f(x) = x**3 - n = 0

(x0, f(x0)) 处的切线与x轴交点(x1, 0)对应的f(x1) 会逐渐收敛到值为0处，即(f(x{n+1} ~ f(xn) ~ 0) ~ (x{n+1} ~ xn)

#include <iostream>
using namespace std;

int main()
{
    double n;
    cin >> n;

    double x = n, eps = 1e-6;
    while(true)
    {
        // x1 = x0 + f(x0)/f'(x0), 终止条件 abs(x{n+1} - xn) < epsion or abs(f(xn) - 0) < epsion, 即收敛
        double fx = x*x*x - n;
        double dfdx = 3*x*x;
        double x1 = x - fx/dfdx;

        if (abs(x1 - x) < eps) break;
        x = x1;
    }

    printf("%.6lf\n", x);
    return 0;
}