#include <complex>
#include <cstdlib>
#include <iostream>
#include <locale.h>
#include <math.h>

using namespace std;
const double Pi = 3.14159;
const double zero = 0.00000001;
double A, B, C, D, p, q, Delta;
int wybor;

int main() {
  setlocale(LC_CTYPE, "Polish");
  cout
      << "Witam w programie do obliczania\npierwiastkow wielomianu 3-stopnia\n";

  for (;;) {
    cout << "-------------------------------" << endl << "\n";
    cout << "1 - zacznij liczyć pierwiastki wielomianu\n";
    cout << "2 - wyjdź z programu\n";
    cin >> wybor;

    switch (wybor) {
    case 1:
      system("cls");
      cout << "\nPodaj A (A!=0): ";
      cin >> A;
      while (A == 0) {
        system("cls");
        cout << "\nBŁĄD !!!! Podaj A (A!=0): ";
        cin >> A;
      }
      cout << "Podaj B: ";
      cin >> B;
      cout << "Podaj C: ";
      cin >> C;
      cout << "Podaj D: ";
      cin >> D;

      p = (C / A) - (B * B) / (3.0 * A * A);

      cout << "\np = " << p;

      q = ((2.0 * B * B * B) / (27.0 * A * A * A)) + (D / A) -
          ((B * C) / (3.0 * A * A));

      cout << "\nq = " << q;

      // Delta = ((q * q) + (4.0 * p * p * p)) / 27.0;
      Delta = pow(q / 2.0, 2.0) + pow(p / 3.0, 3.0);

      cout << "\nDelta = " << Delta << endl;
      cout << "-------------------------------" << endl;

      if (Delta > 0) {
        complex<double> x2;
        complex<double> x3;
        complex<double> wynik;
        double x1;
        double u, v;

        u = pow(-(q / 2.0) + sqrt(abs(Delta)), 1.0 / 3.0);
        v = pow(abs(-(q / 2.0) - sqrt(abs(Delta))), 1.0 / 3.0);

        x1 = u - v - (B / (3 * A));

        x2 = (-(1.0 / 2.0) * (u - v) - (B / (3 * A))) +
             (1i * (sqrt(3.0) / 2.0) * (u + v));
        x3 = (-(1.0 / 2.0) * (u - v) - (B / (3 * A))) -
             (1i * (sqrt(3.0) / 2.0) * (u + v));

        cout << "x1 = " << x1 << endl;
        cout << "x2 = " << real(x2) << " +j " << imag(x2) << endl;
        cout << "x3 = " << real(x3) << " -j " << abs(imag(x3)) << endl;

        // sprawdzenie
        cout << x2 << endl;
        cout << x3 << endl;

        wynik = A * pow(x2, 3) + B * pow(x2, 2) + C * pow(x2, 1) + D;
        cout << wynik << endl;

      }

      else if (Delta < 0) {
        double y1, y2, y3, x1, x2, x3;
        double u, v;
        u = 2 * sqrt(abs(p / 3.0));
        v = acos(((-1.0 * q) / 2.0) * pow(abs(3 / p), 3.0 / 2.0));

        y1 = u * cos(v / 3.0);
        y2 = u * cos((v + 2 * Pi) / 3.0);
        y3 = u * cos((v + 4 * Pi) / 3.0);

        x1 = y1 - (B / (3.0 * A));
        x2 = y2 - (B / (3.0 * A));
        x3 = y3 - (B / (3.0 * A));

        cout << "x1 = " << x1 << endl;
        cout << "x2 = " << x2 << endl;
        cout << "x3 = " << x3 << endl;

        /*  double F = (((3.0 * C) / A) - ((B * 😎 / (A * A))) / 3.0;
          double G = (((2.0 * B * B * 😎 / (A * A * A)) - ((9.0 * B * C) / (A *
          A)) + ((27.0 * D) / A)) /27.0; double H = ((G * G) / 4.0) + ((F * F *
          F) / 27.0); double I = sqrt(((G * G) / 4.0) - H); double J = cbrt(F);
          double K = acos(-(G / (2.0 * I)));
          double L = -J;
          double M = cos(K / 3.0);
          double N = sqrt(3.0) * sin(K / 3.0);
          double P = -(B / (3.0 * A));
          double x1 = (2.0 * J * M) + P;
          double x2 = L * (M + N) + P;
          double x3 = L * (M - N) + P;
          cout << "x[1] = " << x1 << endl;
          cout << "x[2] = " << x2 << endl;
          cout << "x[3] = " << x3 << endl; */
      } else if (Delta == 0) {
        double y1, y2, x1, x2;
        double u;
        u = -1 * pow(q / 2.0, 1.0 / 3.0);
        y1 = 2 * u;
        y2 = -u;

        x1 = y1 - B / 3.0;
        x2 = y2 - B / 3.0;

        cout << "x1 = " << x1 << endl;
        cout << "x2 = " << x2 << endl;
      }

      else {
        cout << "BłĄD" << endl;
      }

      cout << "\n";
      break;

    case 2:
      exit(0);
      break;
    default:
      system("cls");

      break;
    }
  }
}