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Power of Two

Certification: Basic Level Accuracy: 40% Submissions: 10 Points: 5

Write a Java program to determine whether an integer is a power of two. An integer is a power of two if there exists an integer x such that n = 2^x.

Example 1
    

  • Input: n = 16
    • 

  • Output: true
    • 

  • Explanation:

      

    • Step 1: 16 can be expressed as 2^4.
      • 

    • Step 2: 2^4 = 2 * 2 * 2 * 2 = 16
      • 

    • Step 3: Therefore, 16 is a power of two.
      • 

    •
Example 2
    

  • Input: n = 218
    • 

  • Output: false
    • 

  • Explanation:

      

    • Step 1: 218 cannot be expressed as 2^x for any integer x.
      • 

    • Step 2: The closest powers of two are 2^7 = 128 and 2^8 = 256.
      • 

    • Step 3: Since 218 falls between these two powers, it is not a power of two.
      • 

    •
Constraints
    

  • -2^31 ≤ n ≤ 2^31 - 1
    • 

  • Time Complexity: O(1)
    • 

  • Space Complexity: O(1)
    •
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Hint
Solution

Solution Hints

    
  
  • If n is a power of two, it has exactly one bit set to 1 in its binary representation
    • 
  
  • Use bitwise operations to check this property
    • 
  
  • Handle edge cases like n = 0 separately
    • 
  
  • Use the property that n & (n-1) for powers of two equals zero
    •

Steps to solve by this approach:

 Step 1: Check if n is less than or equal to 0. If so, return false as power of two must be positive.
 Step 2: Understand that powers of two in binary representation have exactly one bit set to 1.
 Step 3: Use the bitwise trick: n & (n-1) removes the rightmost set bit in the binary representation.
 Step 4: For powers of two, there's only one bit set to 1, so removing it will result in 0.
 Step 5: Return true if n & (n-1) equals 0, false otherwise.

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