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Power Function

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

Write a C program to implement the power function pow(x, n), which calculates x raised to the power n (i.e., x^n). The algorithm should handle both positive and negative exponents efficiently without using built-in power functions.

Example 1
    
  
  • Input: x = 2.00000, n = 10
    • 
  
  • Output: 1024.00000
    • 
  
  • Explanation: 
    • Step 1: Calculate 2^10 using efficient exponentiation.

    • Step 2: 2^10 = 1024.

    • Step 3: Return 1024.00000 as the result.
    •
Example 2
    
  
  • Input: x = 2.10000, n = 3
    • 
  
  • Output: 9.26100
    • 
  
  • Explanation: 
    • Step 1: Calculate 2.1^3.

    • Step 2: 2.1 * 2.1 * 2.1 = 9.261.

    • Step 3: Return 9.26100 as the result.
    •
Constraints
    
  
  • -100.0 < x < 100.0
    • 
  
  • -2^31 ≤ n ≤ 2^31 - 1
    • 
  
  • -10^4 ≤ x^n ≤ 10^4
    • 
  
  • Time Complexity: O(log n)
    • 
  
  • Space Complexity: O(1)
    •
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Hint
Solution

Solution Hints

    
  
  • Use binary exponentiation (exponentiation by squaring) for efficiency.
    • 
  
  • Handle negative exponents by calculating 1 / pow(x, -n).
    • 
  
  • Use the property: x^n = (x^2)^(n/2) when n is even.
    • 
  
  • Use the property: x^n = x * x^(n-1) when n is odd.
    • 
  
  • Handle edge cases like n = 0 (result is 1) and x = 0.
    •

Steps to solve by this approach:

 Step 1: Handle base cases - when n is 0, x is 0, x is 1, or x is -1.
 Step 2: Convert negative exponent to positive by taking reciprocal of base and making exponent positive.
 Step 3: Use long long to handle the edge case where n is INT_MIN to avoid overflow.
 Step 4: Implement binary exponentiation by repeatedly squaring the base and halving the exponent.
 Step 5: If the current exponent is odd, multiply the result by the current power of the base.
 Step 6: Square the current power and divide the exponent by 2 in each iteration.
 Step 7: Return the final result after processing all bits of the exponent.

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