using System;

namespace CM_Lab10
{
    class Program
    {
        static double f(double x)
        {
            return Math.Sqrt(x * x * x) * Math.Sin(Math.PI * x / 2);
        }
        static double calcDeriv(double x, int order)
        {
            const double h = 1.0e-3;

            if (order == 0) return f(x);

            double y1 = calcDeriv(x - h, order - 1);
            double y2 = calcDeriv(x + h, order - 1);

            return (y2 - y1) / (2 * h);
        }
        static double rectanglesError(double borderA, double borderB, int N)
        {
            double h = (borderB - borderA) / N;
            double mid = (borderA + borderB) / 2;
            double error = (calcDeriv(mid, 2) / 24) * (borderB - borderA) * Math.Pow(h, 2);
            return Math.Abs(error);
        }
        static double trapezoidError(double borderA, double borderB, int N)
        {
            double error;
            double h = (borderA + borderA) / N;
            double mid = (borderB - borderA) / 2;
            error = -(calcDeriv(mid, 2) / 12) * (borderB - borderA) * Math.Pow(h, 2);
            return Math.Abs(error);
        }
        static double simpsonError(double borderA, double borderB, int N)
        {
            double error;
            double m;

            double max = calcDeriv(borderA + borderB, 4) / 2;
            if (Math.Abs(max) < Math.Abs(calcDeriv(borderA, 4)))
            {
                max = calcDeriv(borderA, 4);
            }
            else if (Math.Abs(max) < Math.Abs(calcDeriv(borderB, 4)))
            {
                max = calcDeriv(borderB, 4);
            }

            m = max - (Math.Pow(borderB - borderA, 5)) / (180 * Math.Pow(N, 4));
            error = -(Math.Pow(borderB - borderA, 5) * m) / (180 * Math.Pow(N, 4));

            return error;

        }
        static void leftRectanglesMethod(double borderA, double borderB)
        {
            Console.WriteLine("**********************");
            Console.WriteLine("Left Rectangles Method");
            Console.WriteLine("**********************\n");

            int N;
            Console.Write("Enter N: ");
            N = Convert.ToInt32(Console.ReadLine());
            double h = (borderB - borderA) / N;
            double I = 0;

            double Xi = borderA;
            for (int i = 0; i < N; i++)
            {
                I += f(Xi) * h;
                Console.WriteLine($"X{i} = {Xi:F4}\tY{i} = {f(Xi):F4}");
                Xi += h;
            }
            Console.WriteLine($"Integral from {borderA} to {borderB} = {I} ± {rectanglesError(borderA, borderB, N)}");
        }
        static void rightRectanglesMethod(double borderA, double borderB)
        {
            Console.WriteLine("***********************");
            Console.WriteLine("Right Rectangles Method");
            Console.WriteLine("***********************\n");

            int N;
            Console.Write("Enter N: ");
            N = Convert.ToInt32(Console.ReadLine());
            double h = (borderB - borderA) / N;
            double I = 0;

            double Xi = borderB;
            for (int i = 0; i < N; i++)
            {
                I += f(Xi) * h;
                Console.WriteLine($"X{i + 1} = {Xi:F4}\tY{i + 1} = {f(Xi):F4}");
                Xi -= h;
            }
            Console.WriteLine($"Integral from {borderA} to {borderB} = {I} ± {rectanglesError(borderA, borderB, N)}");
        }
        static void midpointRectanglesMethod(double borderA, double borderB)
        {
            Console.WriteLine("**************************");
            Console.WriteLine("Midpoint Rectangles Method");
            Console.WriteLine("**************************\n");

            int N;
            Console.Write("Enter N: ");
            N = Convert.ToInt32(Console.ReadLine());
            double h = (borderB - borderA) / N;
            double I = 0;

            double Xi = borderA + h / 2;
            for (int i = 0; i < N; i++)
            {
                I += f(Xi) * h;
                Console.WriteLine($"X{i + 1} = {Xi:F4}\tY{i + 1} = {f(Xi):F4}");
                Xi += h;
            }
            Console.WriteLine($"Integral from {borderA} to {borderB} = {I} ± {rectanglesError(borderA, borderB, N)}");
        }
        static void trapezoidMethod(double borderA, double borderB)
        {
            Console.WriteLine("****************");
            Console.WriteLine("Trapezoid Method");
            Console.WriteLine("****************\n");

            int N;
            Console.Write("Enter N: ");
            N = Convert.ToInt32(Console.ReadLine());
            double h = (borderB - borderA) / N;
            double I = 0;

            double Xi = borderA;
            for (int i = 0; i < N; i++)
            {
                I += h * (f(Xi) + f(Xi + h)) / 2;
                Console.WriteLine($"X{i + 1} = {Xi:F4}\tY{i + 1} = {f(Xi):F4}");
                Xi += h;
            }
            Console.WriteLine($"Integral from  {borderA} to {borderB} = {I} ± {trapezoidError(borderA, borderB, N)}");
        }
        static void simpsonMethod(double borderA, double borderB)
        {
            Console.WriteLine("**************");
            Console.WriteLine("Simpson Method");
            Console.WriteLine("**************\n");

            int N;
            Console.Write("Enter N: ");
            N = Convert.ToInt32(Console.ReadLine()) * 2;
            double h = (borderB - borderA) / N;
            double I = 0;

            double Xi = borderA;
            int iter = 1;
            for (int i = 0; i < N; i += 2)
            {
                I += (h / 3) * (f(Xi) + 4 * f(Xi + h) + f(Xi + 2 * h));
                Console.WriteLine($"X{iter} = {Xi:F4}\tY{iter} = {f(Xi):F4}");
                Xi += 2 * h;
                iter++;
            }
            Console.WriteLine($"Integral from {borderA} to {borderB} = {I} ± {simpsonError(borderA, borderB, N)}");
        }
        static void Main(string[] args)
        {
            Console.OutputEncoding = System.Text.Encoding.UTF8;
            leftRectanglesMethod(1, 5);
            rightRectanglesMethod(1, 5);
            midpointRectanglesMethod(1, 5);
            trapezoidMethod(1, 5);
            simpsonMethod(1, 5);
        }
    }
}