#include <iostream>
#include <cmath>
#include <complex>
#include<conio.h>
#include <vector>
#include <iomanip>

using namespace std;
const int n = 5;

complex<double> k[n] = {
        complex<double>(0, 1),
        complex<double>(15, 0),
        complex<double>(10, 0),
        complex<double>(12, 0),
        complex<double>(10, 0),

};

double
coordDescent(double x01, double x02, const double E, const double alp01, const double alp02, complex<double> *koef,
             int k);

complex<double> gorner1f(double x, double y, complex<double> koef[]);

double gornerf(double x, double y, complex<double> koef[]);

void gornerd(double x, double y, complex<double> *a);

//временные корни
vector<double> x1t;
vector<double> x2t;
//нормальные корни
vector<double> x1c;
vector<double> x2c;

//счетчик функций
vector<double> fc;
int fco = 0;

int main() {
    double eps = 0.01, Eps = 0.0000001;
    complex<double> temp[n];
    for (int i = 0; i < n; i++) {
        temp[i] = k[i];
    }
    cout << "COORD DESCENT: " << endl;
    cout << "Finding root 1 :" << endl;
    coordDescent(0, 0, Eps, 1, 1, temp, 1);
    gornerd(x1c[0], x2c[0], temp);
    cout << endl;
    cout << "fc: " << fco << endl;
    fc.push_back(fco);
    cout << endl;
    cout << endl;
    for (int i = 1; i < n - 2; i++) {
        eps *= 2;
        fco = 0;
        cout << "Finding root " << i + 1 << ": " << endl;
        coordDescent(0, 0, eps, 1, 1, temp, 2);
        coordDescent(x1t[i - 1], x2t[i - 1], Eps, 1, 1, k, 1);
        gornerd(x1c[i], x2c[i], temp);
        cout << endl;
        cout << "fc: " << fco << endl;
        fc.push_back(fco);
        cout << endl;
        cout << endl;
    }
    fco = 0;
    cout << "Finding root 4 :" << endl;
    x1t.push_back((-temp[0] / temp[1]).real());
    x2t.push_back((-temp[0] / temp[1]).imag());
    coordDescent(x1t[2], x2t[2], Eps, 1, 1, k, 1);
    cout << endl;
    cout << "fc: " << fco << endl;
    fc.push_back(fco);
    cout << endl;
    cout << endl;
    cout << "fcall: " << fc[0] + fc[1] + fc[2] + fc[3] << endl;
    return 0;
}

// считает значение функции в точке
double gornerf(double x, double y, complex<double> koef[]) {
    return pow(gorner1f(x, y, koef).real(), 2) + pow(gorner1f(x, y, koef).imag(), 2);
}

// считает значение исходного полинома в точке
complex<double> gorner1f(double x, double y, complex<double> koef[]) {
    complex<double> z(x, y);
    complex<double> s = koef[n - 1];
    for (int i = 1; i <= n - 1; ++i) {
        s *= z;
        s += koef[(n - 1) - i];
    }
    return s;
}

// деление полинома на бином
void gornerd(double x, double y, complex<double> *a) {
    complex<double> c(x, y);
    complex<double> b[n];
    b[n - 1] = 0;
    for (int i = n - 2; i >= 0; i--) {
        b[i] = a[i + 1] + c * b[i + 1];
    }
    for (int j = 0; j < n; j++) {
        a[j] = b[j];
    }
}

