1 #include <iostream>  2 #include <string>  3 #include <cstdio>  4 #include <cstring>  5 #include <cmath>  6 #include <vector>  7 #include <algorithm>  8   9 using namespace std; 10  11 const double PI = acos(-1); 12  13 struct Point { 14     double x, y; 15     Point(double x = 0, double y = 0) : x(x), y(y) {} 16 }; 17  18 typedef Point Vector; 19 Vector operator + (const Vector &A, const Vector &B) { return Vector(A.x + B.x, A.y + B.y); } 20 Vector operator - (const Point &A, const Point &B) { return Vector(A.x - B.x, A.y - B.y); } 21 Vector operator * (const Vector &A, const double &p) { return Vector(A.x * p, A.y * p); } 22 Vector operator / (const Vector &A, const double &p) { return Vector(A.x / p, A.y / p); } 23 bool operator < (const Point &a, const Point &b) { return a.x < b.x || (a.x == b.x && a.y < b.y); } 24  25 const double eps = 1e-10; 26 int dcmp(double x) { 27     if(fabs(x) < eps) return 0; 28     else return x < 0 ? -1 : 1; 29 } 30  31 bool operator == (const Point &a, const Point &b) { return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0; } 32  33 double Dot(const Vector &A, const Vector &B) { return A.x * B.x + A.y * B.y; } 34 double Length(const Vector &A) { return sqrt(Dot(A, A)); } 35 double Angle(const Vector &A, const Vector &B) { return acos(Dot(A, B) / Length(A) / Length(B)); } 36  37 double Cross(const Vector &A, const Vector B) { return A.x * B.y - A.y * B.x; } 38 double Area2(const Point &A, const Point &B, const Point &C) { return Cross(B - A, C - A); } 39  40 Vector Rotate(const Vector &A, double rad) { return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad)); } 41  42 Vector Normal(const Vector &A) { 43     double L = Length(A); 44     return Vector(-A.y / L, A.x / L); 45 } 46  47 Point GetLineIntersection(const Point &P, const Vector &v, const Point &Q, const Vector &w) { 48     Vector u = P - Q; 49     double t = Cross(w, u) / Cross(v, w); 50     return P + v * t; 51 } 52  53 double DistanceToLine(const Point &P, const Point &A, const Point &B) { 54     Vector v1 = B - A, v2 = P - A; 55     return fabs(Cross(v1, v2)) / Length(v1); 56 } 57 double DistanceToLine_(const Point &P, const Point &A, const Point &B) { 58     Vector v1 = B - A, v2 = P - A; 59     return Cross(v1, v2) / Length(v1); 60 } 61 double DistanceToSegment(const Point &P, const Point &A, const Point &B) { 62     if(A == B) return Length(P - A); 63     Vector v1 = B - A, v2 = P - A, v3 = P - B; 64     if(dcmp(Dot(v1, v2)) < 0) return Length(v2); 65     else if(dcmp(Dot(v1, v3)) > 0) return Length(v3); 66     else return fabs(Cross(v1, v2)) / Length(v1); 67 } 68  69 Point GetLineProjection(const Point &P, const Point &A, const Point &B) { 70     Vector v = B - A; 71     return A + v * (Dot(v, P - A) / Dot(v, v)); 72 } 73  74 bool SegmentProperIntersection(const Point &a1, const Point &a2, const Point &b1, const Point &b2) { 75     double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1), c3 = Cross(b2 - b1, a1 - b1), c4 = Cross(b2 - b1, a2 - b1); 76     return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0; 77 } 78  79 bool OnSegment(const Point &p, const Point &a1, const Point &a2) { 80     return dcmp(Cross(a1 - p, a2 - p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) < 0; 81 } 82  83 double ConvexPolygonArea(Point *p, int n) { 84     double area = 0; 85     for(int i = 1; i < n - 1; ++i) area += Cross(p[i] - p[0], p[i + 1] - p[0]); 86     return area / 2; 87 } 88  89 double PolygonArea(Point *p, int n) { 90     double area = 0; 91  92     for(int i = 1; i < n - 1; ++i) area += Cross(p[i] - p[0], p[i + 1] - p[0]); 93     return area / 2; 94 } 95  96 struct Line { 97   Point p; 98   Vector v; 99   Line(Point p, Vector v):p(p),v(v) { }100   Point point(double t) {101     return p + v*t;102   }103   Line move(double d) {104     return Line(p + Normal(v)*d, v);105   }106 };107 108 Line getLine(double x1, double y1, double x2, double y2) {109   Point p1(x1,y1);110   Point p2(x2,y2);111   return Line(p1, p2-p1);112 }113 114 struct Circle {115     Point c;116     double r;117 118     Circle(Point c, double r) : c(c), r(r) {}119 120     Point point(const double &a) const {121         return Point(c.x + cos(a) * r, c.y + sin(a) * r);122     }123 };124 125 int getLineCircleIntersection(Line L, Circle C, double &t1, double &t2, vector<Point> &sol) {126     double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y - C.c.y;127     double e = a * a + c * c, f = 2 * (a * b + c * d), g = b * b + d * d - C.r * C.r;128     double delta = f * f - 4 * e * g;129     if(dcmp(delta) < 0) return 0;130     if(dcmp(delta) == 0) {131         t1 = t2 = -f / (2 * e);132         sol.push_back(L.point(t1));133         return 1;134     }135     t1 = (-f - sqrt(delta)) / (2 * e);136     sol.push_back(L.point(t1));137     t2 = (-f + sqrt(delta)) / (2 * e);138     sol.push_back(L.point(t2));139     return 2;140 }141 142 double angle(const Vector &v) { return atan2(v.y, v.x); }143 144 int getCircleCircleIntersection(Circle C1, Circle C2, vector<Point> &sol) {145     double d = Length(C1.c - C2.c);146     if(dcmp(d) == 0) {147         if(dcmp(C1.r - C2.r) == 0) return -1;148         return 0;149     }150     if(dcmp(C1.r + C2.r - d) < 0) return 0;151     if(dcmp(fabs(C1.r - C2.r) - d) > 0) return 0;152 153     double a = angle(C2.c - C1.c);154     double da = acos((C1.r * C1.r + d * d - C2.r * C2.r) / (2 * C1.r * d));155 156     Point p1 = C1.point(a - da), p2 = C1.point(a + da);157 158     sol.push_back(p1);159     if(p1 == p2) return 1;160     sol.push_back(p2);161     return 2;162 }163 164 int getTangents(Point p, Circle C, Vector *v) {165     Vector u = C.c - p;166     double dist = Length(u);167     if(dist < C.r) return 0;168     else if(dcmp(dist - C.r) == 0) {169 //        v[0] = Rotate(u, PI / 2);170         return 1;171     }172     else {173         double ang = asin(C.r / dist);174         v[0] = Rotate(u, -ang);175         v[1] = Rotate(u, +ang);176         return 2;177     }178 }179 180 int getTangents(Circle A, Circle B, Point *a, Point *b) {181     int cnt = 0;182     if(A.r < B.r) { swap(A, B); swap(a, b); }183     int d2 = (A.c.x - B.c.x) * (A.c.x - B.c.x) + (A.c.y - B.c.y) * (A.c.y - B.c.y);184     int rdiff = A.r - B.r;185     int rsum = A.r + B.r;186     if(d2 < rdiff * rdiff) return 0;187 188     double base = atan2(B.c.y - A.c.y, B.c.x - A.c.x);189     if(d2 == 0 && A.r == B.r) return -1;190     if(d2 == rdiff * rdiff) {191         a[cnt] = A.point(base);192         b[cnt] = B.point(base);193         ++cnt;194         return 1;195     }196     double ang = acos((A.r - B.r) / sqrt(d2));197     a[cnt] = A.point(base + ang);198     b[cnt] = B.point(base + ang);199     ++cnt;200     a[cnt] = A.point(base - ang);201     b[cnt] = B.point(base - ang);202     ++cnt;203     if(d2 == rsum * rsum) {204         a[cnt] = A.point(base);205         b[cnt] = B.point(PI + base);206         ++cnt;207     }208     else if(d2 > rsum * rsum) {209         double ang = acos((A.r + B.r) / sqrt(d2));210         a[cnt] = A.point(base + ang);211         b[cnt] = B.point(PI + base + ang);212         ++cnt;213         a[cnt] = A.point(base - ang);214         b[cnt] = B.point(PI + base - ang);215         ++cnt;216     }217     return cnt;218 }219 220 double torad(const double &deg) {221     return deg / 180 * PI;222 }223 224 void get_coord(const double &R, double lat, double lng, double &x, double &y, double &z) {225     lat = torad(lat);226     lng = torad(lng);227     x = R * cos(lat) * cos(lng);228     y = R * cos(lat) * sin(lng);229     z = R * sin(lat);230 }231 232 int ConvexHull(Point *p, int n, Point *ch) {233     sort(p, p + n);234     int m = 0;235     for(int i = 0; i < n; ++i) {236         while(m > 1 && Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]) <= 0) --m;237         ch[m++] = p[i];238     }239     int k = m;240     for(int i = n - 2; i >= 0; --i) {241         while(m > k && Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]) <= 0) --m;242         ch[m++] = p[i];243     }244     if(n > 1) --m;245     return m;246 }247 248 int  isPointInPolygon(Point p, Point *poly, int n) {249     int wn = 0;250     for(int i = 0;i < n; ++i) {251         if(OnSegment(p, poly[i], poly[(i+1)%n])) return -1;252         int k=dcmp(Cross(poly[(i+1)%n]-poly[i], p-poly[i]));253         int d1=dcmp(poly[i].y-p.y);254         int d2=dcmp(poly[(i+1)%n].y-p.y);255         if(k>0&&d1<=0&&d2>0) wn++;256         if(k<0&&d2<=0&&d1>0) wn--;257     }258     if(wn!=0)  return 1;259     else return 0;260 }261 262 Point read_point() {263     Point P;264     scanf("%lf%lf",&P.x,&P.y);265     return P;266 }267 268 int main() {269 270 }