import java.math.BigDecimal;
import java.math.RoundingMode;
public class Main {
    public static double[] xn = {0.135, 0.876, 1.336, 2.301, 2.851};
    public static double[] yn = {2.382,-0.212,-1.305,-3.184,-4.365};
    public static double x = 0;
    public static double[] znam = new double[5];
    public static String[] langStr = new String[5];
    public static double [] lang = new double[5];
    public static String[] p = new String[5];
    public static double[][] razn = new double[5][5];
    public static double [] razn1 =new double[5];
    public static String[] newtStr = new String[5];
    public static double[] newt = new double[5];
    public static double[] a = new double[4];
    public static double [] b = new double[4];
    public static BigDecimal [] a1 = new BigDecimal[4];
    public static BigDecimal [] b1 = new BigDecimal[4];
    public static String [] lineStr = new String[4];
    public static void main(String[] args) {
        lagrange();
        newton();
        lineSpline();
    }
    public static void lagrange(){
        System.out.println("Polimom lagrange:");
        for (int i = 0;i< xn.length;i++){
            double tmp = 1;
            for(int j = 0;j< xn.length;j++){
                if(i!=j){
                    tmp *= xn[i]-xn[j];
                }
            }
            znam[i] = 1/tmp;
            BigDecimal z = new BigDecimal(znam[i]).setScale(3, RoundingMode.HALF_UP);
            p[i]= "p("+i+") = " + z;
            for (int j = 0;j<p.length;j++){
                if(i!=j){
                    p[i]+="(x- "+ xn[j] +")";
                }
            }
            System.out.println(p[i]);
        }
        for(int j = 0;j< p.length;j++){
            int ch= p[j].indexOf("(",2);
            int l = p[j].length();
            p[j] = p[j].substring(ch, l);
        }
        System.out.println("Iteratciony process langrage: ");
        for(int i = 0;i<xn.length;i++){
            znam[i]*=yn[i];
            BigDecimal z = new BigDecimal(znam[i]).setScale(3, RoundingMode.HALF_UP);
            langStr[i] = z+p[i];
            if(znam[i]>0 && i!=0) {
                System.out.println("+ "+langStr[i]);
            }else{
                System.out.println(langStr[i]);
            }
        }
        double ans = 0;
        x =xn[1]+xn[2];
        for(int i = 0;i<xn.length;i++){
            double tmp = 1;
            for(int j = 0;j< xn.length;j++){
                if(i!=j){
                    tmp*= x- xn[j];
                }
            }
            lang[i] = znam[i]*tmp;
        }
        for(Double i:lang){
            ans+=i;
        }
        BigDecimal answer = new BigDecimal(ans).setScale(3, RoundingMode.HALF_UP);
        System.out.println("L4(x1+x2) = "+"L4("+x+") = " + answer);
    }
    public static void newton(){
        System.out.println("\nPolinom Newton:");
        //заполенение y 1 строку razn
        for(int i=0;i< razn.length;i++){
            razn[0][i] = yn[i];
            razn1[0] = yn[0];
        }
        //1 порядок
        for(int i = 1;i< razn.length;i++){
            razn[1][i] = (razn[0][i]-razn[0][i-1])/(xn[i]-xn[i-1]);
        }
        razn1[1] = razn[1][1];
        //2 порядок
        for(int i = 2;i< razn.length;i++){
            razn[2][i] = (razn[1][i]-razn[1][i-1])/(xn[i]-xn[i-2]);
        }
        razn1[2] = razn[2][2];
        //3 порядок
        for(int i = 3;i< razn.length;i++){
            razn[3][i] = (razn[2][i]-razn[2][i-1])/(xn[i]-xn[i-3]);
        }
        razn1[3] = razn[3][3];
        //4 порядок
        for(int i = 4;i< razn.length;i++){
            razn[4][i] = (razn[3][i]-razn[3][i-1])/(xn[i]-xn[i-4]);
        }
        razn1[4] = razn[4][4];
        BigDecimal [] raz = new BigDecimal[5];
        for(int i = 0;i<razn1.length;i++){
            raz[i] = new BigDecimal(razn1[i]).setScale(3,RoundingMode.HALF_UP);
        }
        newtStr[0] = String.valueOf(raz[0]);
        for(int i = 1;i<raz.length;i++) {
            if (razn1[i] < 0) {
                newtStr[i] = String.valueOf(raz[i]);
            } else {
                newtStr[i] = " + " + String.valueOf(raz[i]);
            }
        }
        newtStr[1]+="(x-"+xn[0]+")";
        newtStr[2]+="(x-"+xn[0]+")(x-"+xn[1]+")";
        newtStr[3]+="(x-"+xn[0]+")(x-"+xn[1]+")(x-"+xn[2]+")";
        newtStr[4]+="(x-"+xn[0]+")(x-"+xn[1]+")(x-"+xn[2]+")(x-"+xn[3]+")";
        x =xn[1]+xn[2];
        System.out.print("N4 = ");
        for(int i = 0;i<newtStr.length;i++){
            System.out.println(newtStr[i]);
        }
        newt[0] = razn1[0];
        newt[1] = razn1[1]*(x-xn[0]);
        newt[2] = razn1[2]*(x-xn[0])*(x-xn[1]);
        newt[3] = razn1[3]*(x-xn[0])*(x-xn[1])*(x-xn[2]);
        newt[4] = razn1[4]*(x-xn[0])*(x-xn[1])*(x-xn[2])*(x-xn[3]);
        double ans = newt[0]+newt[1]+newt[2]+newt[3]+newt[4];
        BigDecimal answer = new BigDecimal(ans).setScale(3, RoundingMode.HALF_UP);
        System.out.println("N4(x1+x2) = "+"N4("+x+") = " + answer);
    }
    public static void lineSpline(){
        System.out.println("\nLinear spline:");
        System.out.println("Ф(x) = ");
        for(int i = 1;i< xn.length;i++){
            System.out.println("a"+i+"x + b"+i+", "+xn[i-1]+"<x<"+xn[i]);
        }
        System.out.println("\nSystem: ");
        for(int i = 1;i< xn.length;i++){
            lineStr[i-1] = String.valueOf(xn[i-1])+"a"+String.valueOf(i)+" + b"+String.valueOf(i)
                    +" = "+String.valueOf(yn[i-1])+"\n"
                    +String.valueOf(xn[i])+"a"+String.valueOf(i)+" + b"+String.valueOf(i)
                    +" = "+String.valueOf(yn[i]);
            System.out.println(lineStr[i-1]+"\n");
        }
        System.out.println("Coefficient: ");
        for(int i = 1;i< yn.length;i++){
            a[i-1] = (yn[i-1]-yn[i])/(xn[i-1]-xn[i]);
            b[i-1] = yn[i]-xn[i]*a[i-1];
            a1[i-1] = new BigDecimal(a[i-1]).setScale(3, RoundingMode.HALF_UP);
            b1[i-1] = new BigDecimal(b[i-1]).setScale(3, RoundingMode.HALF_UP);
            System.out.println("a"+i+" = "+a1[i-1]+"\nb"+i+" = "+b1[i-1]+"\n");
        }
        System.out.println("Ф(x) = ");
        int j = 0;
        for(int i = 1;i< xn.length;i++){
            if(b[j]<0) {
                System.out.println(a1[j] + "x " + b1[j] + ", " + xn[i- 1] + "<x<" + xn[i]);
            }else{
                System.out.println(a1[j] + "x + " + b1[j] + ", " + xn[i- 1] + "<x<" + xn[i]);
            }
            j++;
        }
    }
}