112743.cpp

#include <iostream>
#include <cmath>
#include <cstdio>

using namespace std;

double getS(double ax, double ay, double bx, double by);
double getScal(double x, double y, double ax, double ay, double bx, double by);
void print(double ax, double ay, double bx, double by, double cx, double cy, double dx, double dy);
void sortc(double &ax, double &ay, double &bx, double &by);

int main(){

    double ax, bx, ay, by, cx, dx, cy, dy, a1, a2, b1, b2, c1, c2, x, y;
    cin >> ax >> ay >> bx >> by >> cx >> cy >> dx >> dy;

    if (ax == bx && ay == by && cx == dx && cy == dy)
        if (ax == cx && ay == cy)
            printf("%.10f %.10f\n", ax, ay);
        else
            printf("Empty\n");
    else if (getS(bx - ax, by - ay, dx - cx, dy - cy) == 0)
        if (getS(bx - ax, by - ay, cx - ax, cy - ay) == 0 && getS(dx - cx, dy - cy, ax - cx, ay - cy) == 0)
            print(ax, ay, bx, by, cx, cy, dx, dy);
        else
            printf("Empty\n");
    else{
        a1 = by - ay;
        b1 = ax - bx;
        c1 = ay * (bx - ax) - ax * (by - ay);
        a2 = dy - cy;
        b2 = cx - dx;
        c2 = cy * (dx - cx) - cx * (dy - cy);
        if (a1 == 0){
            y = (a1 * c2 / a2 - c1) / (b1 - a1 * b2 / a2);
            x = -(c2 + b2 * y) / a2;
        }else{
            y = (a2 * c1 / a1 - c2) / (b2 - a2 * b1 / a1);
            x = -(c1 + b1 * y) / a1;
        }
        if (getScal(x, y, ax, ay, bx, by) >= 0 && getScal(x, y, bx, by, ax, ay) >= 0 && getScal(x, y, cx, cy, dx, dy) >= 0 &&
                getScal(x, y, dx, dy, cx, cy) >= 0)
            printf("%.10f %.10f\n", x, y);
        else
            printf("Empty\n");
    }


    return 0;
}

double getS(double ax, double ay, double bx, double by){
    return (bx * ay - ax * by);
}

double getScal(double x, double y, double ax, double ay, double bx, double by){
    return (x - ax) * (bx - ax) + (y - ay) * (by - ay);
}

void print(double ax, double ay, double bx, double by, double cx, double cy, double dx, double dy){
    if (ax == bx && ay == by)
        if (getScal(ax, ay, cx, cy, dx, dy) >= 0 && getScal(ax, ay, dx, dy, cx, cy) >= 0)
            printf("%.10f %.10f\n", ax, ay);
        else
            printf("Empty\n");
    else if (cx == dx && cy == dy)
        if (getScal(cx, cy, ax, ay, bx, by) >= 0 && getScal(cx, cy, bx, by, ax, ay) >= 0)
            printf("%.10f %.10f\n", cx, cy);
        else
            printf("Empty\n");
    else if (getScal(ax, ay, cx, cy, dx, dy) >= 0 && getScal(ax, ay, dx, dy, cx, cy) >= 0){
        if (getScal(bx, by, cx, cy, dx, dy) <= 0){
            sortc(ax, ay, cx, cy);
            if (ax == cx && ay == cy)
                printf("%.10f %.10f\n", ax, ay);
            else
                printf("%.10f %.10f\n%.10f %.10f\n", ax, ay, cx, cy);
        }else{
            sortc(ax, ay, dx, dy);
            if (ax == dx && ay == dy)
                printf("%.10f %.10f\n", ax, ay);
            else
                printf("%.10f %.10f\n%.10f %.10f\n", ax, ay, dx, dy);
        }
    }else if (getScal(bx, by, cx, cy, dx, dy) >= 0 && getScal(bx, by, dx, dy, cx, cy) >= 0){
        if (getScal(ax, ay, cx, cy, dx, dy) <= 0){
            sortc(bx, by, cx, cy);
            if (bx == cx && by == cy)
                printf("%.10f %.10f\n", bx, by);
            else
                printf("%.10f %.10f\n%.10f %.10f\n", bx, by, cx, cy);
        }else{
            sortc(bx, by, dx, dy);
            if (bx == dx && by == dy)
                printf("%.10f %.10f\n", bx, by);
            else
                printf("%.10f %.10f\n%.10f %.10f\n", bx, by, dx, dy);
        }
    }else
        printf("Empty\n");
}

void sortc(double &ax, double &ay, double &bx, double &by){
    if (ax > bx){
        swap(ax, bx);
        swap(ay, by);
    }else if (ax == bx){
        if (ay > by){
            swap(ax, bx);
            swap(ay, by);
        }
    }
}