bzoj 3083 遥远的国度 —— 树链剖分

题目：https://www.lydsy.com/JudgeOnline/problem.php?id=3083

换根后路径还是不变，子树分类讨论一下，树剖后线段树维护即可。

代码如下：

#include<cstdio>
#include<cstring>
#include<algorithm>
#define mid ((l+r)>>1)
#define ls (x<<1)
#define rs (x<<1|1)
using namespace std;
typedef long long ll;
int const xn=1e5+;
int n,m,hd[xn],ct,to[xn<<],nxt[xn<<],rt;
int tim,dfn[xn],fa[xn],siz[xn],son[xn],dep[xn],top[xn],id[xn];
ll a[xn],mn[xn<<],lzy[xn<<],inf=1e17;
ll rd()
{
  ll ret=,f=; char ch=getchar();
  while(ch<''||ch>''){if(ch=='-')f=; ch=getchar();}
  while(ch>=''&&ch<='')ret=ret*+ch-'',ch=getchar();
  return f?ret:-ret;
}
ll minn(ll x,ll y){return x<y?x:y;}
void add(int x,int y){to[++ct]=y; nxt[ct]=hd[x]; hd[x]=ct;}
void dfs(int x,int ff)
{
  fa[x]=ff; dep[x]=dep[ff]+; siz[x]=;
  for(int i=hd[x],u;i;i=nxt[i])
    {
      if((u=to[i])==ff)continue;
      dfs(u,x); siz[x]+=siz[u];
      if(siz[u]>siz[son[x]])son[x]=u;
    }
}
void dfsx(int x)
{
  dfn[x]=++tim; id[tim]=x;
  if(son[x])top[son[x]]=top[x],dfsx(son[x]);
  for(int i=hd[x],u;i;i=nxt[i])
    if((u=to[i])!=fa[x]&&u!=son[x])top[u]=u,dfsx(u);
}
void build(int x,int l,int r)
{
  if(l==r){mn[x]=a[id[l]]; return;}//id!!
  build(ls,l,mid); build(rs,mid+,r);
  mn[x]=minn(mn[ls],mn[rs]);
}
void turn(int x,ll v){mn[x]=v; lzy[x]=v;}
void pushdown(int x)
{
  if(!lzy[x])return;
  turn(ls,lzy[x]); turn(rs,lzy[x]);
  lzy[x]=;
}
void update(int x,int l,int r,int L,int R,ll v)
{
  if(l>=L&&r<=R){turn(x,v); return;}
  pushdown(x);
  if(mid>=L)update(ls,l,mid,L,R,v);
  if(mid<R)update(rs,mid+,r,L,R,v);
  mn[x]=minn(mn[ls],mn[rs]);
}
ll query(int x,int l,int r,int L,int R)
{
  if(L>R)return inf;
  if(l>=L&&r<=R)return mn[x];
  pushdown(x); ll ret=inf;
  if(mid>=L)ret=minn(ret,query(ls,l,mid,L,R));
  if(mid<R)ret=minn(ret,query(rs,mid+,r,L,R));
  return ret;
}
void change(int x,int y,ll v)
{
  while(top[x]!=top[y])
    {
      if(dep[top[x]]<dep[top[y]])swap(x,y);
      update(,,n,dfn[top[x]],dfn[x],v); x=fa[top[x]];
    }
  if(dep[x]<dep[y])swap(x,y);
  update(,,n,dfn[y],dfn[x],v);
}
int find(int x,int y)//y in x
{
  while(top[y]!=top[x])
    {
      if(fa[top[y]]==x)return top[y];
      y=fa[top[y]];
    }
  return son[x];
}
ll ask(int x)
{
  if(x==rt)return query(,,n,,n);
  if(dfn[rt]<dfn[x]||dfn[rt]>=dfn[x]+siz[x])
    return query(,,n,dfn[x],dfn[x]+siz[x]-);
  int y=find(x,rt);
  return minn(query(,,n,,dfn[y]-),query(,,n,dfn[y]+siz[y],n));
}
int main()
{
  n=rd(); m=rd();
  for(int i=,x,y;i<n;i++)x=rd(),y=rd(),add(x,y),add(y,x);
  dfs(,); top[]=; dfsx();
  for(int i=;i<=n;i++)a[i]=rd();
  build(,,n);
  rt=rd(); ll z;
  for(int i=,opt,x,y;i<=m;i++)
    {
      opt=rd(); x=rd();
      if(opt==)rt=x;
      if(opt==)y=rd(),z=rd(),change(x,y,z);
      if(opt==)printf("%lld\n",ask(x));
    }
  return ;
}