BZOJ3528: [Zjoi2014]星系调查

唉，看到这题直接想起自己的Day1，还是挺难受的，挺傻一题考试的时候怎么就没弄出来呢……

这两天CP让我给他写个题解，弄了不是很久就把这个题给弄出来了，真不知道考试的时候在干嘛。

明天就出发去北京了，祝自己APIO顺利吧。

 /**************************************************************
     Problem: 3528
     User: zhuohan123
     Language: C++
     Result: Accepted
     Time:1736 ms
     Memory:25408 kb
 ****************************************************************/

 #include <iostream>
 #include <cmath>
 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 using namespace std;
 const double eps=1e-;
 inline int getnum()
 {
     int ans=,fh=;char ch=getchar();
     while(ch<''||ch>''){if(ch=='-')fh*=-;ch=getchar();}
     while(ch>=''&&ch<='')ans=ans*+ch-'',ch=getchar();
     return fh*ans;
 }
 struct info
 {
     int n,x,y,x2,y2,xy;
     info(){n=x=y=x2=y2=xy=;}
     info(int X,int Y){n=;x=X;y=Y;x2=X*X;y2=Y*Y;xy=X*Y;}
     info(int N,int X,int Y,int X2,int Y2,int XY){n=N;x=X;y=Y;x2=X2;y2=Y2;xy=XY;}
     inline friend info operator+(info a,info b){return info(a.n+b.n,a.x+b.x,a.y+b.y,a.x2+b.x2,a.y2+b.y2,a.xy+b.xy);}
     inline friend info operator-(info a,info b){return info(a.n-b.n,a.x-b.x,a.y-b.y,a.x2-b.x2,a.y2-b.y2,a.xy-b.xy);}
     inline info operator+=(info b){n+=b.n;x+=b.x;y+=b.y;x2+=b.x2;y2+=b.y2;xy+=b.xy;return *this;}
     inline double xbar(){return (double)x/(double)n;}
     inline double ybar(){return (double)y/(double)n;}
     inline double A(){return x2-*xbar()*x+n*xbar()*xbar();}
     inline double B(){return *ybar()*x+*xbar()*y-*xy-*n*xbar()*ybar();}
     inline double C(){return y2-*ybar()*y+n*ybar()*ybar();}
     inline double delta()
     {
         if(n==)return ;
         double a=A(),b=B(),c=C(),d=sqrt(a*a+b*b+c*c-*a*c);
         double ans1=(a+c+d)/,ans2=(a+c-d)/;
         if(ans1>ans2)swap(ans1,ans2);
         return ans1>-eps?ans1:ans2;
     }
 };
 int n,m;
 struct point
 {
     int head,f[],deep,incir,wt;
     info x;
 }p[];
 struct edge{int next,to;}g[];int gnum;
 void addedge(int from,int to)
 {
     g[++gnum].to=to;g[gnum].next=p[from].head;p[from].head=gnum;
     g[++gnum].to=from;g[gnum].next=p[to].head;p[to].head=gnum;
 }
 namespace Tree
 {
     void dfs(int po)
     {
         p[po].deep=p[p[po].f[]].deep+;
         for(int i=;i<=;i++)
             p[po].f[i]=p[p[po].f[i-]].f[i-];
         for(int i=p[po].head;i;i=g[i].next)
             if(g[i].to!=p[po].f[])
             {
                 p[g[i].to].x+=p[po].x;
                 p[g[i].to].f[]=po;
                 dfs(g[i].to);
             }
     }
     inline int lca(int u,int v)
     {
         if(p[u].deep>p[v].deep)swap(u,v);
         for(int i=;i>=;i--)
             if(p[p[v].f[i]].deep>=p[u].deep)v=p[v].f[i];
         if(u==v)return u;
         for(int i=;i>=;i--)
             if(p[v].f[i]!=p[u].f[i])v=p[v].f[i],u=p[u].f[i];
         return p[v].f[];
     }
     void solve()
     {
         dfs();
         int q=getnum();
         while(q--)
         {
             int u=getnum(),v=getnum(),l=lca(u,v);
             printf("%.5lf\n",(p[u].x+p[v].x-p[l].x-p[p[l].f[]].x).delta()+eps);
         }
     }
 }
 namespace Circle
 {
     bool ins[];
     int s[],sr;
     int cir[],cnum;
     info cinfo[];
     inline info cirwalk(int l,int r){return cinfo[r]-cinfo[l-];}
     bool dfscir(int po,int from)
     {
         ins[s[++sr]=po]=true;
         for(int i=p[po].head;i;i=g[i].next)
             if(g[i].to!=from)
             {
                 if(ins[g[i].to])
                 {
                     while(s[sr]!=g[i].to)
                     {
                         cir[++cnum]=s[sr];
                         p[s[sr]].incir=cnum;
                         sr--;
                     }
                     cir[++cnum]=g[i].to;
                     p[g[i].to].incir=cnum;
                     return true;
                 }
                 else if(dfscir(g[i].to,po))return true;
             }
         sr--;
         ins[po]=false;return false;
     }
     void dfstree(int po,int wt)
     {
         p[po].wt=wt;
         p[po].deep=p[p[po].f[]].deep+;
         for(int i=;i<=;i++)
             p[po].f[i]=p[p[po].f[i-]].f[i-];
         for(int i=p[po].head;i;i=g[i].next)
             if(g[i].to!=p[po].f[]&&!p[g[i].to].incir)
             {
                 p[g[i].to].x+=p[po].x;
                 p[g[i].to].f[]=po;
                 dfstree(g[i].to,wt);
             }
     }
     inline int lca(int u,int v)
     {
         if(p[u].deep>p[v].deep)swap(u,v);
         for(int i=;i>=;i--)
             if(p[p[v].f[i]].deep>=p[u].deep)v=p[v].f[i];
         if(u==v)return u;
         for(int i=;i>=;i--)
             if(p[v].f[i]!=p[u].f[i])v=p[v].f[i],u=p[u].f[i];
         return p[v].f[];
     }
     void solve()
     {
         dfscir(,);
         for(int i=;i<=cnum;i++)dfstree(cir[i],cir[i]);
         for(int i=;i<=cnum;i++)cir[i+cnum]=cir[i];
         for(int i=;i<=*cnum;i++)cinfo[i]=cinfo[i-]+p[cir[i]].x;
         int q=getnum();
         while(q--)
         {
             int u=getnum(),v=getnum();
             if(p[u].wt==p[v].wt)
             {
                 int l=lca(u,v);
                 printf("%.5lf\n",(p[u].x+p[v].x-p[l].x-p[p[l].f[]].x).delta()+eps);
             }
             else
             {
                 int fu=p[u].wt,fv=p[v].wt;
                 info iu=p[u].x-p[fu].x,iv=p[v].x-p[fv].x;
                 if(p[fu].incir>p[fv].incir)swap(fu,fv);
                 info imid1=cirwalk(p[fu].incir,p[fv].incir);
                 info imid2=cirwalk(p[fv].incir,p[fu].incir+cnum);
                 printf("%.5lf\n",min((iu+imid1+iv).delta(),(iu+imid2+iv).delta())+eps);
             }
         }
     }
 }
 int main(int argc, char *argv[])
 {
     //freopen("1.in","r",stdin);
     //freopen("1.out","w",stdout);
     n=getnum(),m=getnum();
     for(int i=;i<=n;i++)
     {
         int x=getnum(),y=getnum();
         p[i].x=info(x,y);
     }
     for(int i=;i<=m;i++)addedge(getnum(),getnum());
     if(m==n-)Tree::solve();
     else Circle::solve();
     return ;
 }