MAXimal

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ: 11 Jun 2008 10:12
пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ: 20 Jun 2011 0:50

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ [пїЅпїЅпїЅпїЅпїЅпїЅ]

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ

пїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ $AB$ пїЅ $CD$ (пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅ). пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅ.

пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ (пїЅпїЅпїЅпїЅпїЅ) пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅ. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ.

пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ: пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ 'пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ'. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ $AB$ пїЅ $CD$ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ $A$ пїЅ $B$ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ $CD$ , пїЅ, пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅ $C$ пїЅ $D$ пїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ $AB$ . пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ.

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ-пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅ $X$ пїЅ $Y$ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ (пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ "пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ bounding box").

пїЅ пїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅ пїЅпїЅпїЅ, пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ (пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ), пїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅ пїЅпїЅпїЅ, пїЅпїЅпїЅ пїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ:

struct pt {
	int x, y;
};
пїЅ
inline int area (pt a, pt b, pt c) {
	return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
}
пїЅ
inline bool intersect_1 (int a, int b, int c, int d) {
	if (a > b)  swap (a, b);
	if (c > d)  swap (c, d);
	return max(a,c) <= min(b,d);
}
пїЅ
bool intersect (pt a, pt b, pt c, pt d) {
	return intersect_1 (a.x, b.x, c.x, d.x)
		&& intersect_1 (a.y, b.y, c.y, d.y)
		&& area(a,b,c) * area(a,b,d) <= 0
		&& area(c,d,a) * area(c,d,b) <= 0;
}

пїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ bounding box пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ "пїЅпїЅпїЅпїЅпїЅ" пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.

пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ (пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ $\rm area()$ , пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ).

пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ: пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ

пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ, пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ-пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ; пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅ $X$ пїЅ пїЅпїЅ пїЅпїЅпїЅ $Y$ .

пїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ, пїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ, пїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅ $X$ пїЅ $Y$ .

пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅ: пїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ (пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ).

пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ (пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ):

struct pt {
	int x, y;
};
пїЅ
const double EPS = 1E-9;
пїЅ
inline int det (int a, int b, int c, int d) {
	return a * d - b * c;
}
пїЅ
inline bool between (int a, int b, double c) {
	return min(a,b) <= c + EPS && c <= max(a,b) + EPS;
}
пїЅ
inline bool intersect_1 (int a, int b, int c, int d) {
	if (a > b)  swap (a, b);
	if (c > d)  swap (c, d);
	return max(a,c) <= min(b,d);
}
пїЅ
bool intersect (pt a, pt b, pt c, pt d) {
	int A1 = a.y-b.y,  B1 = b.x-a.x,  C1 = -A1*a.x - B1*a.y;
	int A2 = c.y-d.y,  B2 = d.x-c.x,  C2 = -A2*c.x - B2*c.y;
	int zn = det (A1, B1, A2, B2);
	if (zn != 0) {
		double x = - det (C1, B1, C2, B2) * 1. / zn;
		double y = - det (A1, C1, A2, C2) * 1. / zn;
		return between (a.x, b.x, x) && between (a.y, b.y, y)
			&& between (c.x, d.x, x) && between (c.y, d.y, y);
	}
	else
		return det (A1, C1, A2, C2) == 0 && det (B1, C1, B2, C2) == 0
			&& intersect_1 (a.x, b.x, c.x, d.x)
			&& intersect_1 (a.y, b.y, c.y, d.y);
}

пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ $\rm zn$ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅпїЅпїЅпїЅ ${\rm zn} = 0$ , пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ $A$ пїЅ $B$ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ. пїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅ, пїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ $C$ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ:

$\left|\matrix{ A_1 & C_1 \cr A_2 & C_2 }\right|, [...]$

пїЅпїЅпїЅпїЅ пїЅпїЅ ${\rm zn} \ne 0$ , пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ $(x,y)$ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.

пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ (пїЅ.пїЅ. пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ, пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ $a$ пїЅ $b$ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ), пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅ пїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅ пїЅпїЅпїЅпїЅпїЅпїЅпїЅпїЅ.

пїЅ