using System;
using System.Collections.Generic;
using System.Linq;
using System.Xml;

namespace VM
{
    internal class Program
    {

        public static void Main(string[] args)
        {
            List<double> x = new List<double>();
            double eps = Math.Pow(10, -6);
            for(double k = 0; k <= 3; k += 0.4)
                x.Add(k);

            Console.WriteLine("Sin");
            List<double> f = x.Select(t => Si(t,eps)).ToList();
            Print(x, f);

            Console.WriteLine("\nИнтер. полином Ньютона");
            List<double> Ln = x.Select((t, i) => Newton(x, f, f[i])).ToList();
            Print(x,Ln);

            Console.WriteLine("Погрешности:");
            for (int i = 0; i < x.Count; i++)
            {
                Console.WriteLine(Math.Abs(f[i] - Ln[i]));
            }


        }


        #region Newton
        private static double RR(List<double> y, List<double> x)
        {
            if (y.Count > 2)
            {
                var yleft = new List<double>(y);
                var xleft = new List<double>(x);
                xleft.RemoveAt(0);
                yleft.RemoveAt(0);
                var yright = new List<double>(y);
                var xright = new List<double>(x);
                xright.RemoveAt(y.Count - 1);
                yright.RemoveAt(y.Count - 1);
                return (RR(yleft, xleft) - RR(yright, xright)) / (x[x.Count - 1] - x[0]);
            }
            if (y.Count == 2)
            {
                return (y[1] - y[0]) / (x[1] - x[0]);
            }

            throw new Exception("Not available parameter");
        }
        private static double Newton(List<double> xPoints, List<double> yPoints, double x)
        {
            var res = yPoints[0];
            for (var i = 1; i < yPoints.Count; i++)
            {
                var xlist = new List<double>();
                var ylist = new List<double>();
                double buf = 1;
                for(var j = 0; j <= i; j++)
                {
                    xlist.Add(xPoints[j]);
                    ylist.Add(yPoints[j]);
                    if (j<i)
                        buf *= x - xPoints[j];
                }
                // Console.WriteLine(RR(Ylist, Xlist));
                res += RR(ylist, xlist)*buf;
            }
            return res;
        }
        #endregion
        private static double Si(double x,double eps)
        {
            int i = 0;
            double s = 0;
            double ai = x;
            double qn;
            while (Math.Abs(ai) >= eps)
            {
                s +=  ai;
                qn = -x * x * (2 * i + 1) / ((2 * i + 3) * (2 * i + 3) * (2 * i + 2));
                ai *= qn;
                i++;
            }

            return s;
        }
        private static void Print(IReadOnlyList<double> x, IReadOnlyList<double> y)
        {
            for (var i = 0; i < x.Count; i++)
            {
                Console.WriteLine($"{x[i]}:     {y[i]}");
            }
        }
    }
}