public //Полином в точке?
        static double ZPolinom(double[] c, int n, double x) {
        double znach = c[0];
        for (int i = 1; i < n; i++) {
            double xn = 1;
            for (int j = 0; j < i; j++) xn *= x;
            znach += xn * c[i];
        }
        return znach;
    };

    public  //Функция возвращает массив коэфф после перемножения
        static double[] Coefficient(double[] x, int n) {
        double anx[] = new double[n + 2];
        double ann[] = new double[n + 2];
        double res[] = new double[n + 2];

        for (int i = 0; i < n; i++) {
            ann[i] = 0.0;
            anx[i] = 0.0;
            res[i] = 0.0;
            x[i] = (-1) * x[i];
        }
        res[0] = x[0];
        res[1] = 1;
        for (int i = 1; i < n; i++)
            for (int j = 0; j <= i + 1; j++) {
                anx[j + 1] = res[j];
                ann[j] = res[j] * x[i];
                res[j] = anx[j] + ann[j];
            }
        res[n] = 1.0;
        double res1[] = new double[n + 1];
        for (int i = 0; i <= n; i++) {
            res1[i] = res[i];
        }
        return res1;
    };

    public
        static double[] PolinomLagrange(double[] x, double[] cl, double[] y, int n) {
        for (int i = 0; i < n; i++) {
            double xi[] = new double[n - 1];
            int k = 0;

            for (int j = 0; j < n; j++) {
                if (i != j) {
                    xi[k] = x[j];
                    k++;
                }
            }

            double znam = 1;

            for (int j = 0; j < n - 1; j++) {
                znam *= x[i] - xi[j];
            }

            double prom[] = new double[n];
            prom = system.in - &nbspДанный веб -
                сайт выставлен..System.in Coefficient(xi, n - 1);

            for (int j = 0; j < n; j++) {
                cl[j] += prom[j] * y[i] / znam;
            }
        }
        return cl;
    };

    public
        static double[] PolinomNewton(double[] x, double[] cn, double[] y, int n) {
        double dy[][] = new double[n][n];
        for (int i = 0; i < n; i++) {
            for (int j = i; j < n; j++) {
                dy[i][j] = 0.0;
            }
        }

        double h = (x[n - 1] - x[0]) / (n - 1);
        for (int i = 0; i < n; i++) {
            for (int j = i; j < n; j++) {
                if (i == 0) {
                    dy[j][i] = y[j];
                }
                else {
                    dy[j][i] = dy[j][i - 1] - dy[j - 1][i - 1];
                }
            }
        }
        cn[0] = dy[0][0];
        for (int i = 1; i < n; i++) {
            double hn = h;
            int fact = 1;
            double xi[] = new double[i];
            for (int j = 0; j < i; j++) {
                xi[j] = x[j];
            }
            double prom[] = new double[i + 1];
            prom = Coefficient(xi, i);
            for (int j = 1; j < i; j++) {
                hn *= h;
            }
            fact = Fact(i);
            for (int k = 0; k < i + 1; k++) {
                cn[k] += prom[k] * dy[i][i] / hn / fact;
            }
        }
        return cn;
    };



    public //Максимум производной
        static double MaxProizvodnay(double[] x, int n) {
        double xi = 1;
        int s = 1;
        for (int i = 0; i < n; i++) {
            s *= 10 - i;
        }
        for (int i = 0; i < 10 - n; i++) {
            xi *= x[n - 1];
        }
        return xi * s;
    }



    public
        static double w(double[] x, double xi, int n) {
        double znach = 1.0;
        for (int i = 0; i < n; i++) {
            znach *= (xi - x[i]);
        }

        if (znach < 0) znach *= -1;

        return znach;
    }

    public
        static double rn(double[] xnn, int nn, double[] x, int i, int n) {
        double[] y = new double[n];
        for (int k = 0; k < n; k++) {
            y[k] = x[k];
        }

        return MaxProizvodnay(y, n) * w(y, xnn[i], n) / Fact(n);
    }

    public
        static double Rn(double[] x, double[] c, double[] y, int n, int i) {
        double zn = y[i] - ZPolinom(c, n, x[i]);
        if (zn < 0.0) zn *= (-1);
        return zn;
    }





    public // Считает разделенные разности
        static double RazdRazn(double[] x, double[] y, int n) {
        double del, razn = 0.0;
        for (int i = 0; i <= n; i++) {
            del = 1;
            for (int j = 0; j <= n; j++)
                if (i != j) del *= x[i] - x[j];
            razn += y[i] / del;
        }
        return razn;
    }

    public // Считает Полниом ньютона через разделеные разности
        static double[] PolinomNewton2(double[] x, double[] c, double[] y, int n) {
        c[0] = y[0];
        for (int i = 1; i < n; i++) {
            double xi[] = new double[i];
            for (int j = 0; j < i; j++) {
                xi[j] = x[j];
            }
            double prom[] = new double[i + 1];
            prom = Coefficient(xi, i);
            double f = RazdRazn(x, y, i);
            for (int k = 0; k < i + 1; k++) {
                c[k] += prom[k] * f;
            }
        }
        return c;
    }
}