day-107.cpp

/*
  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]

*/

// Calculate half of the result and multiply accordingly if its odd or even.
class Solution {
   public:
    double fastPow(double x, long long n) {
        if (n == 0) return 1;

        double half = fastPow(x, n / 2);

        if (n % 2 == 0) {
            return half * half;
        } else {
            return half * half * x;
        }
    }
    double myPow(double x, int n) {
        long long N = n;
        if (N < 0) {
            x = 1 / x;
            N = abs(N);
        }

        return fastPow(x, N);
    }
};