Treap

 

Graph and Queries

 UVALive - 5031 

第一道Treap，对着白书敲的=_=||

#include <bits/stdc++.h>
using namespace std;
//15:15--16:00
struct Node{
    Node *ch[2]; //左右子树
    int r;   //随机优先级
    int v;   //值
    int s;  //节点总数
    Node(int v):v(v){ch[0]=ch[1]=NULL;r=rand();s=1; }
    bool operator <(const Node &a)const {
        return r<a.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){   //0左旋，1右旋
    Node *k=o->ch[d^1];o->ch[d^1]=k->ch[d];k->ch[d]=o;
    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);  //不用cmp函数，因为可能有相同节点
        insert(o->ch[d],x);
        if(o->ch[d]->r>o->r) rotate(o,d^1);
    }
    o->maintain();
}

void remove(Node* &o,int x){
    int d=o->cmp(x);
    if(d==-1){
        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();
}

const int maxc=500000+10;

struct Command
{
    char type;
    int x,p;  //根据type，p代表k或者v
}command[maxc];

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

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

//并查集
int pa[maxn];
int gf(int x){
    return x==pa[x]?x:pa[x]=gf(pa[x]);
}

//名次树
Node* root[maxn];  //Treap
int kth(Node* o,int k){
    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* &a,Node* &b){
    if(a->ch[0]!=NULL) mergeto(a->ch[0],b);
    if(a->ch[1]!=NULL) mergeto(a->ch[1],b);
    insert(b,a->v);
    delete a;
    a=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;
}
//主程序相关
void add_edge(int x){
    int u=gf(from[x]),v=gf(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[gf(x)],k);
}

void change_weight(int x,int v){
    int u=gf(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));

        //读命令
        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;
            }
            command[c++]=(Command){type,x,p};
        }

        //最终的图
        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(command[i].type=='D') add_edge(command[i].x);
            if(command[i].type=='Q') query(command[i].x,command[i].p);
            if(command[i].type=='C') change_weight(command[i].x,command[i].p);
        }
        printf("Case %d: %.6lf\n",++kase,query_tot/(double)query_cnt);
    }
    return 0;
}