bzoj3639: Query on a tree VII

Posted 2020-09-05 ccz181078

Description

You are given a tree (an acyclic undirected connected graph) with n nodes. The tree nodes are numbered from 1 to n.

Each node has a color, white or black, and a weight.

We will ask you to perfrom some instructions of the following form:

• 0 u : ask for the maximum weight among the nodes which are connected to u, two nodes are connected iff all the node on the path from u to v (inclusive u and v) have a same color.
• 1 u : toggle the color of u(that is, from black to white, or from white to black).
• 2 u w: change the weight of u to w.

Input

The first line contains a number n denoted how many nodes in the tree(1 ≤ n ≤ 10⁵). The next n - 1 lines, each line has two numbers (u,  v) describe a edge of the tree(1 ≤ u,  v ≤ n).

The next 2 lines, each line contains n number, the first line is the initial color of each node(0 or 1), and the second line is the initial weight, let‘s say W_i, of each node(|W_i| ≤ 10⁹).

The next line contains a number m denoted how many operations we are going to process(1 ≤ m ≤ 10⁵). The next m lines, each line describe a operation (t,  u) as we mentioned above(0 ≤ t ≤ 2, 1 ≤ u ≤ n, |w| ≤ 10⁹).

Output

For each query operation, output the corresponding result.

对原树每个点x，另外拆出两个新点代表黑白，x和x的所有子节点连边到对应的新点，这时重构后得到的树上每个连通块颜色相同，且每次颜色修改只会断开两条边再连上两条边

然后可以用平衡树维护森林的括号序列，时间复杂度O((n+m)logn)

#include<cstdio>
#define G *++ptr
const int N=100007;
char buf[N*100],*ptr=buf-1;
int _(){
    int x=0,c=G,f=1;
    while(c<48)c==‘-‘&&(f=-1),c=G;
    while(c>47)x=x*10+c-48,c=G;
    return x*f;
}
int ch[N*6][5],n;
int col[N];
#define lc ch][0
#define rc ch][1
#define fa ch][2
#define val ch][3
#define mxv ch][4
int max(int a,int b){return a>b?a:b;}
void up(int x){
    x[mxv]=max(x[val],max(x[lc][mxv],x[rc][mxv]));
}
void rot(int x){
    int f=x[fa],g=f[fa],d=(x!=f[lc]);
    if(g)g[ch][g[lc]!=f]=x;
    x[fa]=g;
    (f[ch][d]=x[ch][d^1])[fa]=f;
    (x[ch][d^1]=f)[fa]=x;
    up(f),up(x);
}
void sp(int x,int y=0){
    while(x[fa]!=y){
        int f=x[fa];
        if(f[fa]!=y)rot((f[lc]==x)==(f[fa][lc]==f)?f:x);
        rot(x);
    }
}
int gl(int x){
    sp(x);
    while(x[lc])x=x[lc];
    sp(x);
    return x;
}
void lk(int x,int y){
    sp(x);sp(y);
    int z=y[rc],xr=x+n*3;
    (y[rc]=x)[fa]=y;
    up(y);
    sp(xr);
    (xr[rc]=z)[fa]=xr;
    up(xr);
}
void ct(int x){
    int xr=x+n*3;
    
    sp(x);
    int l=x[lc];
    l[fa]=x[lc]=0;
    up(x);
    
    sp(xr);
    int r=xr[rc];
    r[fa]=xr[rc]=0;
    up(xr);
    
    r=gl(r);
    (r[lc]=l)[fa]=r;
    up(r);
}
int F(int w,int t){
    return w+(t+1)*n;
}
void init(){
    const int inf=0x3f3f3f3f;
    0[val]=0[mxv]=-inf;
    for(int i=1;i<=n;++i)col[i]=_();
    for(int i=1;i<=n;++i)i[val]=i[mxv]=_();
    for(int i=n+1;i<=n*6;++i)i[val]=i[mxv]=-inf;
    for(int i=1;i<=n*3;++i)(i[rc]=i+n*3)[fa]=i,up(i);
}
#undef fa
int es[N*2],enx[N*2],e0[N],ep=2;
int fa[N],sz[N],son[N],dep[N],top[N];
void f1(int w,int pa){
    sz[w]=1;
    dep[w]=dep[fa[w]=pa]+1;
    lk(F(w,col[w]),w);
    for(int i=e0[w];i;i=enx[i]){
        int u=es[i];
        if(u!=pa){
            f1(u,w);
            lk(u,F(w,col[u]));
            sz[w]+=sz[u];
            if(sz[u]>sz[son[w]])son[w]=u;
        }
    }
}
void f2(int w,int tp){
    top[w]=tp;
    if(son[w])f2(son[w],tp);
    for(int i=e0[w];i;i=enx[i]){
        int u=es[i];
        if(u!=fa[w]&&u!=son[w])f2(u,u);
    }
}
int up(int x,int y){
    int a=top[x],b=top[y];
    while(a!=b){
        x=fa[a];
        if(x==y)return a;
        a=top[x];
    }
    return son[y];
}
int main(){
    fread(buf,1,sizeof(buf),stdin)[buf]=0;
    n=_();
    for(int i=1,a,b;i<n;++i){
        a=_();b=_();
        es[ep]=b;enx[ep]=e0[a];e0[a]=ep++;
        es[ep]=a;enx[ep]=e0[b];e0[b]=ep++;
    }
    init();
    f1(1,0);f2(1,1);
    for(int q=_();q;--q){
        int o=_(),w=_();
        if(o==0){
            int l=gl(w);
            if(l>n)w=up(w,(l-1)%n+1);
            else w=1;
            sp(w);
            sp(w+n*3,w);
            printf("%d\n",max(w[val],(w+n*3)[lc][mxv]));
        }else if(o==1){
            ct(F(w,col[w]));
            lk(F(w,col[w]^1),w);
            if(w!=1){
                int f=fa[w];
                ct(w);
                lk(w,F(f,col[w]^1));
            }
            col[w]^=1;
        }else{
            sp(w);
            w[val]=_();
            up(w);
        }
    }
    return 0;
}