Gym101635K Blowing Candles

题目链接：http://codeforces.com/gym/101635

题目大意：

　　推荐一篇文章：https://blog.csdn.net/wang_heng199/article/details/74477738

　　该题就是要求凸包的宽度（即平行切线间的最小距离）。

AC代码：

 #include <bits/stdc++.h>

 using namespace std;
 const double inf = 2e9;
 const double esp = 1e-;
 int sgn(double x){
     if(fabs(x)<esp) return ;
     if(x<) return -;
     else    return ;
 }
 struct Point{
     double x,y;
     Point (double _x=,double _y=){
         x=_x,y=_y;
     }
     Point operator - (const Point &b) const{
         return Point(x-b.x,y-b.y);
     }
     double operator ^ (const Point &b) const {
         return x*b.y-y*b.x;
     }
     double operator * (const Point &b) const {
         return x*b.x+y*b.y;
     }
     void input(){
         scanf("%lf%lf",&x,&y);
     }
 };
 double dist(Point a,Point b){
     return sqrt((a-b)*(a-b));
 }
 const int maxn = 2e5+;
 Point List[maxn];
 int Stack[maxn],top;
 bool _cmp(Point p1,Point p2){
     double tmp=(p1-List[])^(p2-List[]);
     if(sgn(tmp)>)   return true;
     else if(sgn(tmp)== && sgn(dist(p1,List[])-dist(p2,List[])) <= )
         return true;
     else
         return false;
 }
 void Graham(int n){
     Point p0=List[];
     int k=;
     for(int i=;i<n;i++){
         if(p0.y>List[i].y || (p0.y == List[i].y && p0.x > List[i].x)){
             p0=List[i];
             k=i;
         }
     }
     swap(List[k],List[]);
     sort(List+,List+n,_cmp);
     if(n==){
         top = ;
         Stack[]=;
         return;
     }
     if(n==){
         top=;
         Stack[]=,Stack[]=;
         return;
     }
     Stack[]=,Stack[]=;
     top=;
     for(int i=;i<n;i++){
         while(top> &&
               (sgn((List[Stack[top-]]-List[Stack[top-]])^(List[i]-List[Stack[top-]]))<=))
                 top--;
         Stack[top++]=i;
     }
 }
 double rotating_calipers(Point p[],int n){
     double ans=inf;
     Point v;
     int cur=;
     for(int i=;i<n;i++){
         v=p[i]-p[(i+)%n];
         while(sgn(v^(p[(cur+)%n]-p[cur]))<)
             cur=(cur+)%n;
         ans=min(ans,
                 ((p[cur]-p[(i+)%n])^(p[i]-p[(i+)%n]))/(dist(p[i],p[(i+)%n])));
     }
     return ans;
 }
 Point p[maxn];
 int main(){
     int N,R;
     scanf("%d%d",&N,&R);
     for(int i=;i<N;i++)
         List[i].input();

     Graham(N);
     for(int i=;i<top;i++)
         p[i]=List[Stack[i]];
     double ans=rotating_calipers(p,top);
     printf("%.16lf\n",ans);
     return ;
 }