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Power of Three

Certification: Basic Level Accuracy: 0% Submissions: 0 Points: 5

Write a C program to check if a given integer is a power of three. An integer n is a power of three if there exists an integer i such that n = 3^i.

Example 1
    
  
  • Input: n = 27
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  • Output: true
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  • Explanation: 
    
      
      
    1. We need to determine if 27 can be expressed as 3^i for some integer i.
      2. 
      
    2. 27 = 3^3 (3 * 3 * 3 = 27)
      3. 
      
    3. Since 27 can be expressed as 3^3, it is a power of three.
      4. 
    
    
  
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Example 2
    
  
  • Input: n = 0
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  • Output: false
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  • Explanation: 
    
      
      
    1. 0 cannot be expressed as 3^i for any integer i.
      2. 
      
    2. 3^i is always positive for any integer i.
      3. 
      
    3. Therefore, 0 is not a power of three.
      4. 
    
    
  
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Constraints
    
  
  • -2^31 <= n <= 2^31 - 1
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  • You must solve this without using loops or recursion
    • 
  
  • Time Complexity: O(1)
    • 
  
  • Space Complexity: O(1)
    •
NumberVariables and Data TypesEYPhillips
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Hint
Solution

Solution Hints

    
  
  • Consider the properties of powers of three
    • 
  
  • In base-10, powers of three have specific patterns
    • 
  
  • Use mathematical properties to check if a number is a power of three
    • 
  
  • Consider that the largest power of three within the 32-bit signed integer range is 3^19 = 1162261467
    • 
  
  • Remember that only positive integers can be powers of three
    •

Steps to solve by this approach:

 Step 1: First, handle the edge cases - negative numbers and zero cannot be powers of three.

 Step 2: Determine the largest power of three that fits within a 32-bit signed integer (3^19 = 1162261467).

 Step 3: Use the mathematical property that if n is a power of three, then the largest power of three (3^19) must be divisible by n.

 Step 4: This works because 3 is a prime number, so 3^19 only has factors that are powers of 3.

 Step 5: Check if 1162261467 % n == 0 to determine if n is a power of three.

 Step 6: This approach achieves O(1) time complexity without using loops or recursion.

 Step 7: Note that this method only works because 3 is prime. A similar approach for powers of non-prime numbers would require additional checks.

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