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Power of Three

Certification: Basic Level Accuracy: 100% Submissions: 1 Points: 5

Write a Java program to determine if an integer is a power of three. An integer is a power of three if there exists an integer x such that n = 3^x.

Example 1
    

  • Input: n = 27
    • 

  • Output: true
    • 

  • Explanation:

      

    • Step 1: 27 can be expressed as 3^3.
      • 

    • Step 2: 3^3 = 3 * 3 * 3 = 27
      • 

    • Step 3: Therefore, 27 is a power of three.
      • 

    •
Example 2
    

  • Input: n = 45
    • 

  • Output: false
    • 

  • Explanation:

      

    • Step 1: 45 cannot be expressed as 3^x for any integer x.
      • 

    • Step 2: The closest powers of three are 3^3 = 27 and 3^4 = 81.
      • 

    • Step 3: Since 45 falls between these two powers, it is not a power of three.
      • 

    •
Constraints
    

  • -2^31 ≤ n ≤ 2^31 - 1
    • 

  • Time Complexity: O(log n)
    • 

  • Space Complexity: O(1)
    •
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Hint
Solution

Solution Hints

    
  
  • Check if n is positive, as powers of three must be positive
    • 
  
  • Repeatedly divide n by 3 and check if the remainder is 0
    • 
  
  • If at any point the remainder is not 0, n is not a power of three
    • 
  
  • If we can divide n by 3 until we get 1, then n is a power of three
    • 
  
  • Alternatively, use a mathematical property: the largest power of 3 in the integer range is 3^19
    •

Steps to solve by this approach:

 Step 1: Check if n is less than or equal to 0. If so, return false as powers of three must be positive.
 Step 2: While n is divisible by 3 (i.e., n % 3 == 0), keep dividing n by 3.
 Step 3: After the division process, if n equals 1, it means the original number was a power of three.
 Step 4: If n is not equal to 1, it means the original number was not a power of three.
 Step 5: Return true if n equals 1, false otherwise.

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