【BZOJ 3123】 [Sdoi2013]森林 主席树启发式合并

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define MAXN 80001
using namespace std;
inline int read(){
    register int sum=0;register char ch=getchar();
    while(ch<‘0‘||ch>‘9‘)ch=getchar();
    while(ch>=‘0‘&&ch<=‘9‘)sum=(sum<<1)+(sum<<3)+ch-‘0‘,ch=getchar();
    return sum;
}
int n,m,T,fa[MAXN],size[MAXN],f[MAXN][20];
struct Via{
    int to,next;
}c[MAXN<<1];
int head[MAXN],t;
struct Seg_Tree{
    Seg_Tree *ch[2];
    int size;
}*root[MAXN],*null;
int pos[MAXN],a[MAXN],deep[MAXN];
int Hash[MAXN],len;
bool v[MAXN];
//*********************Define********************//
inline int find(int x){
    return x==fa[x]?x:(fa[x]=find(fa[x]));
}
inline void Unit_to_(int x,int y){
    fa[find(x)]=find(y);
}
//*******************Union_Find_Sets*************//
inline void add(int x,int y){
    c[++t].to=y,c[t].next=head[x],head[x]=t;
}
//********************Maintain_Tree**************//
int comp(const int x,const int y){
    return a[x]<a[y];
}
inline void HASH(){
    sort(pos+1,pos+n+1,comp);
    for(register int i=1;i<=n;i++)
        if(i==1||a[pos[i]]!=a[pos[i-1]])Hash[++len]=a[pos[i]],a[pos[i]]=len;
        else a[pos[i]]=len;
}
//********************Hash**********************//
void ins(Seg_Tree *&p,Seg_Tree *last,int l,int r,int key){
    p=new Seg_Tree,*p=*last,++p->size;if(l==r)return;
    if(key<=((l+r)>>1))ins(p->ch[0],last->ch[0],l,((l+r)>>1),key);
    else ins(p->ch[1],last->ch[1],((l+r)>>1)+1,r,key);
}
void Dfs_Build(int x,int Fa){
    deep[x]=deep[Fa]+1;v[x]=1;
    for(register int i=1;i<20;i++)f[x][i]=f[f[x][i-1]][i-1];
    ins(root[x],root[Fa],1,len,a[x]);
    for(register int i=head[x];i;i=c[i].next)
        if(c[i].to!=Fa) f[c[i].to][0]=x,Dfs_Build(c[i].to,x);
}
int query(Seg_Tree *A1,Seg_Tree *A2,Seg_Tree *B1,Seg_Tree *B2,int l,int r,int k){
    if(l==r)return l;register int sum=A1->ch[0]->size-A2->ch[0]->size+B1->ch[0]->size-B2->ch[0]->size;
    if(sum>=k)return query(A1->ch[0],A2->ch[0],B1->ch[0],B2->ch[0],l,((l+r)>>1),k);
    else return query(A1->ch[1],A2->ch[1],B1->ch[1],B2->ch[1],((l+r)>>1)+1,r,k-sum);
}
void Del(Seg_Tree *p,Seg_Tree *last){
    if(p==last)return;
    Del(p->ch[0],last->ch[0]),Del(p->ch[1],last->ch[1]);
    delete p;
}
void Delete(int x,int fa){
    for(register int i=head[x];i;i=c[i].next)
        if(c[i].to!=fa)Delete(c[i].to,x);
    Del(root[x],root[fa]),root[x]=null;
}
//********************Seg_Tree******************//
inline int Lca(int x,int y){
    if(deep[x]<deep[y])x^=y^=x^=y;
    register int k=deep[x]-deep[y];
    for(register int i=0;(1<<i)<=k;i++)
        if(k&(1<<i)) x=f[x][i];
    if(x==y)return x;
    for(register int i=19;i>=0;i--)
        if(f[x][i]!=f[y][i])
            x=f[x][i],y=f[y][i];
    return f[x][0];
}
//*********************LCA*********************//
inline void Init(){
    scanf("%*d"),n=read(),m=read(),T=read();
    null=new Seg_Tree,null->ch[0]=null->ch[1]=null,null->size=0,root[0]=null;
    for(register int i=1;i<=n;i++)a[i]=read(),pos[i]=i,root[i]=null,size[i]=1,fa[i]=i;HASH();
    for(register int i=1,x,y;i<=m;i++)x=read(),y=read(),add(x,y),add(y,x),size[find(y)]+=size[find(x)],Unit_to_(x,y);
    for(register int i=1;i<=n;i++)if(!v[i])Dfs_Build(find(i),0);
}
inline void Work(){
    register int x,y,k,lca,ans=0;register char s[1];
    while(T--){
        scanf("%s",s);
        if(s[0]==‘Q‘){
            x=read()^ans,y=read()^ans,k=read()^ans,lca=Lca(x,y);
            printf("%d\n",(ans=Hash[query(root[x],root[lca],root[y],root[f[lca][0]],1,len,k)]));
        }else{
            x=read()^ans,y=read()^ans;if(size[find(x)]>size[find(y)])x^=y^=x^=y;
            Delete(find(x),0),size[find(y)]+=size[find(x)],Unit_to_(x,y);
            f[x][0]=y,add(x,y),add(y,x),Dfs_Build(x,y);
        }
    }
}
//*********************Main********************//
int main(){
    Init();
    Work();
    return 0;
}