using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication6
{
    class Program
    {
        static public void Wyswietl2(double[,] tab)
        {
            for (int i = 0; i < tab.GetLength(0); i++)
            {
                for (int j = 0; j < tab.GetLength(1); j++)
                {
                    Console.Write($"{tab[i, j]} ");
                }
                Console.WriteLine();
            }
        }
        static public void Wyswietl(double[] tab)
        {
            for (int i = 0; i < tab.Length; i++)
            {
                Console.Write($"{tab[i]} ");
            }
            Console.WriteLine();
        }
        static public void UzupelnijY(double[,] tab, double[] Yi)
        {
            for (int i = 0; i < tab.GetLength(0); i++)
            {
                tab[i, tab.GetLength(0)] = Yi[i];
            }
        }
        static public void DajA(double[,] tab, double[] Ai)
        {
            for (int i = 0; i < tab.GetLength(0); i++)
            {
                Ai[i] = tab[i, tab.GetLength(0)];
            }
        }
    }
    class Wielomian
    {
        static public double Licz(int n, double x)
        {
            if (n == 0)
            {
                return 1;
            }
            else
            {
                if (n == 1)
                {
                    return x + 3;
                }
                else
                {
                    return (n * 1.0 / (n * x * x - 2 * n * x + 3) * Licz(n - 2, x) + Licz(n - 1, x));
                }
            }
        }
        static public void Uzupelnij(double[,] tab, double[] x)
        {
            for (int i = 0; i < tab.GetLength(0); i++)
            {
                for (int j = 0; j < tab.GetLength(1) -1; j++)
                {
                    tab[i, j] = Wielomian.Licz(j, x[i]);
                }
            }
        }
        static public double LiczP(double x, double[] Ai)
        {
            double S = 0;
            for (int i = 0; i < Ai.Length; i++)
            {
                S += Licz(i, x) * Ai[i];
            }
            return S;
        }
    }
    class Programik
    {
        static void Pierog(int n, double[,] A)
        {
            int r;
            int liczej = n + 1;
            double max, p;

            for (int k = 0; k < n; k++)
            {
                max = A[k, k];
                r = k;

                for (int i = k; i < n; i++)
                {
                    if (Math.Abs(A[i,k]) > Math.Abs(max))
                    {
                        max = A[i, k];
                        r = i;
                    }
                }
                if (max == 0)
                {
                    Console.WriteLine("Macierz układu osobliwa...");
                    return;
                }
                else
                {
                    for (int j = k; j < liczej; j++)
                    {
                        double pomoc = A[k, j];
                        A[k, j] = A[r, j];
                        A[r, j] = pomoc;
                    }

                    for (int j = k; j < liczej; j++)
                    {
                        A[k, j] = A[k, j] / max;
                    }
                    for (int i = 0; i < n; i++)
                    {
                        if(i != k)
                        {
                            p = A[i, k];
                            for (int j = k; j < liczej; j++)
                            {
                                A[i, j] = A[i, j] - p * A[k, j];
                            }
                        }
                    }
                }
            }
        }
        static void Main(string[] args)
        {
            int n = 5;
            double[] Xi = new double[n + 1];
            double[] Yi = new double[n + 1];
            double[] Ai = new double[n + 1];
            Xi[0] = 1.5;
            Xi[1] = 2.0;
            Xi[2] = 2.5;
            Xi[3] = 3.5;
            Xi[4] = 3.8;
            Xi[5] = 4.1;

            Yi[0] = 2.0;
            Yi[1] = 5.0;
            Yi[2] = -1.0;
            Yi[3] = 0.5;
            Yi[4] = 3.0;
            Yi[5] = 7.0;

            double[,] macierz = new double[n + 1, n + 2];

            Program.UzupelnijY(macierz, Yi);
            Wielomian.Uzupelnij(macierz, Xi);
            Pierog(n + 1, macierz);

            Program.Wyswietl2(macierz);
            Program.DajA(macierz, Ai);

            Program.Wyswietl(Ai);

            double x = 1;
            string pomocy;
            do
            {
                Console.WriteLine("Wpisz wartość od 1.5 do 4.1 (0 = wyjście z pętli)");
                pomocy = Console.ReadLine();
                x = Convert.ToDouble(pomocy);
                Console.WriteLine("Wartość P(x): " + Wielomian.LiczP(x, Ai));

            } while (x != 0);
        }
    }
}