BZOJ 3123: [Sdoi2013]森林 [主席树启发式合并]

3123: [Sdoi2013]森林

题意：一个森林，加边，询问路径上k小值。保证任意时刻是森林

---

LCT没法搞，树上kth肯定要用树上主席树
加边？启发式合并就好了，小的树dfs重建一下
注意

1. 测试点编号不是数据组数！！！
2. 加边的时候要更新邻接链表啊，并且fa要清空
3. 并查集维护size一定初始化1

好了现在我要填报名表了

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long ll;
#define lc(x) t[x].l
#define rc(x) t[x].r
const int N=1e5+5, M=2e5+5;
inline int read(){
    char c=getchar();int x=0,f=1;
    while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}
    return x*f;
}

int n, m, Q, a[N], u, v, k, mp[N]; char s[5];
namespace ufs{
	int fa[N], size[N];
	int find(int x) {return x==fa[x]?x:fa[x]=find(fa[x]);}
} using ufs::size; using ufs::find;

struct edge{int v,ne;}e[M];
int cnt, h[N];
inline void ins(int u, int v) {
	e[++cnt]=(edge){v, h[u]}; h[u]=cnt;
	e[++cnt]=(edge){u, h[v]}; h[v]=cnt;
}
int vis[N], fa[N][18], deep[N];
int lca(int x, int y) {
	if(deep[x]<deep[y]) swap(x, y);
	int bin=deep[x]-deep[y];
	for(int i=0; i<17; i++) if((1<<i)&bin) x=fa[x][i];
	if(x==y) return x;
	for(int i=16; i>=0; i--) 
		if(fa[x][i] != fa[y][i]) x=fa[x][i], y=fa[y][i];
	return fa[x][0];
}


struct ChairTree{
	struct meow{int l,r,size;}t[N*85];
	int sz, root[N];

	void insert(int &x, int l, int r, int p) {
		t[++sz]=t[x]; x=sz;
		t[x].size++;
		if(l==r) return;
		int mid=(l+r)>>1;
		if(p<=mid) insert(lc(x), l, mid, p);
		else insert(rc(x), mid+1, r, p);
	}
	void build(int u) { //printf("build %d %d
",u,fa[u][0]);
		vis[u]=1;
		for(int i=1; (1<<i)<=deep[u]; i++)
			fa[u][i] = fa[ fa[u][i-1] ][i-1];
		root[u] = root[fa[u][0]];
		insert(root[u], 1, *mp, a[u]);
		for(int i=h[u];i;i=e[i].ne) 
			if(e[i].v != fa[u][0]) {
				fa[e[i].v][0]=u; deep[e[i].v]=deep[u]+1;
				build(e[i].v);
			}
	}

	int query(int u, int v, int k) {
		int f=lca(u,v), g=fa[f][0];  
		int x=root[u], y=root[v], l=1, r=*mp; f=root[f]; g=root[g];
		while(l!=r) {
			int lsize = t[lc(x)].size + t[lc(y)].size - t[lc(f)].size - t[lc(g)].size;
			int mid=(l+r)>>1; 
			if(k<=lsize) x=lc(x), y=lc(y), f=lc(f), g=lc(g), r=mid;
			else x=rc(x), y=rc(y), f=rc(f), g=rc(g), l=mid+1, k-=lsize;
		}
		return l;
	}

	void rebuild(int u) {
		for(int i=1; i<17; i++) 
			fa[u][i] = fa[ fa[u][i-1] ][i-1];
		root[u] = root[fa[u][0]];
		insert(root[u], 1, *mp, a[u]);
		for(int i=h[u];i;i=e[i].ne) 
			if(e[i].v != fa[u][0]) {
				fa[e[i].v][0]=u; deep[e[i].v]=deep[u]+1;
				rebuild(e[i].v);
			}
	}
	void Link(int u, int v) { 
		int x=find(u), y=find(v);
		if(size[x]<size[y]) swap(x, y), swap(u, v);
		ufs::fa[y]=x; size[x]+=size[y];
		ins(u, v);
		fa[v][0]=u; deep[v]=deep[u]+1;
		rebuild(v);
	}
}C;


int candy;
int main() {
	freopen("in","r",stdin);

	int T=read(); T+=2333;

	n=read(); m=read(); Q=read();
	for(int i=1; i<=n; i++) a[i]=mp[i]=read(), ufs::fa[i]=i, size[i]=1;
	sort(mp+1, mp+1+n); mp[0]=unique(mp+1, mp+1+n)-mp-1;
	for(int i=1; i<=n; i++) a[i] = lower_bound(mp+1, mp+1+*mp, a[i])-mp;

	for(int i=1; i<=m; i++) {
		u=read(), v=read();
		ins(u,v);
		u=find(u); v=find(v); 
		ufs::fa[v]=u; size[u]+=size[v];
	}
	for(int i=1; i<=n; i++) if(!vis[i]) C.build(i);

	int ans=0;
//candy=1;
	for(int i=1; i<=Q; i++) {
		scanf("%s",s);
		if(candy) u=read(), v=read();
		else u=read()^ans, v=read()^ans;
		if(s[0]=='Q') {
			if(candy) k=read();
			else k=read()^ans;
			ans = mp[C.query(u, v, k)];
			printf("%d
", ans);
		}else C.Link(u, v);
	}
}