import java.io.FileNotFoundException;
import java.io.PrintWriter;
import java.util.Locale;

public class Main {

    private static double a[];
    private static double b[];

    private static final double begin = -4;
    private static final double end = 4;

    private static final int NUM_STEPS = 234;

    private static int n;
    private static int N;

    private static double countF(double x) {
        return Math.abs( Math.abs( Math.abs(x) - 1) - 1);
    }

    private static double countPCosinus(double theta) {
        double res = a[0];
        for (int k=1; k<=N; k++) {
            res += a[k] * Math.cos(theta * k);
        }
        return res;
    }

    private static double thetaCosinus(double x) {
        return Math.PI * N / n + (x - (end + begin) / 2) / (end - begin) * Math.PI * 2 * N / n;
    }


    private static void outputPCosinus() throws FileNotFoundException {
        PrintWriter out = new PrintWriter("trigon.txt");
        StringBuilder sb = new StringBuilder();
        sb.append("ListLinePlot[{{");
        for (int i=0; i<NUM_STEPS; i++) {
            double x = begin + (end - begin) / (NUM_STEPS - 1) * i;
            sb.append("{" + x + ", " + countPCosinus(thetaCosinus(x)) + "},");
        }
        sb.deleteCharAt(sb.length()-1);
        sb.append("},\n{");
        for (int i=0; i<NUM_STEPS; i++) {
            double x = begin + (end - begin) / (NUM_STEPS - 1) * i;
            sb.append("{" + x + ", " + countF(x) + "},");
        }
        sb.deleteCharAt(sb.length()-1);
        sb.append("}}, PlotStyle -> Thickness[0.002]]");

        out.println(sb.toString().replace("E", "e"));
        out.println();
        out.println("Max norm = " + countNormCosinus());
        //out.println("Average  = " + countAverage());
        out.close();
    }


    private static double theta(double x) {
        if (n % 2 == 1)
            return (x - (begin + end) / 2) / (end - begin) * (Math.PI * 4 * N / n);
        else {
            double p = Math.PI * (N-1) / N;
            return (p - Math.PI) * 0.5 + (x - (end + begin) / 2) / (end - begin) * (p + Math.PI);
        }
    }

    private static double countNorm() {
        double mx = 0;
        for (int i=0; i<NUM_STEPS; i++) {
            double x = begin + (end - begin) / (NUM_STEPS - 1) * i;
            mx = Math.max(mx, Math.abs(countP(theta(x)) - countF(x)));
        }
        return mx;
    }


    private static double countNormCosinus() {
        double mx = 0;
        for (int i=0; i<NUM_STEPS; i++) {
            double x = begin + (end - begin) / (NUM_STEPS - 1) * i;
            mx = Math.max(mx, Math.abs(countP(thetaCosinus(x)) - countF(x)));
        }
        return mx;
    }

    private static double countAverage() {
        double res = 0;
        for (int i=0; i<NUM_STEPS; i++) {
            double x = begin + (end - begin) / (NUM_STEPS - 1) * i;
            res += Math.abs(countP(theta(x)) - countF(x));
        }
        return res / NUM_STEPS;
    }

    private static void cosinusInterpolation(int n) throws FileNotFoundException {
        n  = n * 2 - 1;
        Main.n = n;
        Main.N = n / 2;
        if (n % 2 == 1) {
            double coeff = 2.0 / n;
            for (int k=0; k<=N; k++) {
                a[k] = 0;
                for (int j=1; j<=N; j++) {
                    a[k] += Math.cos(coeff * Math.PI * k * j) * countF(begin + (end - begin) / N * j);
                }
                a[k] *= coeff * 2; // To make 4
                a[k] += countF(begin) * coeff; // y0 * 2 / (2N + 1)
            }

            a[0] /= 2;

            outputPCosinus();
        }
    }


    public static void main(String[] args) throws FileNotFoundException {

        a = new double[41];
        b = new double[41];

        //trigonometricInterpolation(20);

//        cosinusInterpolation(20);

        Locale.setDefault(Locale.US);
       PrintWriter out = new PrintWriter("norm.txt");
       StringBuilder sb = new StringBuilder();
       sb.append("ListLinePlot[{{");
       for (int i=2; i<=40; i++) {
           trigonometricInterpolation(i);
           sb.append("{" + i + "," + String.format("%.8f", countNorm()) + "},");
       }

       sb.deleteCharAt(sb.length()-1);
       sb.append("},{");
       for (int i=2; i<=40; i++) {
           cosinusInterpolation(i);
           sb.append("{" + i + "," + String.format("%.8f", countNormCosinus()) + "},");
       }
       sb.deleteCharAt(sb.length()-1);
       sb.append("}}]");
       out.println(sb);
       out.close();

    }


}