MAT 125 - Assignment

#include<bits/stdc++.h>
using namespace std;

#define pb push_back


vector<vector<double> > getSubMatrix(int c, vector< vector<double> > mat)
{
        vector< vector<double> > submat;
        int N = mat.size();

        for(int i=1; i<N; i++)
        {
                vector<double> row;

                for(int j=0; j<N; j++)
                {
                        if(j != c)
                        {
                                row.pb(mat[i][j]);
                        }
                }
                submat.pb(row);
        }
        return submat;
}


double det(vector<vector<double> > mat)
{
        double ret = 0;
        int N = mat.size();

        if(N == 1)
        {
                return mat[0][0];
        }
        else
        {
                for(int c=0; c<N; c++)
                {
                        ret += pow(-1.0, c) * mat[0][c] * det(getSubMatrix(c, mat));
                }
        }

        return ret;
}

struct Solver{

        vector<string>generalEquation;

        void solve( vector<string> ge, vector<vector<double> > mat)
        {
                int N = mat.size();

                for(int c = 0; c<N; c++)
                {
                        double d = det(getSubMatrix(c, mat));

                        if( (c%2) == 1)
                        {
                                d = -d;
                        }

                        if(d > 0.0)
                        {
                                cout<<"+";
                        }

                        if(abs(d) > 0.0)
                        {
                                cout<<d<<ge[c];

                        }

                }

                cout<<" = 0"<<endl;
        }

};



struct Circle{

        vector<double> row(double x, double y)
        {
                vector<double>ret;

                ret.pb(x*x + y*y);
                ret.pb(x);
                ret.pb(y);
                ret.pb(1);

                return ret;

        }

        void run()
        {
                vector<string>ge({"(x^2 + y^2)", "x", "y", ""});
                int N = ge.size();

                vector< vector<double> > mat;

                vector<double>tmp;

                for(int i=0; i<N; i++)
                {
                        tmp.pb(1.0);
                }

                mat.pb(tmp);

                cout<<"Please input 3 points on the circle (x, y): "<<endl;

                double x, y;

                for(int i=0; i<3; i++)
                {
                        cin>>x>>y;

                        mat.pb(row(x, y));
                }


                cout<<"Equation: ";


                Solver solver;

                solver.solve(ge, mat);
        }

};


struct Plane{

        vector<double> row(double x, double y, double z)
        {
                vector<double>ret;

                ret.pb(x);
                ret.pb(y);
                ret.pb(z);
                ret.pb(1);

                return ret;

        }

        void run()
        {
                vector<string>ge({"x", "y", "z", ""});
                int N = ge.size();

                vector< vector<double> > mat;

                vector<double>tmp;

                for(int i=0; i<N; i++)
                {
                        tmp.pb(1.0);
                }

                mat.pb(tmp);

                cout<<"Please input 3 points on the plane (x, y, z): "<<endl;

                double x, y, z;

                for(int i=0; i<3; i++)
                {
                        cin>>x>>y>>z;

                        mat.pb(row(x, y, z));
                }


                cout<<"Equation: ";


                Solver solver;

                solver.solve(ge, mat);
        }

};


struct Parabola{

        vector<double> row(double x, double y)
        {
                vector<double>ret;

                ret.pb(y);
                ret.pb(x*x);
                ret.pb(x);
                ret.pb(1);

                return ret;

        }

        void run()
        {
                vector<string>ge({"y", "x^2", "x", ""});
                int N = ge.size();

                vector< vector<double> > mat;

                vector<double>tmp;

                for(int i=0; i<N; i++)
                {
                        tmp.pb(1.0);
                }

                mat.pb(tmp);

                cout<<"Please input 3 points on the parabola: (x, y) "<<endl;

                double x, y;

                for(int i=0; i<3; i++)
                {
                        cin>>x>>y;

                        mat.pb(row(x, y));
                }

                cout<<"Determinant Equation:"<<endl;
                cout<<"|\ty\tx^2\tx\t1\t|"<<endl;

                for(int i=1; i<=3; i++)
                {
                        cout<<"|\t";
                        for(int j=0; j<N; j++)
                        {
                                cout<<mat[i][j]<<"\t";
                        }
                        cout<<"|";

                        if(i == 1)
                        {
                                cout<<"\t=\t0";
                        }
                        cout<<endl;
                }

                cout<<"And Equation of the Parabola"<<endl;
                Solver solver;
                solver.solve(ge, mat);
        }
};


int main()
{
        int option = -1;
        while(true)
        {
                if(option != -1) cout<<endl;

                cout<<"1: Circle"<<endl<<"2: Plane"<<endl<<"3: Parabola"<<endl<<"0: Exit"<<endl;

                cin>>option;
                if(option == 1)
                {
                        Circle c;
                        c.run();
                }
                else if(option == 2)
                {
                        Plane p;
                        p.run();
                }
                else if(option == 3)
                {
                        Parabola parabola;
                        parabola.run();
                }
                else if(option == 0)
                {
                        break;
                }
        }


}