[CodeForces-606E] Freelancer's Dreams 凸包 模型转换

　　大致题意：

　　　　有一个人想要获得p个经验点和q元钱。现在给出n份工作，每份工作每天能得到Ai的经验值和Bi的钱，问最少需要工作多少天，

　　　　能使得总经验值>=p，总钱>=q。

　　

　　　　先对给出的n份工作以及原点O(0,0)，x轴的最大点(maxx,0)，y轴最大点(0,maxy)构建凸包，根据凸组合，可知凸包上所有得点以

　　　　及凸包边上的点都可以由一天时间得到，那么只要求出射线O~P(p,q)与凸包的交点，即可求出最后的结果。

　　　　

 #include<cstdio>
 #include<iostream>
 #include<cstring>
 #include<algorithm>
 #include<queue>
 #include<set>
 #include<map>
 #include<stack>
 #include<time.h>
 #include<cstdlib>
 #include<cmath>
 #include<list>
 using namespace std;
 #define MAXN 200100
 #define eps 1e-5
 #define For(i,a,b) for(int i=a;i<=b;i++)
 #define Fore(i,a,b) for(int i=a;i>=b;i--)
 #define lson l,mid,rt<<1
 #define rson mid+1,r,rt<<1|1
 #define mkp make_pair
 #define pb push_back
 #define cr clear()
 #define sz size()
 #define met(a,b) memset(a,b,sizeof(a))
 #define iossy ios::sync_with_stdio(false)
 #define fre freopen
 #define pi acos(-1.0)
 #define inf 1e9+9
 #define Vector Point
 const int Mod=1e9+;
 typedef unsigned long long ull;
 typedef long long ll;
 typedef pair<int,int> pii;
 typedef pair<ll,ll> pll;
 int dcmp(double x){
     if(fabs(x)<=eps) return ;
     return x<?-:;
 }
 struct Point {
     double x,y;
     int id;
     int pre,nxt;
     Point(double x=,double y=) : x(x),y(y) {}
     Point operator - (const Point &a)const{ return Point(x-a.x,y-a.y); }
     Point operator + (const Point &a)const{ return Point(x+a.x,y+a.y); }
     Point operator * (const double &a)const{ return Point(x*a,y*a); }
     Point operator / (const double &a)const{ return Point(x/a,y/a); }
     bool operator < (const Point &a)const{    if(x==a.x) return y<a.y;return x<a.x; }
     bool operator == (const Point &a)const{ return dcmp(x-a.x)== && dcmp(y-a.y)==; }
     void read(int iid=) { scanf("%lf%lf",&x,&y);id=iid; }
     void out(){cout<<"Bug: "<<x<<" "<<y<<endl;}
 };
 inline double Cross(Vector a,Vector b) { return a.x*b.y-a.y*b.x; }
 inline double Dot(Vector a,Vector b) { return a.x*b.x+a.y*b.y; }
 inline double dis(Vector a) { return sqrt(Dot(a,a)); }
 int ConvexHull(Point *p,int n,Point *ch){
     int m=;
     sort(p,p+n);
     For(i,,n-){
         p[i].id=i;
         while(m> && Cross(ch[m-]-ch[m-],p[i]-ch[m-])<=) m--;
         ch[m++]=p[i];
     }
     int k=m;
     Fore(i,n-,){
         while(m>k && Cross(ch[m-]-ch[m-],p[i]-ch[m-])<=) m--;
         ch[m++]=p[i];
     }
     if(n>) m--;
     return m;
 }
 inline bool Onsegment(Point a,Point b1,Point b2){
     return dcmp(Cross(b1-a,b2-a))== && dcmp(Dot(b1-a,b2-a))<;
 }
 bool Intersect_Segm_Ray(Point a1,Vector u,Point b1,Point b2){
     double c1=Cross(b1-a1,u),c2=Cross(b2-a1,u);
     if(dcmp(c2)*dcmp(c1)>) return ;
     if(dcmp(c2)*dcmp(c1)<){
         c1=Dot(b1-a1,u);c2=Dot(b2-a1,u);
         return dcmp(c1)>= && dcmp(c2)>=;
     }
     if(c1==) return dcmp(Dot(b1-a1,u))>;
     if(c2==) return dcmp(Dot(b2-a1,u))>;
 }
 Point Intersect_Line_Point(Point p,Vector u,Point q,Vector v){
     Vector w=p-q;
     double t=Cross(v,w)/Cross(u,v);
     return p+u*t;
 }
 int n;
 double maxx,maxy;
 Point p[MAXN],cp;
 Point ch[MAXN];
 int solve(){
     double ans=inf;maxx=;maxy=;
     cin>>n;cp.read();
     For(i,,n-) p[i].read(),maxx=max(p[i].x,maxx),maxy=max(p[i].y,maxy);
     p[n]=Point(,);
     p[n+]=Point(,maxy);
     p[n+]=Point(maxx,);
     int m=ConvexHull(p,n+,ch);
     For(i,,m-){
         if(ch[i]==Point(,) || ch[(i+)%m]==Point(,)) continue;
         if(Intersect_Segm_Ray(Point(,),cp,ch[(i+)%m],ch[i])){
             Point st=Intersect_Line_Point(cp,cp,ch[i],ch[(i+)%m]-ch[i]);
             ans=min(ans,dis(cp)/dis(st));
         }
     }
     printf("%.15lf\n",ans);
 }
 int main(){
 //  fre("in.txt","r",stdin);
     int t=;
     while(t--)solve();
     return ;
 }