Pow(x,n)

描述

Implement pow(x, n).

分析

二分法，$x^n = x^{n/2} \times x^{n/2} \times x^{n\%2}$

代码

Java

// Pow(x, n)
// 二分法，$x^n = x^{n/2} * x^{n/2} * x^{n\%2}$
// 时间复杂度O(logn)，空间复杂度O(1)
public class Solution {
    public double myPow(double x, int n) {
        if (n < 0) return 1.0 / power(x, -n);
        else return power(x, n);
    }
    private static double power(double x, int n) {
        if (n == 0) return 1;
        double v = power(x, n / 2);
        if (n % 2 == 0) return v * v;
        else return v * v * x;
    }
}

C++

// Pow(x, n)
// 二分法，$x^n = x^{n/2} * x^{n/2} * x^{n\%2}$
// 时间复杂度O(logn)，空间复杂度O(1)
class Solution {
public:
    double myPow(double x, int n) {
        if (n < 0) return 1.0 / power(x, -n);
        else return power(x, n);
    }
private:
    double power(double x, int n) {
        if (n == 0) return 1;
        double v = power(x, n / 2);
        if (n % 2 == 0) return v * v;
        else return v * v * x;
    }
};

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