. Incorrect return type.

D. Missing parentheses around (n - 1) causing wrong calculation.

Solution

1. Step 1: Identify issue with negative numbers

   For n = Integer.MIN_VALUE (-2147483648), which is 0x80000000 in two's complement, n-1 = 0x7FFFFFFF (Integer.MAX_VALUE), and 0x80000000 & 0x7FFFFFFF == 0, so it incorrectly returns true.

2. Step 2: Rule out other options

   Return type is correct, it uses AND (&), and operator precedence correctly parses as n & (n - 1) (no missing parentheses needed).

3. Final Answer:

   Method does not handle negative numbers. -> Option A

4. Quick Check:

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

Hint: Include n > 0 to handle zero and negatives [OK]

Common Mistakes:

• Not checking n > 0 before bitwise operation
• Ignoring negative input handling
• Confusing bitwise AND with OR

5. You want to write a Java method that returns true if a given positive integer n is a power of two, and false otherwise. Which of the following implementations correctly handles all positive integers including 1, and excludes zero and negative numbers?

hard

A. return n >= 0 && (n & (n + 1)) == 0;

B. return (n & (n - 1)) == 0;

C. return n != 0 && (n | (n - 1)) == 0;

D. return n > 0 && (n & (n - 1)) == 0;

Solution

1. Step 1: Check for positive number condition

   Zero and negative numbers are not powers of two, so n > 0 is required.

2. Step 2: Use bitwise check for power of two

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

3. Step 3: Analyze other options

   return (n & (n - 1)) == 0; misses positive check, allowing zero. Options C and D use incorrect bitwise operations.

4. Final Answer:

   return n > 0 && (n & (n - 1)) == 0; -> Option D

5. Quick Check:

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

Hint: Check n > 0 before bitwise test [OK]

Common Mistakes:

• Not excluding zero and negative numbers
• Using incorrect bitwise operators
• Missing parentheses around (n - 1)