50_Pow(x, n).py

'''
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]
'''

class Solution(object):
    def myPow(self, x, n):
        """
        :type x: float
        :type n: int
        :rtype: float
        """
        def DFS(x, n):
            if n == 0: return 1     # n**0 = 1
            half = DFS(x, n//2)     # exp: 2**100 = 2**50 * 2**50
            if n%2 == 0:
                return half*half    
            else:
                return half*half*x      # exp: 2**101 = 2**50 * 2**50 * 2
        
        if n < 0:
            return 1/DFS(x, -n)     # n is a negative num
        else:
            return DFS(x, n)