QTREE6&&7 - Query on a tree VI &&VII

树上连通块

不用具体距离，只询问连通块大小或者最大权值

可以类比Qtree5的方法，但是记录东西很多，例如子树有无0/1颜色等

一个trick，两个LCT分离颜色

每个颜色在边上。

仅保留连通块顶部不是相同颜色，使得断边不会被菊花图卡掉

所以内部颜色不用考虑了，专心维护子树值。

查询时候findrt，splay，右儿子即可。

Qtree6

#include<bits/stdc++.h>
#define reg register int
#define il inline
#define fi first
#define se second
#define mk(a,b) make_pair(a,b)
#define numb (ch^'0')
using namespace std;
typedef long long ll;
template<class T>il void rd(T &x){
    char ch;x=;bool fl=false;
    while(!isdigit(ch=getchar()))(ch=='-')&&(fl=true);
    for(x=numb;isdigit(ch=getchar());x=x*+numb);
    (fl==true)&&(x=-x);
}
template<class T>il void output(T x){if(x/)output(x/);putchar(x%+'');}
template<class T>il void ot(T x){if(x<) putchar('-'),x=-x;output(x);putchar(' ');}
template<class T>il void prt(T a[],int st,int nd){for(reg i=st;i<=nd;++i) ot(a[i]);putchar('\n');}

namespace Miracle{
const int N=+;
int n,m;
int f[N];
int co[N];
struct LCT{
    #define ls ch[x][0]
    #define rs ch[x][1]
    int fa[N],ch[N][];
    int sz[N],si[N];
    bool nrt(int x){
        return ch[fa[x]][]==x||ch[fa[x]][]==x;
    }
    void pushup(int x){
        if(x)
        sz[x]=si[x]+sz[ls]+sz[rs]+;
    }
    void rotate(int x){
        int y=fa[x],d=ch[y][]==x;
        fa[ch[y][d]=ch[x][!d]]=y;
        if(nrt(y)) ch[fa[x]=fa[y]][ch[fa[y]][]==y]=x;
        else fa[x]=fa[y];
        fa[ch[x][!d]=y]=x;
        pushup(y);
    }
    void splay(int x){
        while(nrt(x)){
            int y=fa[x],z=fa[y];
            if(nrt(y)){
                rotate((ch[y][]==x)==(ch[z][]==y)?y:x);
            }
            rotate(x);
        }
        pushup(x);
    }
    void access(int x){
        for(reg y=;x;y=x,x=fa[x]){
            //cout<<" xx "<<x<<endl;
            splay(x);si[x]-=sz[y];si[x]+=sz[ch[x][]];
            ch[x][]=y;
            pushup(x);
        }
    }
    int findrt(int x){
        access(x);splay(x);
        while(ch[x][]) x=ch[x][];
        splay(x);
        return x;
    }
    void link(int x){
        //cout<<" link "<<x<<endl;
        splay(x);
        int y=fa[x]=f[x];
        access(y);splay(y);
        si[y]+=sz[x];
        pushup(y);
    }
    void cut(int x){
    //    cout<<" cut "<<x<<endl;
        access(x);splay(x);
    //    cout<<ls<<" "<<ch[x][0]<<endl;
        ls=fa[ls]=;
        pushup(x);
    }
    int query(int x){
        int lp=findrt(x);
    //    cout<<" lp "<<lp<<" "<<sz[lp]<<" "<<si[lp]<<endl;
        return sz[lp]-si[lp]-;
    }
}lct[];
vector<int>to[N];
void dfs(int x){
    for(reg i=;i<(int)to[x].size();++i){
        if(to[x][i]!=f[x]){
            f[to[x][i]]=x;dfs(to[x][i]);
            lct[].link(to[x][i]);
        }
    }
}
int main(){
    rd(n);
    int x,y;
    for(reg i=;i<n;++i)rd(x),rd(y),to[x].push_back(y),to[y].push_back(x);
    for(reg i=;i<=n+;++i) lct[].sz[i]=,lct[].sz[i]=,co[i]=;
    to[n+].push_back();
    dfs(n+);
    int op;
    rd(m);
    while(m--){
        rd(op);rd(x);
        if(!op){
            printf("%d\n",lct[co[x]].query(x));
        }else{
            lct[co[x]].cut(x);
        //    cout<<" after co[x] cut "<<endl;
            lct[co[x]^].link(x);
            co[x]^=;
        }
    }
    return ;
}

