uva 11595 - Crossing Streets EXTREME（切割多边形）

题目链接：uva 11595 - Crossing Streets EXTREME

对初始平面进行切割，得到所有平面，然后处理出所有边，有公共边的两个平面之间可以到达，对于城市的权值可以加到点上，进出各加一次即可。

#include <cstdio>
#include <cstring>
#include <cmath>
#include <queue>
#include <vector>
#include <complex>
#include <algorithm>

using namespace std;
typedef pair<int,int> pii;
const double pi = 4 * atan(1);
const double eps = 1e-3;

inline int dcmp (double x) { if (fabs(x) < eps) return 0; else return x < 0 ? -1 : 1; }
inline double getDistance (double x, double y) { return sqrt(x * x + y * y); }
inline double torad(double deg) { return deg / 180 * pi; }

struct Point {
	double x, y;
	Point (double x = 0, double y = 0): x(x), y(y) {}
	void read () { scanf("%lf%lf", &x, &y); }
	void write () { printf("%lf %lf", x, y); }

	bool operator == (const Point& u) const { return dcmp(x - u.x) == 0 && dcmp(y - u.y) == 0; }
	bool operator != (const Point& u) const { return !(*this == u); }
	bool operator < (const Point& u) const { return dcmp(x - u.x) < 0 || (dcmp(x-u.x)==0 && dcmp(y-u.y) < 0); }
	bool operator > (const Point& u) const { return u < *this; }
	bool operator <= (const Point& u) const { return *this < u || *this == u; }
	bool operator >= (const Point& u) const { return *this > u || *this == u; }
	Point operator + (const Point& u) { return Point(x + u.x, y + u.y); }
	Point operator - (const Point& u) { return Point(x - u.x, y - u.y); }
	Point operator * (const double u) { return Point(x * u, y * u); }
	Point operator / (const double u) { return Point(x / u, y / u); }
	double operator * (const Point& u) { return x*u.y - y*u.x; }
};
typedef Point Vector;
typedef vector<Point> Polygon;

struct Line {
	double a, b, c;
	Line (double a = 0, double b = 0, double c = 0): a(a), b(b), c(c) {}
};

struct DirLine {
	Point p;
	Vector v;
	double ang;
	DirLine () {}
	DirLine (Point p, Vector v): p(p), v(v) { ang = atan2(v.y, v.x); }
	bool operator < (const DirLine& u) const { return ang < u.ang; }
};

struct Circle {
	Point o;
	double r;
	Circle () {}
	Circle (Point o, double r = 0): o(o), r(r) {}
	void read () { o.read(), scanf("%lf", &r); }
	Point point(double rad) { return Point(o.x + cos(rad)*r, o.y + sin(rad)*r); }
	double getArea (double rad) { return rad * r * r / 2; }
};


namespace Punctual {
	double getDistance (Point a, Point b) { double x=a.x-b.x, y=a.y-b.y; return sqrt(x*x + y*y); }
};


namespace Vectorial {
	/* 点积: 两向量长度的乘积再乘上它们夹角的余弦, 夹角大于90度时点积为负 */
	double getDot (Vector a, Vector b) { return a.x * b.x + a.y * b.y; }

	/* 叉积: 叉积等于两向量组成的三角形有向面积的两倍, cross(v, w) = -cross(w, v) */
	double getCross (Vector a, Vector b) { return a.x * b.y - a.y * b.x; }

	double getLength (Vector a) { return sqrt(getDot(a, a)); }
	double getPLength (Vector a) { return getDot(a, a); }
	double getAngle (Vector u) { return atan2(u.y, u.x); }
	double getAngle (Vector a, Vector b) { return acos(getDot(a, b) / getLength(a) / getLength(b)); }
	Vector rotate (Vector a, double rad) { return Vector(a.x*cos(rad)-a.y*sin(rad), a.x*sin(rad)+a.y*cos(rad)); }
	/* 单位法线 */
	Vector getNormal (Vector a) { double l = getLength(a); return Vector(-a.y/l, a.x/l); }
};

namespace ComplexVector {
	typedef complex<double> Point;
	typedef Point Vector;

	double getDot(Vector a, Vector b) { return real(conj(a)*b); }
	double getCross(Vector a, Vector b) { return imag(conj(a)*b); }
	Vector rotate(Vector a, double rad) { return a*exp(Point(0, rad)); }
};

namespace Linear {
	using namespace Vectorial;

