using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.IO;

namespace TaskV5
{
    class Program
    {
        private static List<decimal> X;
        private static List<decimal> C;
        private static List<decimal> Ln;
        private static List<decimal> Sn;
        private static List<decimal> F;
        private static List<decimal> Z;
        private static decimal Y;
        private static decimal e;
        private static decimal eps;
        private static decimal En;
        private static int n;

        static void Main(string[] args)
        {
            decimal a = 0.4M;
            decimal b = 4;
            decimal h = 0.2M;
            e = 10E-7M;
            eps = 10E-5M;
            Y = 0.577215M;

            #region Task 1

            X = new List<decimal>();
            for (decimal i = a; i <= b; i += h)
            {
                X.Add(i);
            }
            n = X.Count;

            C = new List<decimal>();
            foreach (decimal Xi in X)
            {
                C.Add(GetCi(Xi));
            }

            StreamWriter writer = File.CreateText("data.txt");

            writer.WriteLine("X");           
            for (int i = 0; i < n; i++)
            {               
                writer.WriteLine(X[i]);
            }

            writer.WriteLine("C");
            for (int i = 0; i < n; i++)
            {              
                writer.WriteLine(C[i]);
            }

            #endregion

            #region Task 2

            Ln = new List<decimal>();
            for (int i = 0; i < n; i++)
            {
                Ln.Add(GetLn(X[i], i));
            }

            List<decimal> Ex = new List<decimal>();
            for (int i = 0; i < n; i++)
            {
                Ex.Add(Math.Abs(GetCi(X[i] - 0.1M) - GetLn(X[i] - 0.1M, i)));
            }
           
            writer.WriteLine("Ex");
            for (int i = 0; i < n; i++)
            {                
                writer.WriteLine(Ex[i]);
            }

            Ex.Sort();
            En = Ex[Ex.Count - 1];
            writer.WriteLine("En = {0}", En);

            writer.WriteLine("Ln");            
            for (int i = 0; i < n; i++)
            {                
                writer.WriteLine(Ln[i]);
            }                       
           
            #endregion

            #region Task 3

            Sn = new List<decimal>();
            for (int i = 0; i < n; i++)
            {
                Sn.Add(GetSumS(X[i]));
            }    
        
            writer.WriteLine("Sn");            
            for (int i = 0; i < n; i++)
            {                
                writer.WriteLine(Sn[i]);
            }           

            #endregion

            #region Task 4

            F = new List<decimal>();
            for (int i = 0; i < n; i++)
            {
                F.Add(GetF(i));
            }

            Z = new List<decimal>();
            for (int i = 0; i < n; i++)
            {
                Z.Add(GetZ(i));
            }

            writer.WriteLine("F");
            for (int i = 0; i < n; i++)
            {
                writer.WriteLine(F[i]);
            }

            writer.WriteLine("Z");
            for (int i = 0; i < n; i++)
            {
                writer.WriteLine(Z[i]);
            }

            #endregion

            writer.Close();
            Console.Read();
        }

        private static decimal GetCi(decimal Xi)
        {
            decimal Ci;
            decimal S = 0;
            decimal a = (-1) * Xi * Xi / 4;
            decimal q = (-2) * Xi * Xi * n / ((2 * n + 2) * (2 * n + 2) * (2 * n + 1));

            while (Math.Abs(a) > e)
            {
                S += a;
                a *= q;
            }

            Ci = Y + (decimal)Math.Log10((double)Xi) + S;
            return Ci;
        }

        private static decimal GetLn(decimal Xi, int k)
        {
            decimal Ln = 0;

            for (int i = 0; i <= k; i++)
            {
                decimal A = 1;

                for (int j = 0; j <= k; j++)
                {
                    if (i != j)
                    {
                        A *= (Xi - X[j]) / (X[i] - X[j]);
                    }
                }

                Ln += C[i] * A;
            }

            return Ln;
        }

        private static decimal GetSumS(decimal Xi)
        {
            int N = 2;
            while (Math.Abs(GetSN(Xi, N) - GetSN(Xi, 2 * N)) > eps)
            {
                N *= 2;
            }
            return GetSN(Xi, 2 * N);
        }

        private static decimal GetSN(decimal Xi, int N)
        {
            decimal H = Xi / N;
            decimal S = 0;
            for (int i = 1; i <= N; i++)
            {
                decimal Z = (2 * i - 1) * H / 2;
                S += H * ((decimal)Math.Cos((double)Z) - 1) / Z;
            }
            return S;
        }

        private static decimal GetF(int i)
        {
            decimal Fi;
            Fi = C[0] + i * (C[n - 1] - C[0]) / n;
            return Fi;
        }

        private static decimal GetZ(int i)
        {
            decimal z0 = X[i];
            decimal z1 = z0 - GetG(z0, i) * (decimal)Math.Cos((double)z0) / z0;
            decimal zk = z0;
            decimal zk1 = z1;

            while (Math.Abs(zk1 - zk) > eps)
            {                
                decimal zk2 = zk1 - (GetG(zk1, i) * (zk1 - zk)) / (GetG(zk1, i) - GetG(zk, i));
                zk = zk1;
                zk1 = zk2;
            }

            return zk1;
        }

        private static decimal GetG(decimal z, int i)
        {
            decimal G;
            decimal S = 0;
            decimal a = (-1) * z * z / 4;
            decimal q = (-2) * z * z * n / ((2 * n + 2) * (2 * n + 2) * (2 * n + 1));

            while (Math.Abs(a) > e)
            {
                S += a;
                a *= q;
            }

            G = S - F[i];
            return G;
        }     
    }
}