#include <iostream> //exercise 6
#include <string> //there is a set of points on the plane
#include <vector> //find all points which is in rectangle formed by {x1,y1} {x2,y2} {x3,y3} {x4,y4}
#include <algorithm>

using namespace std;

struct dot
{
    int x, y;
    dot(int a, int b) : x(a), y(b) {};
};

vector<dot> DOT;

double sideLength(int a, int b)
{
    return sqrt((DOT[a].x - DOT[b].x) * (DOT[a].x - DOT[b].x) + (DOT[a].y - DOT[b].y) * (DOT[a].y- DOT[b].y));
}

double squareTriangle(int a, int b, int c)
{
    double side1 = sideLength(a, b);
    double side2 = sideLength(b, c);
    double side3 = sideLength(c, a);

    double p = (side1 + side2 + side3) / 2;

    double square = sqrt(p * (p - side1) * (p - side2) * (p - side3));

    return square;
}

int main()
{
    int a, b, counter = 0;

    cout << "Please, input the coordinates of rectangle in true way: like clockwise or counter-clockwise" << endl;
    for(int i = 0; i < 4; i++)
    {
        cout << "Enter the x" << i + 1 << " and y" << i + 1 << endl;
        cin >> a >> b;
        DOT.push_back(dot(a, b));
    }

    cout << "Enter coordinates of other dots. End the input by typing a letter." << endl;
    while(cin >> a)
    {
        cin >> b;
        DOT.push_back(dot(a, b));
        cout << "Coordinates of this dot are " << DOT.back().x << "," << DOT.back().y << endl;
        counter++;
    }

    double eps = 0.000001;
    double square = sideLength(0, 1) * sideLength(2, 1);
    bool was = false;

    for(int i = 0; i < counter; i++)
    {
        double squareSum = squareTriangle(0, 1, i + 4) + squareTriangle(1, 2, i + 4) + squareTriangle(2, 3, i + 4) + squareTriangle(3, 0, i + 4);
        if (abs(squareSum - square) < eps)
        {
            cout << "Lucky dot is " << DOT[i + 4].x << "," << DOT[i + 4].y << endl;
            was = true;
        }
    }

    if(!was)
        cout << "No lucky dots\n";

    system("pause");
    return 0;
}