#include <iostream>
#include <fstream>
#include <windows.h>

using namespace std;

double NFORWARD(double);
double NBACKWARD(double);
double STIRLING(double);

double X[11];
double Y[11];

int main() {
    ofstream fout;
    fout.open("outFile.txt", ios::app);
    SetConsoleOutputCP(CP_UTF8);
    int i;
    double x1, x2, x3;
    ifstream input("input.txt");
    for (i = 0; i < 11; i++) {
        input >> X[i];
        input >> Y[i];
    }
    input >> x1 >> x2 >> x3;
    input.close();
    cout << "x1 = " << x1 << " NFOR | NBACK | STIR" << endl;
    cout << NFORWARD(x1) << " | " << NBACKWARD(x1) << " | " << STIRLING(x1) << endl;
    cout << "x2 = " << x2 << " NFOR | NBACK | STIR" << endl;
    cout << NFORWARD(x2) << " | " << NBACKWARD(x2) << " | " << STIRLING(x2) << endl;
    cout << "x3 = " << x3 << " NFOR | NBACK | STIR" << endl;
    cout << NFORWARD(x3) << " | " << NBACKWARD(x3) << " | " << STIRLING(x3) << endl;
    return 0;
}

double NFORWARD(double x) {
    double a;
    double h, q;
    double delta[11][11];
    int i, j;
    double NEWTON;
    h = X[1] - X[0];
    q = (x - X[0]) / h;
    for (i = 0; i < 11; i++) {
        delta[i][0] = Y[i];
    }
    for (j = 1; j < 11; j++) {
        for (i = 0; i < 11 - j; i++)
            delta[i][j] = delta[i + 1][j - 1] - delta[i][j - 1];
    }
    NEWTON = 0;
    for (i = 0; i < 11; i++) {
        a = 1;
        for (j = 0; j < i; j++) {
            a = a * (q - j) / (j + 1);
        }
        NEWTON = NEWTON + delta[0][i] * a;
    }
    return NEWTON;
}

double NBACKWARD(double x) {
    double a;
    double h, q;
    double delta[11][11];
    int i, j;
    double NEWTON;
    h = X[10] - X[9];
    q = (x - X[10]) / h;
    for (i = 0; i < 11; i++)
        delta[i][0] = Y[10 - i];
    for (j = 1; j < 11; j++) {
        for (i = 0; i < 11 - j; i++)
            delta[i][j] = delta[i][j - 1] - delta[i + 1][j - 1];
    }
    NEWTON = 0;
    for (i = 0; i < 11; i++) {
        a = 1;
        for (j = 0; j < i; j++) {
            a = a * (q + j) / (j + 1);
        }
        NEWTON = NEWTON + delta[0][i] * a;
    }
    return NEWTON;
}

double STIRLING(double x) {
    double a, STIR;
    int n = 5;
    double h, q;
    double delta[11][11];
    int i, j;
    for (i = 0; i < 11; i++)
        delta[i][0] = Y[i];

    for (j = 1; j < 11; j++) {
        for (i = 0; i < 11 - j; i++)
            delta[i][j] = delta[i + 1][j - 1] - delta[i][j - 1];
    }
    h = X[1] - X[0];
    q = (x - X[n]) / h;
    double kvadr;
    double fakt;
    STIR = delta[n][0];
    int par1 = 0, par2 = 1;
    for (i = 1; i < 11; i++) {
        if (i % 2 == 1) {
            fakt = 1;
            kvadr = 1;
            a = q;
            for (j = 1; j < i; j++)
                fakt = fakt * (j + 1);
            for (j = 1; j <= i / 2; j++)
                kvadr = kvadr * (q - j) * (q + j);
            a = a * kvadr / fakt;
            STIR = STIR + (delta[n - par1][i] + delta[n - par1 - 1][i]) * a / 2;
            par1++;
        } else {
            fakt = 1;
            kvadr = 1;
            a = 1;
            for (j = 1; j < i; j++)
                fakt = fakt * (j + 1);
            for (j = 0; j < i / 2; j++)
                kvadr = kvadr * (q - j) * (q + j);
            a = a * kvadr / fakt;
            STIR = STIR + delta[n - par2][i] * a;
            par2++;
        }
    }
    return STIR;
};