#include <iostream>
#include <cmath>
#include <stdarg.h>

using namespace std;

class Vector;
bool kollin2 (Vector &j, Vector &m);

class Vector
{
private:
    int amount;                 //Количество координат
    double coordinates [100];      //Координаты

public:

    void SetAmount (int n) //Методы для координат и необходимого количества
    {
        amount = n;
    }
    void SetCoordinates (double value, int i)
    {
        coordinates [i] = value;
    }

    double& operator[](int i) {
        return coordinates[i];
    }

    int GetAmount () const
    {
        return amount;
    }
    int GetCoordinates (int i) const  //Координаты
    {
        return coordinates [i];
    }
    const Vector operator+ (const Vector& v)
    {
        int  i;

        Vector tmp=v;

        for (i=0; i<this->amount; i++)

            tmp.coordinates [i] = coordinates[i]+v.GetCoordinates(i);
        return tmp;
    }

    const Vector operator- (const Vector& v)
    {
        int  i;

        Vector tmp=v;

        for (i=0; i<this->amount; i++)

            tmp.coordinates [i] = coordinates[i]-v.GetCoordinates(i);
        return tmp;
    }

    friend Vector operator- (const Vector& v) {
        Vector tmp = v;

        for (int i=0; i<v.amount; i++)
            tmp.coordinates [i] = -v.coordinates[i];

        return tmp;

    }

    friend Vector operator+ (const Vector& v) {
        Vector tmp = v;

        for (int i=0; i<v.amount; i++)
            tmp.coordinates [i] = +v.coordinates[i];

        return tmp;

    }

    bool operator== (const Vector& v)
    {
        int flag = 0;
        for (int i=0; i<this->amount; i++){

            if(this->coordinates[i] == v.coordinates[i]) {}
            else
                flag = 1;
        }
        if (flag != 0)
            return false;

        return true;
    }

    bool operator!= (const Vector& v)
    {
        int flag = 0;
        for (int i=0; i<amount; i++){

            if(coordinates[i] != v.coordinates[i]) {
                flag = 1;
            }
        }
        if (flag == 0)
            return false;

        return true;
    }

    double operator* (const Vector& v)
    {
        int  i;

        Vector tmp=v;
        double m=0;

        for (i=0; i<this->amount; i++){

            tmp.coordinates [i] = coordinates[i]*v.GetCoordinates(i);
            m=m+tmp.coordinates[i];};
        return m;
    }

    const Vector operator/ (const Vector& v)
    {

        Vector tmp=v;
        double prom=1;
        for (int i=0; i<this->amount; i++){
            if(coordinates[i]!=0&&v.GetCoordinates(i)!=0) prom=tmp.coordinates[i];}
        for (int i=0; i<this->amount; i++){
            if(coordinates[i]==0&&v.GetCoordinates(i)==0) tmp.coordinates[i]=prom;
            else  {tmp.coordinates [i] = coordinates[i]/v.GetCoordinates(i);
                prom=tmp.coordinates[i];}}
        return tmp;
    }

    bool dioph_eq(double a, double b, double c) {
        return true;
    }

    bool ifCollinear (const Vector& v) {
        Vector tmp = *this/v;
        int cdm=tmp.GetAmount()-1;
        for (int i=0; i<cdm; i++){
            if (tmp.GetCoordinates(i)!=tmp.GetCoordinates(i+1)) return false;
        }
        return true;
    }

    int GCD(int a, int b) {
        while(a != b) {
            if(a > b)
                a -= b;
            else
                a += b;
        }
        return a;
    }

    bool ifCoplanar(Vector& v2, Vector& v3) {

        int flag, c, gcdValue;
        flag = 0;
        for (int i=0; i<amount; i++) {
            gcdValue = GCD(v2.coordinates[i], v3.coordinates[i]);
            c = coordinates[i];
            if (gcdValue % c != 0)
                flag = 1;
        }
        if (flag == 0)
            return true;

        return false;
    }

};

ostream& operator <<(ostream& out , Vector& v) {
    for(int i = 0; i < v.GetAmount(); i++) {
        out << v[i] << " ";
    }
    return out;

}

istream& operator >>(istream& in, Vector& v) {
    for(int i = 0; i < v.GetAmount(); i++) {
        in >> v[i];
    }
    return in;
}



bool kollinsys (int n, ...){
    va_list  args;
    va_start(args, n);

    Vector v = va_arg(args, Vector);
    for(int i = 0; i < n-1; i++) {
        Vector u = va_arg(args, Vector);
        if(!u.ifCollinear(v)) return false;
    }

    va_end(args);
    return true;
}

int main ()
{
    setlocale (LC_ALL,"rus");
    Vector Vector1;
    Vector Vector2;
    Vector Vector3;
    Vector Vector4;
    Vector Vector5;

    int n;
    int i;
    double value;

    cout << "Введите количество координат векторов:\n";
    cin >> n;
    Vector1.SetAmount (n);
    cout << "Введите координаты вектора 1:\n";
    cin >> Vector1;
    Vector2.SetAmount (n);
    cout << "Введите координаты вектора 2:\n";
    cin >> Vector2;
    Vector3.SetAmount (n);
    cout << "Введите координаты вектора 3:\n";
    cin >> Vector3;

    Vector sumVector;
    Vector resVector;
    sumVector=Vector1+Vector2;
    resVector=Vector1-Vector2;
    cout << "\nВектор 1:\n" << Vector1 << "\n";
    cout << "Вектор 2:\n" << Vector2 << "\n";
    cout << "Вектор 3:\n" << Vector3 << "\n\n";

    cout<<"Вычитаем из вектора 1 вектор 2 = "<<resVector<<"\n";
    cout<<"Складываем вектор 1 с вектором 2 = "<<sumVector<<"\n";

    double m=Vector1*Vector2;
    cout<< "Скалярное произведение векторов 1 и 2: " <<m;

    Vector4 = -Vector1;
    cout<< "\nОтрицательный вектор 1: " << Vector4 << endl;

    bool a, b;
    a=Vector2==Vector1;
    b=Vector2!=Vector1;
    if (a==true && b==false)
        cout<<"Векторы 1 и 2 равны\n";
    else
        cout<<"Векторы 1 и 2 неравны\n";

            cout << "\nВектор 1:\n" << Vector1 << "\n";
    cout << "Вектор 2:\n" << Vector2 << "\n";


    bool coll1=Vector1.ifCollinear(Vector2);
    bool kollinbg=kollinsys(3,Vector1,Vector2,Vector3);
    if (coll1 == true)
        cout<<"Векторы 1 и 2 коллинеарны\n";
    else
        cout<<"Векторы 1 и 2 неколлинеарны\n";


    bool cop = Vector1.ifCoplanar(Vector2, Vector3);
    if (cop == true)
        cout<< "Векторы 1, 2 и 3 компланарны\n";
    else
        cout<< "Векторы 1, 2 и 3 некомпланарны\n";

    cout<<"Проверка на коллинеарность системы из векторов 1, 2, 3 = "<<kollinbg<<endl;

    return 0;
}