03 Fast Exponentiation

Fast Exponentiation Formula

$$x^n=\left\{ \begin{array}{ll} x^\frac{n}{2}\times x^\frac{n}{2}&\text{when x is even and } n >= 0 \\ x^\frac{n}{2}\times x^\frac{n}{2} \times x&\text{when x is odd and } n >= 0 \\ x^\frac{n}{2}\times x^\frac{n}{2}&\text{when x is even and } n < 0 \\ x^\frac{n}{2}\times x^\frac{n}{2} \times \frac{1}{x} &\text{when x is odd and } n < 0 \\ \end{array} \right.$$

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LeetCode: Pow(x, n)

100% fastest solution

double myPow(double x, int n) {
    if(n == 0)
        return 1;
    double temp = myPow(x, n / 2);
    return temp * temp * ((n & 1) ? ((n >= 0) ? x : (1 / x)) : 1);
}

Same solution, easy to understand

double myPow(double x, int n) {
    if(n == 0)
        return 1;
    double temp = myPow(x, n / 2);
    if(n & 1) {
        if(n >= 0)
            return temp * temp * x;
        else 
            return temp * temp / x;
    } else 
        return temp * temp;
}