LA 5031 圖詢問（Treap）

熟悉了Treap樹的常用操作.

#include<cstdlib>

struct Node{
	Node *ch[2];
	int r;           //隨機優先值
	int v;           //值 
	int s;           //結點總數 
	Node(int v):v(v){ch[0]=ch[1]=NULL; r=rand(); s=1;}
	bool operator <(const Node &rhs) const{ return r<rhs.r; }
	int cmp(int x)const{
		if(x==v) return -1;
		return x<v ? 0 : 1;
	}
	
	void maintain(){
		s=1;
		if(ch[0]!=NULL) s+=ch[0]->s;
		if(ch[1]!=NULL) s+=ch[1]->s;
	}	
};


void rotate(Node* &o,int d){
	Node *k=o->ch[d^1]; o->ch[d^1]=k->ch[d]; k->ch[d]=0;
	o->maintain(); k->maintain(); o=k;	
}

void insert(Node* &o,int x){
	if(o==NULL) o=new Node(x);
	else{
		int d=(x<o->v ? 0 : 1);
		if(o->ch[d]->r> o->r)  rotate(o,d^1);      //如果插入的節點優先級高就旋轉 
	}
	o->maintain();
}


void remove(Node* &o,int x){
	int d=o->cmp(x);
	if(d==-1){                    //有左右兩棵子樹的情況 
 		Node *u=o;
 		if(o->ch[0]!=NULL && o->ch[1]!=NULL){
 			int d2=(o->ch[0]->r > o->ch[1]->r ? 1 : 0);
 			rotate(o,d2); remove(o->ch[d2],x);
		 }
	
	else{
		if(o->ch[0]==NULL) o=o->ch[1]; else o=o->ch[0];
		delete u;
	}
}
	else
	remove(o->ch[d],x);
	if(o!=NULL) o->maintain();

}


#include<cstdio>
#include<cstring>
#include<vector>
using namespace std;

const int maxc=500000+10;
struct Command{
	char type;
	int x,p;
} commands[maxc];

const int maxn=20000+10;
const int maxm=60000+10;

int n,m,weight[maxn],from[maxm],to[maxm],removed[maxm];

//並查集相關 
int pa[maxn];
int findset(int x){return pa[x]!=x ? pa[x]=findset(pa[x]) : x;}

Node* root[maxn]; //Treap

int kth(Node* o,int k){    //第k大的值 
	if(o==NULL || k<0 || k>o->s) return 0;
	int s=(o->ch[1]==NULL ? 0: o->ch[1]->s);
	if(k==s+1) return o->v;
	else if(k<=s) return kth(o->ch[1],k);
	else return kth(o->ch[0],k-s-1);
}

void mergeto(Node* &src,Node* &dest){
	if(src->ch[0]!=NULL) mergeto(src->ch[0],dest);
	if(src->ch[1]!=NULL) mergeto(src->ch[1],dest);
	insert(dest,src->v);
	delete src;
	src=NULL;
	
}

void removetree(Node* &x){
	if(x->ch[0]!=NULL) removetree(x->ch[0]);
	if(x->ch[1]!=NULL) removetree(x->ch[1]);
	delete x;
	x=NULL;
}

void add_edge(int x){
	int u=findset(from[x]),v=findset(to[x]);
	if(u!=v){
		if(root[u]->s < root[v]->s) {pa[u]=v; mergeto(root[u],root[v]);}
		else{pa[v]=u; mergeto(root[v],root[u]);}
	}
}


int query_cnt;
long long query_tot;

void query(int x,int k){
	query_cnt++;
	query_tot+=kth(root[findset(x)],k);	
}

void change_weight(int x,int v){
	int u=findset(x);
	remove(root[u],weight[x]);
	insert(root[u],v);
	weight[x]=v;
}


int main(){
	int kase=0;
	while(scanf("%d%d",&n,&m)==2 && n){
		for(int i=1;i<=n;i++) scanf("%d",&weight[i]);
		for(int i=1;i<=m;i++) scanf("%d%d",&from[i],&to[i]);
		memset(removed,0,sizeof(removed));
	

	int c=0;
	for(; ;){
		char type;
		int x,p=0,v=0;
		scanf(" %c",&type);
		if(type=='E') break;
		scanf("%d",&x);
		if(type=='D') removed[x]=1;
		if(type=='Q') scanf("%d",&p);
		if(type=='C'){
			scanf("%d",&v);
			p=weight[x];
			weight[x]=v;
		}
		commands[c++]=(Command){type,x,p};		
	}
	
	for(int i=1;i<=n;i++){
		pa[i]=i;if(root[i]!=NULL) removetree(root[i]);
		root[i]=new Node(weight[i]);
	}
	
	for(int i=1;i<=m;i++) if(!removed[i]) add_edge(i);
	
	//反向操作
	query_tot=query_cnt=0;
	for(int i=c-1;i>=0;i--){
		if(commands[i].type=='D') add_edge(commands[i].x);
		if(commands[i].type=='Q') query(commands[i].x,commands[i].p);
		if(commands[i].type=='C') change_weight(commands[i].x,commands[i].p);
		
	} 
	printf("Case %d: %.6lf\n",++kase,query_tot/(double)query_cnt);
}
	return 0;
}