BZOJ3083 遥远的国度（树链剖分+线段树）

　　考虑暴力树剖。那么修改路径和查询子树最小值非常简单。

　　对于换根当然不能真的给他转一下，我们只记录当前根是哪个。对于查询，如果查询点不在当前根到原根的路径上，显然换根是对答案没有影响的；如果是当前根，答案就是整棵树最小值，否则即是要查询该路径上的后代所在子树外的点的最小值，去掉这段区间就可以了。

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
#define N 100010
#define int unsigned int
#define inf 2147483649
int read()
{
    int x=,f=;char c=getchar();
    while (c<''||c>'') {if (c=='-') f=-;c=getchar();}
    while (c>=''&&c<='') x=(x<<)+(x<<)+(c^),c=getchar();
    return x*f;
}
int n,m,root,p[N],a[N],t=,cnt=;
int dfn[N],id[N],fa[N],son[N],deep[N],size[N],top[N];
int L[N<<],R[N<<],tree[N<<],lazy[N<<];
struct data{int to,nxt;
}edge[N<<];
void addedge(int x,int y){t++;edge[t].to=y,edge[t].nxt=p[x],p[x]=t;}
void dfs1(int k)
{
    size[k]=;
    for (int i=p[k];i;i=edge[i].nxt)
    if (edge[i].to!=fa[k])
    {
        deep[edge[i].to]=deep[k]+;
        fa[edge[i].to]=k;
        dfs1(edge[i].to);
        size[k]+=size[edge[i].to];
        if (size[edge[i].to]>size[son[k]]) son[k]=edge[i].to;
    }
}
void dfs2(int k,int from)
{
    id[k]=++cnt;dfn[cnt]=k;
    top[k]=from;
    if (son[k]) dfs2(son[k],from);
    for (int i=p[k];i;i=edge[i].nxt)
    if (edge[i].to!=fa[k]&&edge[i].to!=son[k])
    dfs2(edge[i].to,edge[i].to);
}
void build(int k,int l,int r)
{
    L[k]=l,R[k]=r;
    if (l==r) {tree[k]=a[dfn[l]];return;}
    int mid=l+r>>;
    build(k<<,l,mid);
    build(k<<|,mid+,r);
    tree[k]=min(tree[k<<],tree[k<<|]);
}
void down(int k)
{
    tree[k<<]=tree[k<<|]=lazy[k];
    lazy[k<<]=lazy[k<<|]=lazy[k];
    lazy[k]=;
}
void up(int k){tree[k]=min(tree[k<<],tree[k<<|]);}
int query(int k,int l,int r)
{
    if (l>r) return inf;
    if (L[k]==l&&R[k]==r) return tree[k];
    if (lazy[k]) down(k);
    int mid=L[k]+R[k]>>;
    if (r<=mid) return query(k<<,l,r);
    else if (l>mid) return query(k<<|,l,r);
    else return min(query(k<<,l,mid),query(k<<|,mid+,r));
}
void modify(int k,int l,int r,int x)
{
    if (L[k]==l&&R[k]==r) {tree[k]=lazy[k]=x;return;}
    if (lazy[k]) down(k);
    int mid=L[k]+R[k]>>;
    if (r<=mid) modify(k<<,l,r,x);
    else if (l>mid) modify(k<<|,l,r,x);
    else modify(k<<,l,mid,x),modify(k<<|,mid+,r,x);
    up(k);
}
void jump_modify(int x,int y,int z)
{
    while (top[x]!=top[y])
    {
        if (deep[top[x]]<deep[top[y]]) swap(x,y);
        modify(,id[top[x]],id[x],z);
        x=fa[top[x]];
    }
    if (deep[x]<deep[y]) swap(x,y);
    modify(,id[y],id[x],z);
}
int getans(int k)
{
    if (k==root) return query(,,n);
    int x=k,y=root;
    while (top[x]!=top[y])
    {
        if (deep[top[x]]<deep[top[y]]) swap(x,y);
        x=fa[top[x]];
    }
    if (deep[x]<deep[y]) swap(x,y);
    if (k==y)
    {
        for (int i=p[k];i;i=edge[i].nxt)
        if (id[edge[i].to]<=id[root]&&id[root]<=id[edge[i].to]+size[edge[i].to]-)
        return min(query(,,id[edge[i].to]-),query(,id[edge[i].to]+size[edge[i].to],n));
    }
    else return query(,id[k],id[k]+size[k]-);
}
signed main()
{
#ifndef ONLINE_JUDGE
    freopen("bzoj3083.in","r",stdin);
    freopen("bzoj3083.out","w",stdout);
    const char LL[]="%I64d\n";
#else
    const char LL[]="%lld\n";
#endif
    n=read(),m=read();
    for (int i=;i<n;i++)
    {
        int x=read(),y=read();
        addedge(x,y),addedge(y,x);
    }
    for (int i=;i<=n;i++) a[i]=read();
    dfs1();
    dfs2(,);
    build(,,n);
    root=read();
    while (m--)
    {
        int op=read();
        if (op==) root=read();
        else if (op==) printf("%d\n",getans(read()));
        else
        {
            int x=read(),y=read(),z=read();
            jump_modify(x,y,z);
        }
    }
    return ;
}