	Line getLine (double x1, double y1, double x2, double y2) { return Line(y2-y1, x1-x2, y1*x2-x1*y2); }
	Line getLine (double a, double b, Point u) { return Line(a, -b, u.y * b - u.x * a); }

	bool getIntersection (Line p, Line q, Point& o) {
		if (fabs(p.a * q.b - q.a * p.b) < eps)
			return false;
		o.x = (q.c * p.b - p.c * q.b) / (p.a * q.b - q.a * p.b);
		o.y = (q.c * p.a - p.c * q.a) / (p.b * q.a - q.b * p.a);
		return true;
	}

	/* 直线pv和直线qw的交点 */
	bool getIntersection (Point p, Vector v, Point q, Vector w, Point& o) {
		if (dcmp(getCross(v, w)) == 0) return false;
		Vector u = p - q;
		double k = getCross(w, u) / getCross(v, w);
		o = p + v * k;
		return true;
	}

	/* 点p到直线ab的距离 */
	double getDistanceToLine (Point p, Point a, Point b) { return fabs(getCross(b-a, p-a) / getLength(b-a)); }
	double getDistanceToSegment (Point p, Point a, Point b) {
		if (a == b) return getLength(p-a);
		Vector v1 = b - a, v2 = p - a, v3 = p - b;
		if (dcmp(getDot(v1, v2)) < 0) return getLength(v2);
		else if (dcmp(getDot(v1, v3)) > 0) return getLength(v3);
		else return fabs(getCross(v1, v2) / getLength(v1));
	}

	/* 点p在直线ab上的投影 */
	Point getPointToLine (Point p, Point a, Point b) { Vector v = b-a; return a+v*(getDot(v, p-a) / getDot(v,v)); }

	/* 判断线段是否存在交点 */
	bool haveIntersection (Point a1, Point a2, Point b1, Point b2) {
		double c1=getCross(a2-a1, b1-a1), c2=getCross(a2-a1, b2-a1), c3=getCross(b2-b1, a1-b1), c4=getCross(b2-b1,a2-b1);
		return dcmp(c1)*dcmp(c2) < 0 && dcmp(c3)*dcmp(c4) < 0;
	}

	/* 判断点是否在线段上 */
	bool onSegment (Point p, Point a, Point b) { return dcmp(getCross(a-p, b-p)) == 0 && dcmp(getDot(a-p, b-p)) < 0; }
	bool onLeft(DirLine l, Point p) { return dcmp(l.v * (p-l.p)) >= 0; }
}

namespace Triangular {
	using namespace Vectorial;

	double getAngle (double a, double b, double c) { return acos((a*a+b*b-c*c) / (2*a*b)); }
	double getArea (double a, double b, double c) { double s =(a+b+c)/2; return sqrt(s*(s-a)*(s-b)*(s-c)); }
	double getArea (double a, double h) { return a * h / 2; }
	double getArea (Point a, Point b, Point c) { return fabs(getCross(b - a, c - a)) / 2; }
	double getDirArea (Point a, Point b, Point c) { return getCross(b - a, c - a) / 2; }
};

namespace Polygonal {
	using namespace Vectorial;
	using namespace Linear;

	double getArea (Point* p, int n) {
		double ret = 0;
		for (int i = 0; i < n-1; i++)
			ret += (p[i]-p[0]) * (p[i+1]-p[0]);
		return ret/2;
	}

	/* 凸包 */
	int getConvexHull (Point* p, int n, Point* ch) {
		sort(p, p + n);
		int m = 0;
		for (int i = 0; i < n; i++) {
			/* 可共线 */
			//while (m > 1 && dcmp(getCross(ch[m-1]-ch[m-2], p[i]-ch[m-1])) < 0) m--;
			while (m > 1 && dcmp(getCross(ch[m-1]-ch[m-2], p[i]-ch[m-1])) <= 0) m--;
			ch[m++] = p[i];
		}
		int k = m;
		for (int i = n-2; i >= 0; i--) {
			/* 可共线 */
			//while (m > k && dcmp(getCross(ch[m-1]-ch[m-2], p[i]-ch[m-2])) < 0) m--;
			while (m > k && dcmp(getCross(ch[m-1]-ch[m-2], p[i]-ch[m-2])) <= 0) m--;
			ch[m++] = p[i];
		}
		if (n > 1) m--;
		return m;
	}

