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Number is a Power of Another Number

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 10

Write a C# program to determine if a given number x is a power of another number y. In other words, check if there exists an integer n such that y^n = x.

Example 1
    
  
  • Input: x = 1024, y = 2
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  • Output: true
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  • Explanation: 
    
      
      
    • 2^10 = 1024, so 1024 is a power of 2.
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Example 2
    
  
  • Input: x = 100, y = 10
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  • Output: true
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  • Explanation: 
    
      
      
    • 10^2 = 100, so 100 is a power of 10.
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Constraints
    
  
  • 1 ≤ x ≤ 2^31 - 1
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  • 1 ≤ y ≤ 2^31 - 1
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  • Time Complexity: O(log x)
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  • Space Complexity: O(1)
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NumberVariables and Data TypesKPMGPhillips
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Hint
Solution

Solution Hints

    
  
  • Use the property of logarithms to solve this problem.
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  • Consider edge cases like x = 1 or y = 1.
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  • Be careful about floating-point precision when using logarithms.
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  • You can also use repeated division to check if y divides x perfectly until x becomes 1.
    •

Steps to solve by this approach:

 Step 1: Handle the edge cases: if x is 1, return true; if y is 1, return true only if x is also 1.
 Step 2: If y is 0, return false (since 0 raised to any positive power is 0, not a positive x).
 Step 3: Use a while loop to repeatedly divide x by y as long as x is greater than 1.
 Step 4: Inside the loop, check if x is divisible by y. If not, return false.
 Step 5: If x is divisible by y, update x by dividing it by y.
 Step 6: After the while loop, check if x is equal to 1. If it is, return true; otherwise, return false.

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