URAL 1062-Triathlon (semi-flat)

At first glance, this question seems very simple. Then I think u, v, and w cannot win if they are all smaller than others. Otherwise, they will win, however, this approach is half the same.

The conclusion that win is not true, but win's conclusion does not just exclude this condition.

List the conditions of this person and others

If all of them are win, x/v + y/u + (k-x-y)/w (I) is met) <x/v + y/u + (k-x-y)/w (j) Form n straight lines (half plane), and then calculate the intersection. If there is an intersection, yes, otherwise No

 

#include <stdio.h>   #include <math.h>   #include <algorithm>   using namespace std;  const double eps = 1e-8;    struct Point  {      double x,y;      Point(double x=0,double y=0):x(x),y(y) {}  };    typedef Point Vector;    Vector operator - (Point A, Point B)  {      return Vector(A.x-B.x, A.y-B.y);  }  struct Line  {      Point p;      Vector v;      double ang;      Line() {}      Line(Point p,Vector v):p(p),v(v)      {          ang=atan2(v.y,v.x);      }      bool operator < (const Line& L) const      {          return ang<L.ang;      }  };    double Cross(Vector A, Vector B)  {      return A.x*B.y - A.y*B.x;  }    bool Onleft(Line L, Point p)  {      return Cross(L.v, p-L.p)>0;  }    Point GetIntersection(Line a, Line b)  {      Vector u = a.p-b.p;      double t = Cross(b.v, u)/Cross(a.v, b.v);      return Point(a.p.x+a.v.x*t, a.p.y+a.v.y*t);  }    int BPMJ(Line *L, int n, Point *poly)  {      sort(L,L+n);      int first,last;      Point *p = new Point[n];      Line *q = new Line[n];      q[first=last=0] = L[0];      for(int i=1; i<n; i++)      {          while(first<last && !Onleft(L[i],p[last-1]))last--;          while(first<last && !Onleft(L[i],p[first]))first++;          q[++last] = L[i];          if(fabs(Cross(q[last].v,q[last-1].v))<eps)          {              last--;              if(Onleft(q[last], L[i].p))q[last] = L[i];          }          if(first<last) p[last-1] = GetIntersection(q[last-1], q[last]);      }      while(first<last && !Onleft(q[first], p[last-1])) last--;      if(last-first<=1)return 0;      p[last] = GetIntersection(q[last], q[first]);      int m = 0;      for(int i=first; i<=last; i++)          poly[m++] = p[i];      return m;  }    double k=10000.0;  int u[110],v[110],w[110];  Point poly[110];  Line L[110];    int main()  {      int n;      while(scanf("%d",&n)==1)      {          for(int i=0; i<n; i++)          {              scanf("%d%d%d",&u[i],&v[i],&w[i]);          }          for(int i=0; i<n; i++)          {              int f=0;              for(int j=0; j<n; j++)              {                  if(j!=i && u[i]<=u[j] && v[i]<=v[j] && w[i]<=w[j])                  {                      f=1;                      break;                  }              }              if(f==1)                  printf("No\n");              else              {                  Point p;                  int ct=0;                  for(int j=0; j<n; j++)                  {                      if(j!=i && u[i]>=u[j] && v[i]>=v[j] && w[i]>=w[j])                          continue;                      else if(j!=i)                      {                          double A=k/v[j]-k/v[i]-k/w[j]+k/w[i];                          double B=k/u[j]-k/u[i]-k/w[j]+k/w[i];                          double C=k/w[j]-k/w[i];                          if(fabs(A)>fabs(B))                              p=Point(-C/A,0);                          else                              p=Point(0,-C/B);                          Vector v(B,-A);                          L[ct++] = Line(p,v);                      }                  }                  L[ct++] = Line(Point(0,0), Vector(0,-1));                  L[ct++] = Line(Point(0,0), Vector(1,0));                  L[ct++] = Line(Point(0,1), Vector(-1,1));                  if(BPMJ(L,ct,poly))printf("Yes\n");                  else printf("No\n");              }          }      }      return 0;  }  #include <stdio.h>#include <math.h>#include <algorithm>using namespace std;const double eps = 1e-8;struct Point{    double x,y;    Point(double x=0,double y=0):x(x),y(y) {}};typedef Point Vector;Vector operator - (Point A, Point B){    return Vector(A.x-B.x, A.y-B.y);}struct Line{    Point p;    Vector v;    double ang;    Line() {}    Line(Point p,Vector v):p(p),v(v)    {        ang=atan2(v.y,v.x);    }    bool operator < (const Line& L) const    {        return ang<L.ang;    }};double Cross(Vector A, Vector B){    return A.x*B.y - A.y*B.x;}bool Onleft(Line L, Point p){    return Cross(L.v, p-L.p)>0;}Point GetIntersection(Line a, Line b){    Vector u = a.p-b.p;    double t = Cross(b.v, u)/Cross(a.v, b.v);    return Point(a.p.x+a.v.x*t, a.p.y+a.v.y*t);}int BPMJ(Line *L, int n, Point *poly){    sort(L,L+n);    int first,last;    Point *p = new Point[n];    Line *q = new Line[n];    q[first=last=0] = L[0];    for(int i=1; i<n; i++)    {        while(first<last && !Onleft(L[i],p[last-1]))last--;        while(first<last && !Onleft(L[i],p[first]))first++;        q[++last] = L[i];        if(fabs(Cross(q[last].v,q[last-1].v))<eps)        {            last--;            if(Onleft(q[last], L[i].p))q[last] = L[i];        }        if(first<last) p[last-1] = GetIntersection(q[last-1], q[last]);    }    while(first<last && !Onleft(q[first], p[last-1])) last--;    if(last-first<=1)return 0;    p[last] = GetIntersection(q[last], q[first]);    int m = 0;    for(int i=first; i<=last; i++)        poly[m++] = p[i];    return m;}double k=10000.0;int u[110],v[110],w[110];Point poly[110];Line L[110];int main(){    int n;    while(scanf("%d",&n)==1)    {        for(int i=0; i<n; i++)        {            scanf("%d%d%d",&u[i],&v[i],&w[i]);        }        for(int i=0; i<n; i++)        {            int f=0;            for(int j=0; j<n; j++)            {                if(j!=i && u[i]<=u[j] && v[i]<=v[j] && w[i]<=w[j])                {                    f=1;                    break;                }            }            if(f==1)                printf("No\n");            else            {                Point p;                int ct=0;                for(int j=0; j<n; j++)                {                    if(j!=i && u[i]>=u[j] && v[i]>=v[j] && w[i]>=w[j])                        continue;                    else if(j!=i)                    {                        double A=k/v[j]-k/v[i]-k/w[j]+k/w[i];                        double B=k/u[j]-k/u[i]-k/w[j]+k/w[i];                        double C=k/w[j]-k/w[i];                        if(fabs(A)>fabs(B))                            p=Point(-C/A,0);                        else                            p=Point(0,-C/B);                        Vector v(B,-A);                        L[ct++] = Line(p,v);                    }                }                L[ct++] = Line(Point(0,0), Vector(0,-1));                L[ct++] = Line(Point(0,0), Vector(1,0));                L[ct++] = Line(Point(0,1), Vector(-1,1));                if(BPMJ(L,ct,poly))printf("Yes\n");                else printf("No\n");            }        }    }    return 0;}