	int isPointInPolygon (Point o, Point* p, int n) {
		int wn = 0;
		for (int i = 0; i < n; i++) {
			int j = (i + 1) % n;
			if (onSegment(o, p[i], p[j]) || o == p[i]) return 0; // 边界上
			int k = dcmp(getCross(p[j] - p[i], o-p[i]));
			int d1 = dcmp(p[i].y - o.y);
			int d2 = dcmp(p[j].y - o.y);
			if (k > 0 && d1 <= 0 && d2 > 0) wn++;
			if (k < 0 && d2 <= 0 && d1 > 0) wn--;
		}
		return wn ? -1 : 1;
	}

	/* 旋转卡壳 */
	void rotatingCalipers(Point *p, int n, vector<pii>& sol) {
		sol.clear();
		int j = 1; p[n] = p[0];
		for (int i = 0; i < n; i++) {
			while (getCross(p[j+1]-p[i+1], p[i]-p[i+1]) > getCross(p[j]-p[i+1], p[i]-p[i+1]))
				j = (j+1) % n;
			sol.push_back(make_pair(i, j));
			sol.push_back(make_pair(i + 1, j + 1));
		}
	}

	void rotatingCalipersGetRectangle (Point *p, int n, double& area, double& perimeter) {
		p[n] = p[0];
		int l = 1, r = 1, j = 1;
		area = perimeter = 1e20;

		for (int i = 0; i < n; i++) {
			Vector v = (p[i+1]-p[i]) / getLength(p[i+1]-p[i]);
			while (dcmp(getDot(v, p[r%n]-p[i]) - getDot(v, p[(r+1)%n]-p[i])) < 0) r++;
			while (j < r || dcmp(getCross(v, p[j%n]-p[i]) - getCross(v,p[(j+1)%n]-p[i])) < 0) j++;
			while (l < j || dcmp(getDot(v, p[l%n]-p[i]) - getDot(v, p[(l+1)%n]-p[i])) > 0) l++;
			double w = getDot(v, p[r%n]-p[i])-getDot(v, p[l%n]-p[i]);
			double h = getDistanceToLine (p[j%n], p[i], p[i+1]);
			area = min(area, w * h);
			perimeter = min(perimeter, 2 * w + 2 * h);
		}
	}

	/* 计算半平面相交可以用增量法，o(n^2)，初始设置4条无穷大的半平面 */
	/* 用有向直线A->B切割多边形u，返回左侧。可能退化成单点或线段 */
	Polygon cutPolygon (Polygon u, Point a, Point b) {
		Polygon ret;
		int n = u.size();
		for (int i = 0; i < n; i++) {
			Point c = u[i], d = u[(i+1)%n];
			if (dcmp((b-a)*(c-a)) >= 0) ret.push_back(c);
			if (dcmp((b-a)*(c-d)) != 0) {
				Point t;
				getIntersection(a, b-a, c, d-c, t);
				if (onSegment(t, c, d))
					ret.push_back(t);
			}
		}
		return ret;
	}

	/* 半平面相交 */
	int halfPlaneIntersection(DirLine* li, int n, Point* poly) {
		sort(li, li + n);

		int first, last;
		Point* p = new Point[n];
		DirLine* q = new DirLine[n];
		q[first=last=0] = li[0];

		for (int i = 1; i < n; i++) {
			while (first < last && !onLeft(li[i], p[last-1])) last--;
			while (first < last && !onLeft(li[i], p[first])) first++;
			q[++last] = li[i];

			if (dcmp(q[last].v * q[last-1].v) == 0) {
				last--;
				if (onLeft(q[last], li[i].p)) q[last] = li[i];
			}

			if (first < last)
				getIntersection(q[last-1].p, q[last-1].v, q[last].p, q[last].v, p[last-1]);
		}

		while (first < last && !onLeft(q[first], p[last-1])) last--;
		if (last - first <= 1) { delete [] p; delete [] q; return 0; }
		getIntersection(q[last].p, q[last].v, q[first].p, q[first].v, p[last]);

		int m = 0;
		for (int i = first; i <= last; i++) poly[m++] = p[i];
		delete [] p; delete [] q;
		return m;
	}

