/* Program na vypocitanie rovnice o troch neznamych pomocou Sarrusovho pravidla o determinantoch... aspon myslim ze sa to tak nejako vola ;-)
Spravu o chybach posielajte na moonware@inmail.sk, aj ked ja dufam ze tu ziadne nebudu, a ak aj budu, ze na ne pridem sam :-) */
// verzia 1.5.2 - zmena z signed int na float a long double
// verzia 1.5.1 - pridanie volby exit; po zadani zlej hodnoty program nezacina od zaciatku
// verzia 1.5 - zmena pomenovania premennych z obycajnych na array (odstranenie constructora a destructora - uz nepotrebne)
// verzia 1.4 - zmena zobrazovania postupu riesenia, pridanie helpu
// zmena mena z rovnice_o_troch_neznamych na ro3n kvoli zjednoduseniu; prva verzia s tymto menom je 1.4
// verzia 1.3.1 - pridane "rovnica nema riesenie", teda zabranenie spadnutiu programu, ak D0 == 0
// verzia 1.3 - #define VERSION + postup + otazka na konci (zelate si vypocitat dalsi priklad?)
// verzia 1.2 - oprava chyby s deklaraciou globalnych premennych
// verzia 1.1 - zmena z int na signed int + pridanie destructora (a teda aj zmena vacsiny premennych na pointerov s pouzitim new a delete)

#include <iostream>
#include <cstdlib>
#include <string>

#define VERSION 1.5.2;

using namespace std;

long double a [3][4];

class cDeterminant {
	public:
		void postup (long double D0, long double D1, long double D2, long double D3) {
			// hlavny determinant ---------------------------------------------------------------
			cout << "\nPostup riesenia:\n" << endl;
			cout << "    | " << a[0][0] << " " << a[0][1] << " " << a[0][2] << " |" << endl;
			cout << "D = | " << a[1][0] << " " << a[1][1] << " " << a[1][2] << " | = (" << (a[0][0] * a[1][1] * a[2][2]) << ") + (" << (a[1][0] * a[2][1] * a[0][2]) << ") + (" << (a[2][0] * a[0][1] * a[1][2]) << ") - (" << (a[2][0] * a[1][1] * a[0][2]) << ") - (" << (a[0][0] * a[2][1] * a[1][2]) << ") - (" << (a[1][0] * a[0][1] * a[2][2]) << ") = " << D0 << endl;
			cout << "    | " << a[2][0] << " " << a[2][1] << " " << a[2][2] << " |\n" << endl;
			cout << "(D = " << a[0][0] << "." << a[1][1] << "." << a[2][2] << " + " << a[1][0] << "." << a[2][1] << "." << a[0][2] << " + " << a[2][0] << "." << a[0][1] << "." << a[1][2] << " - (" << a[2][0] << "." << a[1][1] << "." << a[0][2] << ") - (" << a[0][0] << "." << a[2][1] << "." << a[1][2] << ") - (" << a[1][0] << "." << a[0][1] << "." << a[2][2] << ") = " << D0 << ")\n" << endl;
			// determinant D1 -------------------------------------------------------------------
			cout << "     | " << a[0][3] << " " << a[0][1] << " " << a[0][2] << " |" << endl;
			cout << "D1 = | " << a[1][3] << " " << a[1][1] << " " << a[1][2] << " | = (" << (a[0][3] * a[1][1] * a[2][2]) << ") + (" << (a[1][3] * a[2][1] * a[0][2]) << ") + (" << (a[2][3] * a[0][1] * a[1][2]) << ") - (" << (a[2][3] * a[1][1] * a[0][2]) << ") - (" << (a[0][3] * a[2][1] * a[1][2]) << ") - (" << (a[1][3] * a[0][1] * a[2][2]) << ") = " << D1 << endl;
			cout << "     | " << a[2][3] << " " << a[2][1] << " " << a[2][2] << " |\n" << endl;
