花花酱 LeetCode 50. Pow(x, n)

Implement pow(x, n), which calculates x raised to the power n (xⁿ).

Example 1:

Input: 2.00000, 10
Output: 1024.00000

Example 2:

Input: 2.10000, 3
Output: 9.26100

Example 3:

Input: 2.00000, -2
Output: 0.25000
Explanation: 2-2 = 1/22 = 1/4 = 0.25

Note:

• -100.0 < x < 100.0
• n is a 32-bit signed integer, within the range [−2³¹, 2³¹ − 1]

Solution: Recursion

square x and cut n in half.
if n is negative, compute 1.0 / pow(x, |n|)

pow(x, n) := pow(x * x, n / 2) * (x if n % 2 else 1)
pow(x, 0) := 1 

Example:
pow(x, 5) = pow(x^2, 2) * x 
          = pow(x^4, 1) * x 
          = pow(x^8, 0) * x^4 * x
          = 1 * x^4 * x = x^5

Time complexity: O(logn)
Space complexity: O(logn)