	/* 去除多边形共线点 */
	Polygon simplify (const Polygon& poly) {
		Polygon ret;
		int n = poly.size();
		for (int i = 0; i < n; i++) {
			Point a = poly[i];
			Point b = poly[(i+1)%n];
			Point c = poly[(i+2)%n];
			if (dcmp((b-a)*(c-b)) != 0 && (ret.size() == 0 || b != ret[ret.size()-1]))
				ret.push_back(b);
		}
		return ret;
	}
};

namespace Circular {
	using namespace Linear;
	using namespace Vectorial;
	using namespace Triangular;

	/* 直线和原的交点 */
	int getLineCircleIntersection (Point p, Point q, Circle O, double& t1, double& t2, vector<Point>& sol) {
		Vector v = q - p;
		/* 使用前需清空sol */
		//sol.clear();
		double a = v.x, b = p.x - O.o.x, c = v.y, d = p.y - O.o.y;
		double e = a*a+c*c, f = 2*(a*b+c*d), g = b*b+d*d-O.r*O.r;
		double delta = f*f - 4*e*g;
		if (dcmp(delta) < 0) return 0;
		if (dcmp(delta) == 0) {
			t1 = t2 = -f / (2 * e);
			sol.push_back(p + v * t1);
			return 1;
		}

		t1 = (-f - sqrt(delta)) / (2 * e); sol.push_back(p + v * t1);
		t2 = (-f + sqrt(delta)) / (2 * e); sol.push_back(p + v * t2);
		return 2;
	}

	/* 圆和圆的交点 */
	int getCircleCircleIntersection (Circle o1, Circle o2, vector<Point>& sol) {
		double d = getLength(o1.o - o2.o);

		if (dcmp(d) == 0) {
			if (dcmp(o1.r - o2.r) == 0) return -1;
			return 0;
		}

		if (dcmp(o1.r + o2.r - d) < 0) return 0;
		if (dcmp(fabs(o1.r-o2.r) - d) > 0) return 0;

		double a = getAngle(o2.o - o1.o);
		double da = acos((o1.r*o1.r + d*d - o2.r*o2.r) / (2*o1.r*d));

		Point p1 = o1.point(a-da), p2 = o1.point(a+da);

		sol.push_back(p1);
		if (p1 == p2) return 1;
		sol.push_back(p2);
		return 2;
	}

	/* 过定点作圆的切线 */
	int getTangents (Point p, Circle o, Vector* v) {
		Vector u = o.o - p;
		double d = getLength(u);
		if (d < o.r) return 0;
		else if (dcmp(d - o.r) == 0) {
			v[0] = rotate(u, pi / 2);
			return 1;
		} else {
			double ang = asin(o.r / d);
			v[0] = rotate(u, -ang);
			v[1] = rotate(u, ang);
			return 2;
		}
	}

	/* a[i] 和 b[i] 分别是第i条切线在O1和O2上的切点 */
	/* have some problems */
	int getTangents (Circle o1, Circle o2, Point* a, Point* b) {
		int cnt = 0;
		if (o1.r < o2.r) { swap(o1, o2); swap(a, b); }
		double d2 = getLength(o1.o - o2.o); d2 = d2 * d2;
		double rdif = o1.r - o2.r, rsum = o1.r + o2.r;
		if (d2 < rdif * rdif) return 0;
		if (dcmp(d2) == 0 && dcmp(o1.r - o2.r) == 0) return -1;

		double base = getAngle(o2.o - o1.o);
		if (dcmp(d2 - rdif * rdif) == 0) {
			a[cnt] = o1.point(base); b[cnt] = o2.point(base); cnt++;
			return cnt;
		}

		double ang = acos( rdif / sqrt(d2) );
		a[cnt] = o1.point(base+ang); b[cnt] = o2.point(base+ang); cnt++;
		a[cnt] = o1.point(base-ang); b[cnt] = o2.point(base-ang); cnt++;

		if (dcmp(d2 - rsum * rsum) == 0) {
			a[cnt] = o1.point(base); b[cnt] = o2.point(base); cnt++;
		} else if (d2 > rsum * rsum) {
			double ang = acos( rsum / sqrt(d2) );
			a[cnt] = o1.point(base+ang); b[cnt] = o2.point(pi+base+ang); cnt++;
			a[cnt] = o1.point(base-ang); b[cnt] = o2.point(pi+base-ang); cnt++;
		}
		return cnt;
	}