			cout << "(D1 = " << a[0][3] << "." << a[1][1] << "." << a[2][2] << " + " << a[1][3] << "." << a[2][1] << "." << a[0][2] << " + " << a[2][3] << "." << a[0][1] << "." << a[1][2] << " - (" << a[2][3] << "." << a[1][1] << "." << a[0][2] << ") - (" << a[0][3] << "." << a[2][1] << "." << a[1][2] << ") - (" << a[1][3] << "." << a[0][1] << "." << a[2][2] << ") = " << D1 << ")\n" << endl;
			// determinant D2 -------------------------------------------------------------------
			cout << "     | " << a[0][0] << " " << a[0][3] << " " << a[0][2] << " |" << endl;
			cout << "D2 = | " << a[1][0] << " " << a[1][3] << " " << a[1][2] << " | = (" << (a[0][0] * a[1][3] * a[2][2]) << ") + (" << (a[1][0] * a[2][3] * a[0][2]) << ") + (" << (a[2][0] * a[0][3] * a[1][2]) << ") - (" << (a[2][0] * a[1][3] * a[0][2]) << ") - (" << (a[0][0] * a[2][3] * a[1][2]) << ") - (" << (a[1][0] * a[0][3] * a[2][2]) << ") = " << D2 << endl;
			cout << "     | " << a[2][0] << " " << a[2][3] << " " << a[2][2] << " |\n" << endl;
			cout << "(D2 = " << a[0][0] << "." << a[1][3] << "." << a[2][2] << " + " << a[1][0] << "." << a[2][3] << "." << a[0][2] << " + " << a[2][0] << "." << a[0][3] << "." << a[1][2] << " - (" << a[2][0] << "." << a[1][3] << "." << a[0][2] << ") - (" << a[0][0] << "." << a[2][3] << "." << a[1][2] << ") - (" << a[1][0] << "." << a[0][3] << "." << a[2][2] << ") = " << D2 << ")\n" << endl;
			// determinant D3 -------------------------------------------------------------------
			cout << "     | " << a[0][0] << " " << a[0][1] << " " << a[0][3] << " |" << endl;
			cout << "D3 = | " << a[1][0] << " " << a[1][1] << " " << a[1][3] << " | = (" << (a[0][0] * a[1][1] * a[2][3]) << ") + (" << (a[1][0] * a[2][1] * a[0][3]) << ") + (" << (a[2][0] * a[0][1] * a[1][3]) << ") - (" << (a[2][0] * a[1][1] * a[0][3]) << ") - (" << (a[0][0] * a[2][1] * a[1][3]) << ") - (" << (a[1][0] * a[0][1] * a[2][3]) << ") = " << D3 << endl;
			cout << "     | " << a[2][0] << " " << a[2][1] << " " << a[2][3] << " |\n" << endl;
			cout << "(D3 = " << a[0][0] << "." << a[1][1] << "." << a[2][3] << " + " << a[1][0] << "." << a[2][1] << "." << a[0][3] << " + " << a[2][0] << "." << a[0][1] << "." << a[1][3] << " - (" << a[2][0] << "." << a[1][1] << "." << a[0][3] << ") - (" << a[0][0] << "." << a[2][1] << "." << a[1][3] << ") - (" << a[1][0] << "." << a[0][1] << "." << a[2][3] << ") = " << D3 << ")\n" << endl;}
		long double vypocitajD () {
			return ((a[0][0] * a[1][1] * a[2][2]) + (a[1][0] * a[2][1] * a[0][2]) + (a[2][0] * a[0][1] * a[1][2]) - (a[2][0] * a[1][1] * a[0][2]) - (a[0][0] * a[2][1] * a[1][2]) - (a[1][0] * a[0][1] * a[2][2]));}
		long double vypocitajD1 () {
			return ((a[0][3] * a[1][1] * a[2][2]) + (a[1][3] * a[2][1] * a[0][2]) + (a[2][3] * a[0][1] * a[1][2]) - (a[2][3] * a[1][1] * a[0][2]) - (a[0][3] * a[2][1] * a[1][2]) - (a[1][3] * a[0][1] * a[2][2]));}
		long double vypocitajD2 () {
			return ((a[0][0] * a[1][3] * a[2][2]) + (a[1][0] * a[2][3] * a[0][2]) + (a[2][0] * a[0][3] * a[1][2]) - (a[2][0] * a[1][3] * a[0][2]) - (a[0][0] * a[2][3] * a[1][2]) - (a[1][0] * a[0][3] * a[2][2]));}
		long double vypocitajD3 () {
			return ((a[0][0] * a[1][1] * a[2][3]) + (a[1][0] * a[2][1] * a[0][3]) + (a[2][0] * a[0][1] * a[1][3]) - (a[2][0] * a[1][1] * a[0][3]) - (a[0][0] * a[2][1] * a[1][3]) - (a[1][0] * a[0][1] * a[2][3]));}
};

void help () {
	cout << "\n-----------Napoveda programu ro3n-----------" << endl;
