Newton

#include <bits/stdc++.h>
using namespace std;
double evaluatePolynomial(const vector<double>& coeffs, double x) {
    double result = 0.0;
    int n = coeffs.size();
    for (int i = 0; i < n; ++i) {
        result += coeffs[i] * pow(x, n - 1 - i);
    }
    return result;
}
double evaluatePolynomialDerivative(const vector<double>& coeffs, double x) {
    double result = 0.0;
    int n = coeffs.size();
    for (int i = 0; i < n - 1; ++i) {
        result += coeffs[i] * (n - 1 - i) * pow(x, n - 2 - i);
    }
    return result;
}

int main() {
    vector<double> coeffs;
    double x0, x1, f0, g0, e;
    int step, N;
    double startInterval, endInterval, intervalStep;
    vector<double> roots;
    cout << setprecision(6) << fixed;
    int degree;
    cout << "Enter the degree of the polynomial: ";
    cin >> degree;

    cout << "Enter the coefficients of the polynomial (highest degree to constant term):" << endl;
    for (int i = 0; i <= degree; ++i) {
        double coeff;
        cin >> coeff;
        coeffs.push_back(coeff);
    }
    cout << "Enter tolerable error: ";
    cin >> e;
    cout << "Enter maximum iterations: ";
    cin >> N;
    cout << "Enter start of interval: ";
    cin >> startInterval;
    cout << "Enter end of interval: ";
    cin >> endInterval;
    cout << "Enter interval step (small value like 0.1): ";
    cin >> intervalStep;
    cout << "Newton-Raphson Method for Multiple Roots" << endl;
    for (double guess = startInterval; guess <= endInterval; guess += intervalStep) {
        x0 = guess;
        step = 1;

        while (step <= N) {
            g0 = evaluatePolynomialDerivative(coeffs, x0);
            f0 = evaluatePolynomial(coeffs, x0);

            if (g0 == 0.0) {
                break; 
            }

            x1 = x0 - f0 / g0;

            if (fabs(evaluatePolynomial(coeffs, x1)) <= e) {
                bool isUnique = true;
                for (double root : roots) {
                    if (fabs(root - x1) < e) {
                        isUnique = false;
                        break;
                    }
                }
                if (isUnique) {
                    roots.push_back(x1);
                    cout << "Found root: x = " << x1 << " with f(x) = " << evaluatePolynomial(coeffs, x1) << endl;
                }
                break; 
            }

            x0 = x1;
            step = step + 1;
        }
    }
    sort(roots.begin(), roots.end());
    cout << endl << "All unique roots found: " << endl;
    for (double root : roots) {
        cout << "Root: " << root << endl;
    }

    return 0;
}