	/* 三点确定外切圆 */
	Circle CircumscribedCircle(Point p1, Point p2, Point p3) {  
		double Bx = p2.x - p1.x, By = p2.y - p1.y;  
		double Cx = p3.x - p1.x, Cy = p3.y - p1.y;  
		double D = 2 * (Bx * Cy - By * Cx);  
		double cx = (Cy * (Bx * Bx + By * By) - By * (Cx * Cx + Cy * Cy)) / D + p1.x;  
		double cy = (Bx * (Cx * Cx + Cy * Cy) - Cx * (Bx * Bx + By * By)) / D + p1.y;  
		Point p = Point(cx, cy);  
		return Circle(p, getLength(p1 - p));  
	}

	/* 三点确定内切圆 */
	Circle InscribedCircle(Point p1, Point p2, Point p3) {  
		double a = getLength(p2 - p3);  
		double b = getLength(p3 - p1);  
		double c = getLength(p1 - p2);  
		Point p = (p1 * a + p2 * b + p3 * c) / (a + b + c);  
		return Circle(p, getDistanceToLine(p, p1, p2));  
	} 

	/* 三角形一顶点为圆心 */
	double getPublicAreaToTriangle (Circle O, Point a, Point b) {
		if (dcmp((a-O.o)*(b-O.o)) == 0) return 0;
		int sig = 1;
		double da = getPLength(O.o-a), db = getPLength(O.o-b);
		if (dcmp(da-db) > 0) {
			swap(da, db);
			swap(a, b);
			sig = -1;
		}

		double t1, t2;
		vector<Point> sol;
		int n = getLineCircleIntersection(a, b, O, t1, t2, sol);

		if (dcmp(da-O.r*O.r) <= 0) {
			if (dcmp(db-O.r*O.r) <= 0)	return getDirArea(O.o, a, b) * sig;

			int k = 0;
			if (getPLength(sol[0]-b) > getPLength(sol[1]-b)) k = 1;

			double ret = getArea(O.o, a, sol[k]) + O.getArea(getAngle(sol[k]-O.o, b-O.o));
			double tmp = (a-O.o)*(b-O.o);
			return ret * sig * dcmp(tmp);
		}

		double d = getDistanceToSegment(O.o, a, b);
		if (dcmp(d-O.r) >= 0) {
			double ret = O.getArea(getAngle(a-O.o, b-O.o));
			double tmp = (a-O.o)*(b-O.o);
			return ret * sig * dcmp(tmp);
		}


		double k1 = O.r / getLength(a - O.o), k2 = O.r / getLength(b - O.o);
		Point p = O.o + (a - O.o) * k1, q = O.o + (b - O.o) * k2;
		double ret1 = O.getArea(getAngle(p-O.o, q-O.o));
		double ret2 = O.getArea(getAngle(sol[0]-O.o, sol[1]-O.o)) - getArea(O.o, sol[0], sol[1]);
		double ret = (ret1 - ret2), tmp = (a-O.o)*(b-O.o);
		return ret * sig * dcmp(tmp);
	}

	double getPublicAreaToPolygon (Circle O, Point* p, int n) {
		if (dcmp(O.r) == 0) return 0;
		double area = 0;
		for (int i = 0; i < n; i++) {
			int u = (i + 1) % n;
			area += getPublicAreaToTriangle(O, p[i], p[u]);
		}
		return fabs(area);
	}
};

using namespace Polygonal;
const int maxn = 1005;
const double inf = 1e6;

struct Edge {
	int be;
	Point a, b;
	Edge () {}
	Edge (Point a, Point b, int be): a(a), b(b), be(be) {}
	bool operator < (const Edge& u) const { return a < u.a || (a == u.a && b < u.b); }
	bool operator == (const Edge& u) const { return !((*this)<u || u<(*this)); }
};

int N, C, Q, W[maxn], D[maxn], vis[maxn];
vector<Edge> T;
vector<int> G[maxn];
vector<Polygon> faces, newfaces;

int isPointInPolygon (Point o, Polygon p) {
	int wn = 0, n = p.size();
	for (int i = 0; i < n; i++) {
		int j = (i + 1) % n;
		if (onSegment(o, p[i], p[j]) || o == p[i]) return 0; // 边界上
		int k = dcmp(getCross(p[j] - p[i], o-p[i]));
		int d1 = dcmp(p[i].y - o.y);
		int d2 = dcmp(p[j].y - o.y);
		if (k > 0 && d1 <= 0 && d2 > 0) wn++;
		if (k < 0 && d2 <= 0 && d1 > 0) wn--;
	}
	return wn ? -1 : 1;
}