	cout << "Predpokladajme, ze chceme vypocitat sustavu:" << endl;
	cout << "5x - y + z = 4" << endl;
	cout << "2x + y - 3z = 8" << endl;
	cout << "x - 2y + 5z = -7" << endl;
	cout << "\n1. krok - zadanie hodnot" << endl;
	cout << "  Postupne zadavame hodnoty premennych, kde:" << endl;
	cout << "   a       b      c      d" << endl;
	cout << "  (5)x + (-1)y + (1)z = (4)" << endl;
	cout << "   e      f       g      h" << endl;
	cout << "  (2)x + (1)y + (-3)z = (8)" << endl;
	cout << "   i       j      k       l" << endl;
	cout << "  (1)x + (-2)y + (5)z = (-7)" << endl;
	cout << "  teda:" << endl;
	cout << "  a = 5; b = -1; c = 1; d = 4" << endl;
	cout << "  e = 2; f = 1; g = -3; h = 8" << endl;
	cout << "  i = 1; j = -2; k = 5; l = -7" << endl;
	cout << "  Kazde zadane cislo odsuhlasime stlacenim\n  klavesy enter (return)." << endl;
	cout << "\n2. krok - vysledok" << endl;
	cout << "  Po zadani vsetkych potrebnych informacii\n  sa zobrazi najprv postup." << endl;
	cout << "  Su tu vypocitane vsetky styri\n  determinanty." << endl;
	cout << "  Nizsie je zobrazeny vysledok - x, y, z." << endl;
	cout << "  Potom mame moznost program ukoncit,\n  alebo vypocitat dalsi priklad." << endl;
	cout << "  Podla vyberu napiseme A alebo N\n  a stlacime klavesu enter (return).\n" << endl;
}

int main () {
	znova:
	cout << "\n******************************************" << endl;
	cout << "*           ro3n verzia 1.5.2            *" << endl;
	cout << "* -------------------------------------- *" << endl;
	cout << "* Priklad rovnice:                       *" << endl;
	cout << "* ax + by + cz = d                       *" << endl;
	cout << "* ex + fy + gz = h                       *" << endl;
	cout << "* ix + jy + kz = l                       *" << endl;
	cout << "* -------------------------------------- *" << endl;
	cout << "* Napiste help pre viac informacii.      *" << endl;
	cout << "* Napiste exit pre ukoncenie programu.   *" << endl;
	cout << "******************************************" << endl;
	zadajte:
	cout << "Zadajte: " << endl;
	char buffer [50];
	// ---------------------------------------------------------------------------------------------
	znova_a:
	cout << "a = "; cin.getline (buffer, 50); 
	if ((buffer[0] == 'h') && (buffer[1] == 'e') && (buffer[2] == 'l') && (buffer[3] == 'p')) 
	{help (); goto zadajte;} 
	else if ((buffer[0] == 'e') && (buffer[1] == 'x') && (buffer[2] == 'i') && (buffer[3] == 't'))
	{cout << "Dovidenia!" << endl; return 0;}
	else {a[0][0] = atof (buffer); if (a[0][0] == 0) 
	{cout << "\nError, zadajte znovu platne cele cislo, okrem nuly" << endl; goto znova_a;}}
	// ---------------------------------------------------------------------------------------------
	znova_b:
	cout << "b = "; cin.getline (buffer, 50); 
	if ((buffer[0] == 'h') && (buffer[1] == 'e') && (buffer[2] == 'l') && (buffer[3] == 'p')) 
	{help (); goto zadajte;} 
	else if ((buffer[0] == 'e') && (buffer[1] == 'x') && (buffer[2] == 'i') && (buffer[3] == 't'))
	{cout << "Dovidenia!" << endl; return 0;}
	else {a[0][1] = atof (buffer); if (a[0][1] == 0) 
	{cout << "\nError, zadajte znovu platne cele cislo, okrem nuly" << endl; goto znova_b;}}
