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



Example 1:

Input: x = 2.00000, n = 10
Output: 1024.00000
Example 2:

Input: x = 2.10000, n = 3
Output: 9.26100
Example 3:

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


Constraints:

-100.0 < x < 100.0
-231 <= n <= 231-1
-104 <= xn <= 104
"""


class Solution(object):
    def myPow(self, x, n):
        """
        :type x: float
        :type n: int
        :rtype: float
        """

        if n < 0:
            x = 1 / x
            n *= -1

        return pow_(x, n)

    # time O(log(n))
    # space O(log(n))


def pow_(x, n):
    if n == 0:
        return 1

    half = pow_(x, n // 2)

    if n % 2 == 0:
        return half * half

    return half * half * x