void addEdge (Point a, Point b, int idx) {
	if (a > b) swap(a, b);
	T.push_back(Edge(a, b, idx));
}

int find (Point t) {
	for (int j = 0; j < N; j++) {
		if (isPointInPolygon (t, faces[j]) <= 0) return j;
	}
	return -1;
}

void build () {
	T.clear();
	N = faces.size();

	for (int i = 0; i < N; i++) {
		G[i].clear();
		int k = faces[i].size();
		//	printf("%d:%d\n", i, k);
		for (int j = 0; j < k; j++)
			addEdge(faces[i][j], faces[i][(j+1)%k], i);
	}
	//printf("%lu!!!!\n", T.size());

	sort(T.begin(), T.end());
	for (int i = 1; i < T.size(); i++) {
		if (T[i-1] == T[i]) {
			G[T[i-1].be].push_back(T[i].be);
			G[T[i].be].push_back(T[i-1].be);
		}
	}
}

void init () {
	Polygon cur;
	cur.push_back(Point(-inf, -inf));
	cur.push_back(Point(inf, -inf));
	cur.push_back(Point(inf, inf));
	cur.push_back(Point(-inf, inf));

	faces.clear();
	faces.push_back(cur);

	Point ca, cb;
	double a, b, c;
	for (int i = 0; i < N; i++) {
		scanf("%lf%lf%lf", &a, &b, &c);
		while (dcmp(b) == 0 && dcmp(a) == 0);

		if (dcmp(a)) {
			ca = Point((b+c)/(-a), 1);
			cb = Point((-b+c)/(-a), -1);
		} else {
			ca = Point(1, (a+c)/(-b));
			cb = Point(-1, (-a+c)/(-b));
		}

		//	printf("sum:%lu\n", faces.size());

		newfaces.clear();
		for (int j = 0; j < faces.size(); j++) {
			Polygon left = cutPolygon(faces[j], ca, cb);
			Polygon right = cutPolygon(faces[j], cb, ca);

			/*
			   ca.write(), printf(" ");
			   cb.write(), printf("\n");
			   for (int t = 0; t < faces[j].size(); t++)
			   printf("%lf %lf\n", faces[j][t].x, faces[j][t].y);
			   printf("left:%lu, right:%lu\n", left.size(), right.size());
			   printf("\n");
			   */

			if (left.size() >= 3) newfaces.push_back(left);
			if (right.size() >= 3) newfaces.push_back(right);
		}
		faces = newfaces;
	}

	build ();

	int x, y, value;
	memset(W, 0, sizeof(W));
	for (int i = 0; i < C; i++) {
		scanf("%d%d%d", &x, &y, &value);
		int k = find(Point(x, y));
		//	printf("%d\n", k);
		W[k] += value;
	}
}

int bfs (int s, int e) {
	//printf("%d %d\n", s, e);
	memset(D, -1, sizeof(D));
	memset(vis, 0, sizeof(vis));
	queue<int> que;

	que.push(s);
	D[s] = 0;
	vis[s] = 1;

	/*
	   for (int i = 0; i < N; i++) {
	   printf("%d %d %lu:", i, W[i], faces[i].size());
	   for (int j = 0; j < G[i].size(); j++)
	   printf(" %d", G[i][j]);
	   printf("\n");
	   }
	   */

	while (!que.empty()) {
		int u = que.front();
		que.pop();
		vis[u] = 0;
		for (int i = 0; i < G[u].size(); i++) {
			int v = G[u][i];
			if (D[v] == -1 || D[v] > D[u] + 1 + W[v] + W[u]) {
				D[v] = D[u] + 1 + W[v] + W[u];
				if (vis[v] == 0) {
					que.push(v);
					vis[v] = 1;
				}
			}
		}
	}
	return D[e];
}

int main () {
	int cas = 1;
	while (scanf("%d%d%d", &N, &C, &Q) == 3 && N + C + Q) {
		init();

		printf("Case %d:\n", cas++);
		Point s, e;
		while (Q--) {
			s.read(), e.read();
			printf("%d\n", bfs(find(s), find(e)));
		}
	}
	return 0;
}