	// ---------------------------------------------------------------------------------------------
	znova_c:
	cout << "c = "; cin.getline (buffer, 50); 
	if ((buffer[0] == 'h') && (buffer[1] == 'e') && (buffer[2] == 'l') && (buffer[3] == 'p')) 
	{help (); goto zadajte;} 
	else if ((buffer[0] == 'e') && (buffer[1] == 'x') && (buffer[2] == 'i') && (buffer[3] == 't'))
	{cout << "Dovidenia!" << endl; return 0;}
	else {a[0][2] = atof (buffer); if (a[0][2] == 0) 
	{cout << "\nError, zadajte znovu platne cele cislo, okrem nuly" << endl; goto znova_c;}}
	// ---------------------------------------------------------------------------------------------
	znova_d:
	cout << "d = "; cin.getline (buffer, 50); 
	if ((buffer[0] == 'h') && (buffer[1] == 'e') && (buffer[2] == 'l') && (buffer[3] == 'p')) 
	{help (); goto zadajte;} 
	else if ((buffer[0] == 'e') && (buffer[1] == 'x') && (buffer[2] == 'i') && (buffer[3] == 't'))
	{cout << "Dovidenia!" << endl; return 0;}
	else {a[0][3] = atof (buffer); if (a[0][3] == 0) 
	{cout << "\nError, zadajte znovu platne cele cislo, okrem nuly" << endl; goto znova_d;}}
	// ---------------------------------------------------------------------------------------------
	znova_e:
	cout << "e = "; cin.getline (buffer, 50); 
	if ((buffer[0] == 'h') && (buffer[1] == 'e') && (buffer[2] == 'l') && (buffer[3] == 'p')) 
	{help (); goto zadajte;} 
	else if ((buffer[0] == 'e') && (buffer[1] == 'x') && (buffer[2] == 'i') && (buffer[3] == 't'))
	{cout << "Dovidenia!" << endl; return 0;}
	else {a[1][0] = atof (buffer); if (a[1][0] == 0) 
	{cout << "\nError, zadajte znovu platne cele cislo, okrem nuly" << endl; goto znova_e;}}
	// ---------------------------------------------------------------------------------------------
	znova_f:
	cout << "f = "; cin.getline (buffer, 50); 
	if ((buffer[0] == 'h') && (buffer[1] == 'e') && (buffer[2] == 'l') && (buffer[3] == 'p')) 
	{help (); goto zadajte;} 
	else if ((buffer[0] == 'e') && (buffer[1] == 'x') && (buffer[2] == 'i') && (buffer[3] == 't'))
	{cout << "Dovidenia!" << endl; return 0;}
	else {a[1][1] = atof (buffer); if (a[1][1] == 0) 
	{cout << "\nError, zadajte znovu platne cele cislo, okrem nuly" << endl; goto znova_f;}}
	// ---------------------------------------------------------------------------------------------
	znova_g:
	cout << "g = "; cin.getline (buffer, 50); 
	if ((buffer[0] == 'h') && (buffer[1] == 'e') && (buffer[2] == 'l') && (buffer[3] == 'p')) 
	{help (); goto zadajte;} 
	else if ((buffer[0] == 'e') && (buffer[1] == 'x') && (buffer[2] == 'i') && (buffer[3] == 't'))
	{cout << "Dovidenia!" << endl; return 0;}
	else {a[1][2] = atof (buffer); if (a[1][2] == 0) 
	{cout << "\nError, zadajte znovu platne cele cislo, okrem nuly" << endl; goto znova_g;}}
	// ---------------------------------------------------------------------------------------------
	znova_h:
	cout << "h = "; cin.getline (buffer, 50); 
	if ((buffer[0] == 'h') && (buffer[1] == 'e') && (buffer[2] == 'l') && (buffer[3] == 'p')) 
	{help (); goto zadajte;} 
	else if ((buffer[0] == 'e') && (buffer[1] == 'x') && (buffer[2] == 'i') && (buffer[3] == 't'))
	{cout << "Dovidenia!" << endl; return 0;}
	else {a[1][3] = atof (buffer); if (a[1][3] == 0) 
