LA 2218 (半平面交) Triathlon

  1 //#define LOCAL
  2 #include <cstdio>
  3 #include <cstring>
  4 #include <algorithm>
  5 #include <cmath>
  6 #include <vector>
  7 using namespace std;
  8 
  9 const double eps = 1e-6;
 10 const int maxn = 100 + 10;
 11 int v[maxn], u[maxn], w[maxn];
 12 
 13 struct Point
 14 {
 15     double x, y;
 16     Point(double x=0, double y=0):x(x), y(y) {}
 17 };
 18 typedef Point Vector;
 19 Point operator + (Point a, Point b) { return Point(a.x+b.x, a.y+b.y); }
 20 Point operator - (Point a, Point b) { return Point(a.x-b.x, a.y-b.y); }
 21 Vector operator * (Vector a, double p) { return Vector(a.x*p, a.y*p); }
 22 Vector operator / (Vector a, double p) { return Vector(a.x/p, a.y/p); }
 23 bool operator < (const Point& a, const Point& b)
 24 { return a.x < b.x || (a.x == b.x && a.y < b.y); }
 25 bool operator == (const Point& a, const Point& b)
 26 { return a.x == b.x && a.y == b.y; }
 27 double Dot(const Vector& a, const Vector& b) { return a.x*b.x + a.y*b.y; }
 28 double Cross(const Vector& a, const Vector& b) { return a.x*b.y - a.y*b.x; }
 29 double Length(const Vector& a) { return sqrt(Dot(a, a)); }
 30 Vector Normal(const Vector& a)
 31 {
 32     double l = Length(a);
 33     return Vector(-a.y/l, a.x);
 34 }
 35 
 36 double PolygonArea(const vector<Point>& p)
 37 {
 38     int n = p.size();
 39     double ans = 0.0;
 40     for(int i = 1; i < n-1; ++i)
 41         ans += Cross(p[i]-p[0], p[i+1]-p[0]);    
 42     return ans/2;
 43 }
 44 
 45 struct Line
 46 {
 47     Point P;
 48     Vector v;
 49     double ang;
 50     Line() {}
 51     Line(Point p, Vector v):P(p), v(v) { ang = atan2(v.y, v.x); }
 52     bool operator < (const Line& L) const
 53     {
 54         return ang < L.ang;
 55     }
 56 };
 57 
 58 bool OnLeft(const Line& L, Point p)
 59 {
 60     return Cross(L.v, p-L.P) > 0;
 61 }
 62 
 63 Point GetLineIntersevtion(const Line& a, const Line& b)
 64 {
 65     Vector u = a.P - b.P;
 66     double t = Cross(b.v, u) / Cross(a.v, b.v);
 67     return a.P + a.v*t;
 68 }
 69 
 70 vector<Point> HalfplaneIntersection(vector<Line> L)
 71 {
 72     int n = L.size();
 73     sort(L.begin(), L.end());
 74 
 75     int first, last;
 76     vector<Point> p(n);
 77     vector<Line> q(n);
 78     vector<Point> ans;
 79 
 80     q[first=last=0] = L[0];
 81     for(int i = 1; i < n; ++i)
 82     {
 83         while(first < last && !OnLeft(L[i], p[last-1])) last--;
 84         while(first < last && !OnLeft(L[i], p[first])) first++;
 85         q[++last] = L[i];
 86         if(fabs(Cross(q[last].v, q[last-1].v)) < eps)
 87         {
 88             last--;
 89             if(OnLeft(q[last], L[i].P)) q[last] = L[i];
 90         }
 91         if(first < last) p[last-1] = GetLineIntersevtion(q[last-1], q[last]);
 92     }
 93     while(first < last && !OnLeft(q[first], p[last-1])) last--;
 94     if(last - first <= 1)    return ans;
 95     p[last] = GetLineIntersevtion(q[first], q[last]);
 96 
 97     for(int i = first; i <= last; ++i)    ans.push_back(p[i]);
 98     return ans;
 99 }
100 
101 int main(void)
102 {
103     #ifdef    LOCAL
104         freopen("2218in.txt", "r", stdin);
105     #endif
106     
107     int n;
108     while(scanf("%d", &n) == 1 && n)
109     {
110         for(int i = 0; i < n; ++i) scanf("%d%d%d", &v[i], &u[i], &w[i]);
111         for(int i = 0; i < n; ++i)
112         {
113             int ok = 1;
114             double k = 10000;
115             vector<Line> L;
116             for(int j = 0; j < n; ++j) if(j != i)
117             {
118                 if(v[i]<=v[j] && u[i]<=u[j] && w[i]<=w[j]) { ok = 0; break; }
119                 if(v[i]>v[j] && u[i]>u[j] && w[i]>w[j]) continue;
120 
121                 double a = (k/v[j]-k/v[i]+k/w[i]-k/w[j]);
122                 double b = (k/u[j]-k/u[i]+k/w[i]-k/w[j]);
123                 double c = k/w[j]-k/w[i];
124                 //L.push_back(Line(Point(0, -c/b), Vector(b, -a)));
125                 Point P;
126                 Vector V(b, -a);
127                 if(fabs(a) > fabs(b))    P = Point(-c/a, 0);
128                 else P = Point(0, -c/b);
129                 L.push_back(Line(P, V));
130             }
131             if(ok)
132             {
133                 L.push_back(Line(Point(0, 0), Vector(0, -1)));
134                 L.push_back(Line(Point(0, 0), Vector(1, 0)));
135                 L.push_back(Line(Point(0, 1), Vector(-1, 1)));
136                 vector<Point> Poly = HalfplaneIntersection(L);
137                 if(Poly.empty()) ok = 0;
138             }
139             if(ok) puts("Yes"); else puts("No");
140         }
141     }
142 
143     return 0;
144 }