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=30005,M=100005,Q=40005;
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[2*M],goal[2*M];
int vis[N],outp[Q],val[4*N],laz[4*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=0;
    siz[nde]=1,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],0}]=true;
            DFS(goal[i],nde,dth+1);
            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]=1,laz[nde]=-1;
    else
    {
        int mid=(l+r)/2,ls=2*nde,rs=2*nde+1;
        create(ls,l,mid),create(rs,mid+1,r);
        val[nde]=val[ls]+val[rs],laz[nde]=-1; 
    }
}
void release(int nde,int l,int r)
{
    if(~laz[nde])
    {
        int mid=(l+r)/2,ls=2*nde,rs=2*nde+1;
        laz[ls]=laz[nde],laz[rs]=laz[nde];
        val[ls]=(mid-l+1)*laz[nde];
        val[rs]=(r-mid)*laz[nde];
        laz[nde]=-1;
    }
}
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+1),laz[nde]=task;
    else
    {
        int mid=(l+r)/2,ls=2*nde,rs=2*nde+1; release(nde,l,r);
        change(ls,l,mid,nl,nr,task),change(rs,mid+1,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 0;
    else if(l>=nl&&r<=nr)
        return val[nde];
    else
    {
        int mid=(l+r)/2,ls=2*nde,rs=2*nde+1; release(nde,l,r);
        return query(ls,l,mid,nl,nr)+query(rs,mid+1,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(1,1,n,dfn[lca],dfn[lca]);
    while(top[x]!=top[y])
    {
        if(dep[top[x]]<dep[top[y]]) swap(x,y);
        change(1,1,n,dfn[top[x]],dfn[x],0); x=anc[top[x]];
    }
    if(dep[x]>dep[y]) swap(x,y);
    change(1,1,n,dfn[x],dfn[y],0),change(1,1,n,dfn[lca],dfn[lca],mem);
}
int path_query(int x,int y)
{
    int ret=0;
    while(top[x]!=top[y])
    {
        if(dep[top[x]]<dep[top[y]]) swap(x,y);
        ret+=query(1,1,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(1,1,n,dfn[lca],dfn[lca]);
    return ret+query(1,1,n,dfn[x],dfn[y])-dec;
}
int main ()
{
    scanf("%d%d",&n,&m);
    for(int i=1;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=1;i<=m;i++)
        if(mp[edg[i]]) 
        {
            link(edg[i].n1,edg[i].n2);
            link(edg[i].n2,edg[i].n1); 
        }
    mp.clear(); DFS(1,0,1); 
    memset(p,0,sizeof p),cnt=0;
    for(int i=1;i<=m;i++)
        if(mp[edg[i]]) 
        {
            link(edg[i].n1,edg[i].n2);
            link(edg[i].n2,edg[i].n1);  
        }
    mark(1,1); create(1,1,n); 
    for(int i=1;i<=tot;i++)
        if(!qry[i].t) mp[qry[i]]=true;
    for(int i=1;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[0]]=path_query(qry[i].n1,qry[i].n2);
        else path_change(qry[i].n1,qry[i].n2);
    }
    while(outp[0]) printf("%d
",outp[outp[0]--]);
    return 0;
}