[CareerCup] 7.5 A Line Cut Two Squares in Half 平均分割两个正方形的直线

class Point {
public:
    double _x, _y;
    Point(double x, double y): _x(x), _y(y) {};
};

class Line {
public:
    Point _start, _end;
    Line(Point start, Point end): _start(start), _end(end) {};
};

/*
  (left, top)_________
            |         |
            |         | size
            |_________|
                      (right, down)  
*/
class Square {
public:
    double _left, _top, _right, _down, _size;
    Square(double left, double top, double right, double down, double size): _left(left), _top(top), _right(right), _down(down), _size(size) {};
    Point middle() {
        return Point((_left + _right) * 0.5, (_top + _down) * 0.5);
    }
    // Return the point whrere the line connecting mid1 and mid2 intercepts the edge of square 1.
    Point extend(Point mid1, Point mid2, double size) {
        double xdir = mid1._x < mid2._x ? -1 : 1;
        double ydir = mid1._y < mid2._y ? -1 : 1;
        if (mid1._x == mid2._x) return Point(mid1._x, mid1._y + ydir * size * 0.5);
        double slope = (mid1._y - mid2._y) / (mid1._x - mid2._x);
        double x1 = 0, y1 = 0;
        if (fabs(slope) == 1) {
            x1 = mid1._x + xdir * size * 0.5;
            y1 = mid1._y + ydir * size * 0.5;
        } else if (fabs(slope) < 1) {
            x1 = mid1._x + xdir * size * 0.5;
            y1 = slope * (x1 - mid1._x) + mid1._y;
        } else {
            y1 = mid1._y + ydir * size * 0.5;
            x1 = (y1 - mid1._y) / slope + mid1._x;
        }
        return Point(x1, y1);
    }
    // Calculate the line that connecting two mids
    Line cut(Square other) {
        Point p1 = extend(middle(), other.middle(), _size);
        Point p2 = extend(middle(), other.middle(), -1 * _size);
        Point p3 = extend(other.middle(), middle(), other._size);
        Point p4 = extend(other.middle(), middle(), -1 * other._size);
        Point start = p1, end = p1;
        vector<Point> points = {p2, p3, p4};
        for (int i = 0;i < points.size(); ++i) {
            if (points[i]._x < start._x || (points[i]._x == start._x && points[i]._y < start._y)) {
                start = points[i];
            } else if (points[i]._x > end._x || (points[i]._x == end._x && points[i]._y > end._y)) {
                end = points[i];
            }
        }
        return Line(start, end);
    }
};