}
signed main(){
    Miracle::main();
    return ;
}

/*
   Author: *Miracle*
   Date: 2019/3/15 10:57:40
*/

Qtree7

#include<bits/stdc++.h>
#define reg register int
#define il inline
#define fi first
#define se second
#define mk(a,b) make_pair(a,b)
#define numb (ch^'0')
using namespace std;
typedef long long ll;
template<class T>il void rd(T &x){
    char ch;x=;bool fl=false;
    while(!isdigit(ch=getchar()))(ch=='-')&&(fl=true);
    for(x=numb;isdigit(ch=getchar());x=x*+numb);
    (fl==true)&&(x=-x);
}
template<class T>il void output(T x){if(x/)output(x/);putchar(x%+'');}
template<class T>il void ot(T x){if(x<) putchar('-'),x=-x;output(x);putchar(' ');}
template<class T>il void prt(T a[],int st,int nd){for(reg i=st;i<=nd;++i) ot(a[i]);putchar('\n');}

namespace Miracle{
const int N=1e5+;
const int inf=0x3f3f3f3f;
int n,m;
int fa[N];
struct LCT{
    struct node{
        int ch[],fa;
        int val;
        int ans;
        priority_queue<int>q,d;
        void dele(int c){
            d.push(c);
        }
        void ins(int c){
            q.push(c);
        }
        int top(){
            while(!q.empty()&&!d.empty()&&q.top()==d.top()) q.pop(),d.pop();
            if(!q.empty()) return q.top();
            return -inf;
        }
    }t[N];
    bool nrt(int x){
        return t[t[x].fa].ch[]==x||t[t[x].fa].ch[]==x;
    }
    void pushup(int x){
        t[x].ans=max(t[x].val,max(t[x].top(),max(t[t[x].ch[]].ans,t[t[x].ch[]].ans)));
    }
    void rotate(int x){
        int y=t[x].fa,d=t[y].ch[]==x;
        t[t[y].ch[d]=t[x].ch[!d]].fa=y;
        if(nrt(y)) t[t[x].fa=t[y].fa].ch[t[t[y].fa].ch[]==y]=x;
        else t[x].fa=t[y].fa;
        t[t[x].ch[!d]=y].fa=x;
        pushup(y);
    }
    void splay(int x){
        while(nrt(x)){
            int y=t[x].fa,z=t[y].fa;
            if(nrt(y)){
                rotate((t[y].ch[]==x)==(t[z].ch[]==y)?y:x);
            }rotate(x);
        }
        pushup(x);
    }
    void access(int x){
        for(reg y=;x;y=x,x=t[x].fa){
            splay(x);t[x].dele(t[y].ans);
            t[x].ins(t[t[x].ch[]].ans);
            t[x].ch[]=y;
            pushup(x);
        }
    }
    int findrt(int x){
        access(x);splay(x);
        while(t[x].ch[]) x=t[x].ch[];
        splay(x);
        return x;
    }
    void link(int x){
    //    cout<<" link "<<x<<" t.fa "<<t[x].fa<<" fa "<<fa[x]<<" ans "<<t[x].ans<<" val "<<t[x].val<<endl;
        splay(x);
        int y=t[x].fa=fa[x];
        access(y);splay(y);
        t[y].ins(t[x].ans);
        pushup(y);
    }
    void cut(int x){
        access(x);splay(x);
        t[x].ch[]=t[t[x].ch[]].fa=;
        pushup(x);
    }
    void chan(int x,int c){//chan val
        access(x);splay(x);
        t[x].val=c;
        pushup(x);
    }
    int query(int x){
        int lp=findrt(x);
        return t[t[lp].ch[]].ans;
    }
}lct[];
vector<int>to[N];
int co[N],wei[N];
void dfs(int x){
    //cout<<x<<endl;
    for(reg i=;i<(int)to[x].size();++i){
        int y=to[x][i];
        if(y==fa[x]) continue;
        fa[y]=x;
        dfs(y);
        lct[co[y]].link(y);
    }
}
int main(){

    rd(n);
    lct[].t[].ans=lct[].t[].val=-inf;
    lct[].t[].ans=lct[].t[].val=-inf;
    lct[].t[n+].ans=lct[].t[n+].val=-inf;
    lct[].t[n+].ans=lct[].t[n+].val=-inf;
    int x,y;
    for(reg i=;i<n;++i){
        rd(x);rd(y);
        to[x].push_back(y);to[y].push_back(x);
    }
    to[n+].push_back();
    for(reg i=;i<=n;++i){
        rd(co[i]);
    }
    for(reg i=;i<=n;++i){
        rd(wei[i]);
    //    cout<<" i "<<i<<" "<<wei[i]<<endl;
        lct[].t[i].val=lct[].t[i].ans=wei[i];
        lct[].t[i].val=lct[].t[i].ans=wei[i];
    }
    wei[n+]=-inf;
    dfs(n+);

    rd(m);int op;
    while(m--){
        rd(op);rd(x);
        if(op==){
            printf("%d\n",lct[co[x]].query(x));
        }else if(op==){
            lct[co[x]].cut(x);lct[co[x]^].link(x);
            co[x]^=;
        }else{
            rd(y);
            lct[].chan(x,y);
            lct[].chan(x,y);
        }
    }
    return ;
}

}
signed main(){
    Miracle::main();
    return ;
}

/*
   Author: *Miracle*
   Date: 2019/3/15 14:12:29
*/