#include <iostream>
#include <cmath>

using namespace std;


double pole1(double* x, double* y, int n){
    double P =0;
    for(int i=0; i<n; i++){
        P +=(x[i]*y[(i+1)%n]-x[(i+1)%n]*y[i]);
    }
    return fabs(P/2);
}

double pole2(double* x, double* y, int n){
    double P =0;
    for(int i=0; i<n; i++){
        P += ((x[i]+x[(i+1)%n])*(y[(i+1)%n]-y[i]));
    }
    return fabs(P/2);
}

//suma pol trojkatow
double pole3(double* x, double* y, int n, double xn, double yn){
    double P =0;
    for(int i=0; i<n; i++){
        P += fabs((x[(i+1)%n]-x[i])*(yn-y[i])-(y[(i+1)%n]-y[i])*(xn-x[i]));
    }
    return P/2;
}

bool czyWew(double* x, double* y, int n, double xn, double yn){
    if(pole2(x,y,n)==pole3(x,y,n,xn,yn)){
        return true;
    }
    else{
        return false;
    }
}

//
//double pole3(double* x, double* y, int n){
//    double P = 0;
//    int i =0 ;
//    double ax =x[i+1]-x[i];
//    double ay =y[i+1]-y[i];
//    double bx =x[i+2]-x[i+1];
//    double by =y[i+2]-y[i+1];
//    return fabs(ax*by-ay*bx)/2;
//}

int main()
{
    int n=3;
    double x[] = {1,5,1};
    double y[] = {4,1,1};

    double xn= 2;
    double yn= 2;
    cout << (pole1(x,y,n)) <<endl;
    cout << (pole2(x,y,n)) <<endl;
    cout <<  pole3(x,y,n, xn, yn) <<endl;

    double x2[] = {1,1,3,1,0};
    double y2[] = {1,0,1,3,1};
    cout << pole1(x2,y2,5) <<endl;
    cout << pole2(x2,y2,5) <<endl;
    double xn2= 1.5;
    double yn2= 1.5;
    cout << "Jesli wezmiemy punkt wewnatrz figury to pole bedzie takie samo" <<endl;
    cout <<  pole3(x2,y2,5, xn, yn) <<endl;

    cout << "A jesli wezmiemy punkt poza figura to pole juz bedzie inne" <<endl;
    cout <<  pole3(x2,y2,5,1.01,3) <<endl;

    if (czyWew(x2,y2,5,1.01,3)){
        cout << "Punkt (1.01,3) znajduje sie wew. figury" <<endl;
    }
    else{
        cout << "Punkt (1.01,3) znajduje sie zew. figury" <<endl;
    }


    return 0;
}