解题：AHOI 2005 航线规划

题面

这种不断删边的首先肯定想到时光倒流啊=。=

在最后剩下的连通图上跑出一棵搜索树，先将边权都赋为$1$，那么两点间的关键航线就是链上边权和，而每加入一条非树边$u,v$都会使得$u,v$链上的边的边权变为零。写个树剖，先把非树边加进去，然后逆着做一下就行了。

 #include<map>
 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 using namespace std;
 const int N=,M=,Q=;
 struct a
 {
     int n1,n2,t;
     int mn(){return min(n1,n2);}
     int mx(){return max(n1,n2);}
 }edg[M],qry[Q];
 bool operator < (a x,a y)
 {
     return x.mn()==y.mn()?x.mx()<y.mx():x.mn()<y.mn();
 }
 map<a,bool> mp;
 int n,m,typ,tot,num,cnt;
 int p[N],noww[*M],goal[*M];
 int vis[N],outp[Q],val[*N],laz[*N];
 int dfn[N],siz[N],anc[N],dep[N],imp[N],top[N];
 void link(int f,int t)
 {
     noww[++cnt]=p[f];
     goal[cnt]=t,p[f]=cnt;
 }
 void DFS(int nde,int fth,int dth)
 {
     int tmp=;
     siz[nde]=,vis[nde]=true;
     anc[nde]=fth,dep[nde]=dth;
     for(int i=p[nde];i;i=noww[i])
         if(goal[i]!=fth&&!vis[goal[i]])
         {
             mp[(a){nde,goal[i],}]=true;
             DFS(goal[i],nde,dth+);
             siz[nde]+=siz[goal[i]];
             if(siz[goal[i]]>tmp)
                 tmp=siz[goal[i]],imp[nde]=goal[i];
         }
 }
 void mark(int nde,int tpp)
 {
     top[nde]=tpp,dfn[nde]=++num;
     if(imp[nde])
     {
         mark(imp[nde],tpp);
         for(int i=p[nde];i;i=noww[i])
             if(goal[i]!=imp[nde]&&goal[i]!=anc[nde])
                 mark(goal[i],goal[i]);
     }
 }
 void create(int nde,int l,int r)
 {
     if(l==r)
         val[nde]=,laz[nde]=-;
     else
     {
         int mid=(l+r)/,ls=*nde,rs=*nde+;
         create(ls,l,mid),create(rs,mid+,r);
         val[nde]=val[ls]+val[rs],laz[nde]=-;
     }
 }
 void release(int nde,int l,int r)
 {
     if(~laz[nde])
     {
         int mid=(l+r)/,ls=*nde,rs=*nde+;
         laz[ls]=laz[nde],laz[rs]=laz[nde];
         val[ls]=(mid-l+)*laz[nde];
         val[rs]=(r-mid)*laz[nde];
         laz[nde]=-;
     }
 }
 void change(int nde,int l,int r,int nl,int nr,int task)
 {
     if(l>nr||r<nl)
         return ;
     else if(l>=nl&&r<=nr)
         val[nde]=task*(r-l+),laz[nde]=task;
     else
     {
         int mid=(l+r)/,ls=*nde,rs=*nde+; release(nde,l,r);
         change(ls,l,mid,nl,nr,task),change(rs,mid+,r,nl,nr,task);
         val[nde]=val[ls]+val[rs];
     }
 }
 int query(int nde,int l,int r,int nl,int nr)
 {
     if(l>nr||r<nl)
         return ;
     else if(l>=nl&&r<=nr)
         return val[nde];
     else
     {
         int mid=(l+r)/,ls=*nde,rs=*nde+; release(nde,l,r);
         return query(ls,l,mid,nl,nr)+query(rs,mid+,r,nl,nr);
     }
 }
 int LCA(int x,int y)
 {
     while(top[x]!=top[y])
     {
         if(dep[top[x]]<dep[top[y]])
         swap(x,y); x=anc[top[x]];
     }
     return dep[x]<dep[y]?x:y;
 }
 void path_change(int x,int y)
 {
     int lca=LCA(x,y),mem=query(,,n,dfn[lca],dfn[lca]);
     while(top[x]!=top[y])
     {
         if(dep[top[x]]<dep[top[y]]) swap(x,y);
         change(,,n,dfn[top[x]],dfn[x],); x=anc[top[x]];
     }
     if(dep[x]>dep[y]) swap(x,y);
     change(,,n,dfn[x],dfn[y],),change(,,n,dfn[lca],dfn[lca],mem);
 }
 int path_query(int x,int y)
 {
     int ret=;
     while(top[x]!=top[y])
     {
         if(dep[top[x]]<dep[top[y]]) swap(x,y);
         ret+=query(,,n,dfn[top[x]],dfn[x]); x=anc[top[x]];
     }
     if(dep[x]>dep[y]) swap(x,y);
     int lca=LCA(x,y),dec=query(,,n,dfn[lca],dfn[lca]);
     return ret+query(,,n,dfn[x],dfn[y])-dec;
 }
 int main ()
 {
     scanf("%d%d",&n,&m);
     for(int i=;i<=m;i++)
     {
         scanf("%d%d",&edg[i].n1,&edg[i].n2);
         mp[edg[i]]=true;
     }
     while(scanf("%d",&typ)&&~typ)
     {
         qry[++tot].t=typ;
         scanf("%d%d",&qry[tot].n1,&qry[tot].n2);
         if(!typ) mp[qry[tot]]=false;
     }
     for(int i=;i<=m;i++)
         if(mp[edg[i]])
         {
             link(edg[i].n1,edg[i].n2);
             link(edg[i].n2,edg[i].n1);
         }
     mp.clear(); DFS(,,);
     memset(p,,sizeof p),cnt=;
     for(int i=;i<=m;i++)
         if(mp[edg[i]])
         {
             link(edg[i].n1,edg[i].n2);
             link(edg[i].n2,edg[i].n1);
         }
     mark(,); create(,,n);
     for(int i=;i<=tot;i++)
         if(!qry[i].t) mp[qry[i]]=true;
     for(int i=;i<=m;i++)
         if(!mp[edg[i]]) path_change(edg[i].n1,edg[i].n2);
     for(int i=tot;i;i--)
     {
         if(qry[i].t) outp[++outp[]]=path_query(qry[i].n1,qry[i].n2);
         else path_change(qry[i].n1,qry[i].n2);
     }
     while(outp[]) printf("%d\n",outp[outp[]--]);
     return ;
 }