	{cout << "\nError, zadajte znovu platne cele cislo, okrem nuly" << endl; goto znova_h;}}
	// ---------------------------------------------------------------------------------------------
	znova_i:
	cout << "i = "; cin.getline (buffer, 50); 
	if ((buffer[0] == 'h') && (buffer[1] == 'e') && (buffer[2] == 'l') && (buffer[3] == 'p')) 
	{help (); goto zadajte;} 
	else if ((buffer[0] == 'e') && (buffer[1] == 'x') && (buffer[2] == 'i') && (buffer[3] == 't'))
	{cout << "Dovidenia!" << endl; return 0;}
	else {a[2][0] = atof (buffer); if (a[2][0] == 0) 
	{cout << "\nError, zadajte znovu platne cele cislo, okrem nuly" << endl; goto znova_i;}}
	// ---------------------------------------------------------------------------------------------
	znova_j:
	cout << "j = "; cin.getline (buffer, 50); 
	if ((buffer[0] == 'h') && (buffer[1] == 'e') && (buffer[2] == 'l') && (buffer[3] == 'p')) 
	{help (); goto zadajte;} 
	else if ((buffer[0] == 'e') && (buffer[1] == 'x') && (buffer[2] == 'i') && (buffer[3] == 't'))
	{cout << "Dovidenia!" << endl; return 0;}
	else {a[2][1] = atof (buffer); if (a[2][1] == 0) 
	{cout << "\nError, zadajte znovu platne cele cislo, okrem nuly" << endl; goto znova_j;}}
	// ---------------------------------------------------------------------------------------------
	znova_k:
	cout << "k = "; cin.getline (buffer, 50); 
	if ((buffer[0] == 'h') && (buffer[1] == 'e') && (buffer[2] == 'l') && (buffer[3] == 'p')) 
	{help (); goto zadajte;} 
	else if ((buffer[0] == 'e') && (buffer[1] == 'x') && (buffer[2] == 'i') && (buffer[3] == 't'))
	{cout << "Dovidenia!" << endl; return 0;}
	else {a[2][2] = atof (buffer); if (a[2][2] == 0) 
	{cout << "\nError, zadajte znovu platne cele cislo, okrem nuly" << endl; goto znova_k;}}
	// ---------------------------------------------------------------------------------------------
	znova_l:
	cout << "l = "; cin.getline (buffer, 50); 
	if ((buffer[0] == 'h') && (buffer[1] == 'e') && (buffer[2] == 'l') && (buffer[3] == 'p')) 
	{help (); goto zadajte;} 
	else if ((buffer[0] == 'e') && (buffer[1] == 'x') && (buffer[2] == 'i') && (buffer[3] == 't'))
	{cout << "Dovidenia!" << endl; return 0;}
	else {a[2][3] = atof (buffer); if (a[2][3] == 0) 
	{cout << "\nError, zadajte znovu platne cele cislo, okrem nuly" << endl; goto znova_l;}}
	// ---------------------------------------------------------------------------------------------
	cout << endl;
	cDeterminant determinant;
	long double D0 = determinant.vypocitajD ();
	long double D1 = determinant.vypocitajD1 ();
	long double D2 = determinant.vypocitajD2 ();
	long double D3 = determinant.vypocitajD3 ();
	determinant.postup (D0, D1, D2, D3);
	long double x, y, z;
	if (D0 == 0) {cout << "\nRovnica nema riesenie." << endl;} else {
		x = D1 / D0;
		y = D2 / D0;
		z = D3 / D0;
		cout << "\nx = D1 : D = " << x << "\ny = D2 : D = " << y << "\nz = D3 : D = " << z << endl;}
	vypocitat_dalsi_priklad_a_n:
	cout << "\nZelate si vypocitat dalsi priklad? [A/N] "; cin.getline (buffer, 2); if ((buffer[0] == 'A') || (buffer[0] == 'a')) {goto znova;} else if ((buffer[0] == 'N') || (buffer[0] == 'n')) {cout << "\nDovidenia!" << endl;} else {goto vypocitat_dalsi_priklad_a_n;};
	return 0;
}