// координатный спуск
double
coordDescent(double x01, double x02, const double E, const double alp01, const double alp02, complex<double> *koef,
             int k) {
    double x1 = x01;
    double x2 = x02;
    double alp1 = alp01;
    double alp2 = alp02;
    int count2 = 0;
    int count1 = 0;
    int n = 2;
    double xu = 0, xn = 1;

    double f1, f2, f;
    f = (gornerf(x1, x2, koef));
    fco++;
    double eps = 0.00000001;
    cout << "x1 " << x1 << " x2 " << x2 << " f " << f << " a1 " << alp1 << " a2 " << alp2 << endl;
    while (abs(f) > E) {
        alp1 = abs(alp1);
        alp2 = abs(alp2);
        f1 = gornerf(x1 + eps, x2, koef);
        f2 = gornerf(x1 - eps, x2, koef);
        fco = fco + 2;
        cout << endl;
        cout << setprecision(20) << "x1 " << x1 - eps << " x2 " << x2 << " f " << f2 << " a1 " << alp1 << " a2 " << alp2
             << endl;
        cout << setprecision(20) << "x1 " << x1 + eps << " x2 " << x2 << " f " << f1 << " a1 " << alp1 << " a2 " << alp2
             << endl;
        if (f1 <= f2) {
            x1 = x1 + eps;
            f = f1;
            cout << "Xplus" << endl;
        } else {
            x1 = x1 - eps;
            f = f2;
            cout << "Xminus" << endl;
            alp1 *= -1;
        }
        count1 = 0;
        count2 = 0;
        while (count1 < n && count2 < 1) {
            f1 = gornerf(x1 + alp1, x2, koef);
            fco++;
            while (f1 < f) {
                x1 = x1 + alp1;
                cout << "OkX" << "x1 " << x1 << " x2 " << x2 << " f " << f << " f1 " << f1 << " a1 " << alp1 << " a2 "
                     << alp2 << endl;
                count2 += 1;
                f = f1;

                if (count2 > 1)cout << "Second step with this ax" << endl;
                f1 = gornerf(x1 + alp1, x2, koef);

            }
            if (f1 > f) {
                alp1 *= 0.5;
                cout << "NeokX " << "x1 " << x1 << " x2 " << x2 << " f " << f << " f1 " << f1 << " a1 " << alp1
                     << " a2 " << alp2 << endl;
                count1++;
            }
        }
        count1 = 0;
        count2 = 0;
        f1 = gornerf(x1, x2 + eps, koef);
        f2 = gornerf(x1, x2 - eps, koef);
        fco = fco + 2;
        cout << endl;
        cout << setprecision(20) << "x1 " << x1 << " x2 " << x2 - eps << " f " << f2 << " a1 " << alp1 << " a2 " << alp2
             << endl;
        cout << setprecision(20) << "x1 " << x1 << " x2 " << x2 + eps << " f " << f1 << " a1 " << alp1 << " a2 " << alp2
             << endl;

        if (f1 <= f2) {
            x2 = x2 + eps;
            f = f1;
            cout << "Yplus" << endl;
        } else {
            x2 = x2 - eps;
            f = f2;
            cout << "Yminus" << endl;
            alp2 *= -1;
        }
        while (count2 < n && count1 < 1) {
            f1 = gornerf(x1, x2 + alp2, koef);
            fco++;
            while (f1 < f) {
                x2 = x2 + alp2;
                cout << "OkY " << "x1 " << x1 << " x2 " << x2 << " f " << f << " f1 " << f1 << " a1 " << alp1 << " a2 "
                     << alp2 << endl;
                count2 += 1;
                f = f1;
                if (count2 > 1)cout << "Second step with this ay" << endl;
                f1 = gornerf(x1, x2 + alp2, koef);

            }
            if (f1 > f) {
                alp2 *= 0.5;
                cout << "NeokY " << "x1 " << x1 << " x2 " << x2 << " f " << f << " f1 " << f1 << " a1 " << alp1
                     << " a2 " << alp2 << endl;
                count2++;
            }
        }
    }
    if (k == 1) {
        cout << endl;
        cout << "Exact root: " << " x: " << x1 << " y: " << x2 << " f: " << f << endl;
        x1c.push_back(x1);
        x2c.push_back(x2);
    }
    if (k == 2) {
        cout << endl;
        cout << "Aprox root: " << " x: " << x1 << " y: " << x2 << " f: " << f << endl;
        x1t.push_back(x1);
        x2t.push_back(x2);
    }
    return 0;
}