朴素的算法变异

Question

伙计我正在进行多项式评估并使用Naive，Horner和FFT等算法 现在我的问题中有一条陈述说明。

Run a variation of the naïve algorithm, where the exponentiation
is performed by repeated squaring, a decrease-by-half algorithm

我不明白，我目前的Naive算法是：

public Complex naive(Polynomial poly, Complex x) {
    Complex p = new Complex();
    for (int i = poly.getCoef().length - 1; i >= 0; i--) {
        Complex power = new Complex(1, 0);
        for (int j = 1; j <= i; j++) {
            power = power.multiply(x);

        }
        p = p.add(poly.getCoef()[i].multiply(power));
        multiplyCountNaive++;
    }
    return p;

}

请解释需要修改的内容。 谢谢

Answer 1

我知道它应该是这样的

public Complex naive2(Polynomial poly, Complex x) {
    Complex p = new Complex();
    for (int i = poly.getCoef().length - 1; i >= 0; i--) {
        p = p.add(poly.getCoef()[i].multiply(expo(x, i)));
        multiplyCountNaive2++;
    }
    return p;

}

private Complex expo(Complex a, int b) {
    if (b == 0) {
        return new Complex(1, 0);
    } else if (b == 1) {
        return a;
    }

    if (b % 2 == 0) {
        return expo(a.multiply(a), b / 2);
    } else {
        return a.multiply(expo(a.multiply(a), (b - 1) / 2));
    }

}