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

namespace MetodyObliczeniowe
{
    class Program
    {
        static double h;
        static double Y(double x)
        {
            return Math.Pow(x, 2) - x;
            //return Math.Pow(x, 2) + x + 1;
        }

        static double F(double x, double y)
        {
             return Math.Sqrt(y + x) + x - 1;
           // return 1 + 2 * Math.Sqrt(y - x - 1);
        }
        static double Yk_Euler(double x, double y)
        {
            return y + h * F(x, y);
        }

        static double Yk_ModifiedEuler(double x, double y)
        {
            return y + h * F(x + h / 2, y + (h / 2) * F(x, y));
        }

        static void Main(string[] args)
        {
            int N = -1;
            double a =- 1;
            String DataString = "";

            while (N < 1)
            {
                Console.WriteLine("Podaj liczbę naturalną N >= 1.");
                N = Int32.Parse(Console.ReadLine());
            }

            while(a <= 1)
            {
                Console.WriteLine("Podaj liczbę rzeczywistą a większą od 1.");
                a = Double.Parse(Console.ReadLine());
            }


            h = (a - 1) / N;

            double[] xk = new double[N+1];

            for (int i = 0; i <= N; i++)
                xk[i] = 1 + i * h;

            for (int i = 0; i <= N; i++)
                DataString += "x" + i + " = " + xk[i] + "\n";

            Console.WriteLine("\nN = {0} \nh = {1} \n" + DataString, N, h);

            Console.WriteLine("Metoda Eulera:");

            double[] yk_Euler = new double[N + 1];

            yk_Euler[0] = Y(1);

            for (int i = 1; i <= N; i++)
                yk_Euler[i] = Yk_Euler(xk[i - 1], yk_Euler[i - 1]);

            for (int i = 0; i <= N; i++)
                Console.WriteLine("y" + i + " =  {0}", yk_Euler[i]);

            for (int i = 1; i <= N; i++)
                Console.WriteLine("y(x" + i + ") = {0}",  Y(xk[i]));


            double[] AbsDiffrenceValueEuler = new double[N+1];

            for (int i = 1; i <= N; i++)
                AbsDiffrenceValueEuler[i] = Math.Abs(yk_Euler[i] - Y(xk[i]));

            Console.WriteLine("Błąd maksymalny tej metody : {0}", AbsDiffrenceValueEuler.Max());

            Console.WriteLine("\nZmodyfikowana metoda Eulera : ");

            double[] yk_ModifiedEuler = new double[N + 1];

            yk_ModifiedEuler[0] = Y(1);

            for (int i = 1; i <= N; i++)
                yk_ModifiedEuler[i] = Yk_ModifiedEuler(xk[i - 1], yk_Euler[i - 1]);

            for (int i = 0; i <= N; i++)
                Console.WriteLine("y" + i + " =  {0}", yk_ModifiedEuler[i]);

            for (int i = 1; i <= N; i++)
                Console.WriteLine("y(x" + i + ") = {0}", Y(xk[i]));

            double[] AbsDiffrenceValueMEuler = new double[N + 1];

            for (int i = 1; i <= N; i++)
                AbsDiffrenceValueMEuler[i] = Math.Abs(yk_ModifiedEuler[i] - Y(xk[i]));

            Console.WriteLine("Błąd maksymalny tej metody : {0}", AbsDiffrenceValueMEuler.Max());

            Console.ReadLine();
        }
    }
}