[CERC2016]凸轮廓线

题意

https://www.luogu.org/problem/P3680

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思考

拆点即可。

注意精度。

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代码

 // luogu-judger-enable-o2
 #include<bits/stdc++.h>
 using namespace std;
 typedef long double ld;
 const ld eps=1E-;
 const ld pi=acos(-);
 const ld inf=1E9;
 inline bool equal(ld x,ld y)
 {
     return abs(x-y)<=eps;
 }
 struct pt
 {
     ld x,y;
     pt(ld a=,ld b=){x=a,y=b;}
     pt operator+(const pt&A){return pt(x+A.x,y+A.y);}
     pt operator-(const pt&A){return pt(x-A.x,y-A.y);}
     pt operator*(ld d){return pt(x*d,y*d);}
     pt operator/(ld d){return pt(x/d,y/d);}
     ld operator*(const pt&A){return x*A.y-y*A.x;}
     void out(){cout<<"("<<x<<","<<y<<")";}
 };
 struct line
 {
     pt A,B;
     line(pt a=pt(),pt b=pt())
     {
         A=a,B=b;
     }
 };
 inline int cross(pt A,pt B)
 {
     ld d=A*B;
     if(equal(d,))
         return ;
     return d>?:-;
 }
 inline ld dis(pt A,pt B)
 {
     return sqrt((A.x-B.x)*(A.x-B.x)+(A.y-B.y)*(A.y-B.y));
 }
 inline pt intersection(line a,line b)
 {
     pt A=b.B-b.A,B=a.B-a.A,C=b.A-a.A;
     if(cross(A,B)==)
         return pt(inf,inf);
     ld d=-(B*C)/(B*A);
     return b.A+A*d;
 }
 inline pt foot(pt A,line a)
 {
     return intersection(line(A,A+pt(a.B.y-a.A.y,a.A.x-a.B.x)),a);
 }
 inline bool seg(line a,line b)
 {
     return cross(a.A-b.A,b.B-b.A)*cross(a.B-b.A,b.B-b.A)==-&&
            cross(b.A-a.A,a.B-a.A)*cross(b.B-a.A,a.B-a.A)==-;
 }
 pt O(,);
 bool cmp(pt A,pt B)
 {
     ld x=atan2(A.y-O.y,A.x-O.x),y=atan2(B.y-O.y,B.x-O.x);
     if(equal(x,y))
         return dis(A,O)<dis(B,O);
     return x<y;
 }
 vector<pt>convex(vector<pt>P)
 {
     int pos=;
     for(int i=;i<P.size();++i)
         if(P[i].x<P[pos].x)
             pos=i;
     swap(P[pos],P[]);
     O=P[];
     sort(P.begin()+,P.end(),cmp);
     vector<pt>ans;
     int now=;
     for(int i=;i<P.size();++i)
     {
         while(now>&&cross(P[i]-ans[now-],ans[now-]-ans[now-])!=-)
             ans.pop_back(),--now;
         ans.push_back(P[i]);
         ++now;
     }
     return ans;
 }
 inline bool cmpLine(line a,line b)
 {
     return atan2(a.A.y-a.B.y,a.A.x-a.B.x)<atan2(b.A.y-b.B.y,b.A.x-b.B.x);
 }
 inline bool onClockwise(line a,line b,line c)//b,c的交点在a顺时针方向
 {
     return cross(intersection(b,c)-a.A,a.B-a.A)==;
 }
 inline bool isSame(line a,line b)
 {
     return cross(a.A-b.B,b.A-b.B)==;
 }
 line wait[];
 vector<line>halfPlane(vector<line>A)
 {
     vector<line>ans;
     sort(A.begin(),A.end(),cmpLine);
     int l=,r=;
     for(int i=;i<A.size();++i)
     {
         while(l<r&&!isSame(A[i],wait[r])&&onClockwise(A[i],wait[r-],wait[r]))
             --r;
         while(l<r&&!isSame(A[i],wait[l])&&onClockwise(A[i],wait[l],wait[l+]))
             ++l;
         if(!isSame(A[i],wait[r])||r==)
             wait[++r]=A[i];
         else if(!onClockwise(wait[r],wait[r-],A[i]))
             wait[r]=A[i];
     }
     while(l<r&&onClockwise(wait[l],wait[r],wait[r-]))
         --r;
     while(l<r&&onClockwise(wait[r],wait[l],wait[l+]))
         ++l;
     for(int i=l;i<=r;++i)
         ans.push_back(wait[i]);
     return ans;
 }
 inline ld length(vector<pt>P)
 {
     ld sum=;
     for(int i=;i<P.size();++i)
         sum+=dis(P[i-],P[i]);
     sum+=dis(P[P.size()-],P[]);
     return sum;
 }
 const ld base=;
 int main()
 {
     ios::sync_with_stdio(false);
     int n;
     cin>>n;
     vector<pt>P;
     for(int i=;i<=n;++i)
     {
         char ch;
         cin>>ch;
         ld x=i;
         if(ch=='S')
         {
             P.push_back(pt(x,));
             P.push_back(pt(x+,));
             P.push_back(pt(x+,));
             P.push_back(pt(x,));
         }
         else if(ch=='T')
         {
             P.push_back(pt(x,));
             P.push_back(pt(x+,));
             P.push_back(pt(x+0.5,sqrt()/));
         }
         else
         {
             for(ld j=;j<base;j+=)
             {
                 ld ra=*pi/base*j;
                 P.push_back(pt(x+0.5+cos(ra)/,0.5+sin(ra)/));
             }
         }
     }
     ld ans=length(convex(P));
     cout<<fixed<<setprecision()<<ans<<endl;
     return ;
 }