428. Pow(x, n)【medium】

Implement pow(x, n).

 Notice

You don't need to care about the precision of your answer, it's acceptable if the expected answer and your answer 's difference is smaller than 1e-3.

 

Example

Pow(2.1, 3) = 9.261
Pow(0, 1) = 0
Pow(1, 0) = 1

Challenge 

O(logn) time

参考了@grandyang 的代码

解法一：

class Solution {
public:
    double myPow(double x, int n) {
        double res = 1.0;
        for (int i = n; i != 0; i /= 2) {
            if (i % 2 != 0) {
                res *= x;
            }
            x *= x;
        }
        return n < 0 ? 1 / res : res;
    }
};        

迭代

解法二：

class Solution {
public:
    double myPow(double x, int n) {
        if (n < 0) {
            return 1 / power(x, -n);
        }

        return power(x, n);
    }
    double power(double x, int n) {
        if (n == 0) {
            return 1;
        }

        double half = power(x, n / 2);
        if (n % 2 == 0) {
            return half * half;
        }
        
        return x * half * half;
    }
};

解法三：

class Solution {
public:
    /**
     * @param x the base number
     * @param n the power number
     * @return the result
     */
    double myPow(double x, int n) {
        if (n == 0) {
            return 0;
        }
        if (n == 1) {
            return x;
        }
        if (n == -1) {
            return 1 / x;
        }

        return myPow(x, n / 2) * myPow(x, n - n / 2);
    }
};

会超时