Write a program to find f(x) by using Lagrange Interpolation/ Newtonian Interpolation.

#include <iostream>
using namespace std;

#define MAX 20

// -------- Lagrange Interpolation --------
double lagrange(double x[], double y[], int n, double xp) {
    double yp = 0.0;

    for (int i = 0; i < n; i++) {
        double term = y[i];
        for (int j = 0; j < n; j++) {
            if (j != i)
                term *= (xp - x[j]) / (x[i] - x[j]);
        }
        yp += term;
    }
    return yp;
}

// -------- Newton Forward Interpolation --------
double newtonForward(double x[], double y[][MAX], int n, double xp) {
    double h = x[1] - x[0];
    double p = (xp - x[0]) / h;
    double yp = y[0][0];

    double fact = 1, pterm = 1;
    for (int i = 1; i < n; i++) {
        fact *= i;
        pterm *= (p - (i - 1));
        yp += (pterm * y[0][i]) / fact;
    }
    return yp;
}

int main() {
    int n, choice;
    double x[MAX], y[MAX][MAX], xp;

    cout << "Enter number of data points: ";
    cin >> n;

    cout << "Enter x values:\n";
    for (int i = 0; i < n; i++)
        cin >> x[i];

    cout << "Enter corresponding y values:\n";
    for (int i = 0; i < n; i++)
        cin >> y[i][0];

    cout << "Enter value of x to find f(x): ";
    cin >> xp;

    cout << "\nChoose Method:\n";
    cout << "1. Lagrange Interpolation\n";
    cout << "2. Newton Forward Interpolation\n";
    cout << "Enter choice: ";
    cin >> choice;

    if (choice == 1) {
        double result = lagrange(x, y[0], n, xp);
        cout << "f(" << xp << ") = " << result << endl;
    }
    else if (choice == 2) {
        // Build forward difference table
        for (int j = 1; j < n; j++) {
            for (int i = 0; i < n - j; i++) {
                y[i][j] = y[i + 1][j - 1] - y[i][j - 1];
            }
        }

        double result = newtonForward(x, y, n, xp);
        cout << "f(" << xp << ") = " << result << endl;
    }
    else {
        cout << "Invalid choice!" << endl;
    }

    return 0;
}