LA

题意：一个N个点（编号从1开始），M条边的无向图（编号从1开始），有3种操作：

D X：把编号为X的边删了；

Q X K：查询编号为X的结点所在连通分量第K大的元素；

C X V：将编号为X的结点的权值修改为V。

问所有查询的结果的平均值（1 <= N <= 20000, 0 <= M <= 60000, -10^6 <= 点权 <= 10^6, 1 <= Q操作次数 <= 2 * 10^5, C操作次数 <= 2 * 10^5）。

题目链接：https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=3032

——>>LJ《训练指南》Treap树的例题，题目中关于Q操作的话：among all vertexes currently connected with vertex X，总觉得指的是与X直接相连的结点，可实现上却应理解为X所在连通分量的所有结点。

#include <cstdio>
#include <cstring>
#include <cstdlib>

using namespace std;

const int maxn = 20000 + 10;
const int maxm = 60000 + 10;
const int maxc = 500000 + 10;

struct Command{
    char type;
    int x, p;
    Command(char type = '', int x = 0, int p = 0):type(type), x(x), p(p){}
};

struct Node{
    Node *ch[2];
    int r;
    int v;
    int s;
    Node(int v):v(v){
        ch[0] = ch[1] = NULL;
        r = rand();
        s = 1;
    }

    bool operator < (const Node& e) const{
        return r < e.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;
    }
};

int N, M, weight[maxn], from[maxm], to[maxm], fa[maxn], kase, c, query_cnt;
long long query_tot;
bool removed[maxm];
Command commands[maxc];
Node *root[maxn];

int Find(int x){
    return x == fa[x] ? x : Find(fa[x]);
}

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 rotate(Node* &o, int d){
    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;
        insert(o->ch[d], x);
        if(o->ch[d] > o) 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] > o->ch[1] ? 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();
}

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 addEdge(int x){
    int u = Find(from[x]);
    int v = Find(to[x]);
    if(u != v){
        if(root[u]->s < root[v]->s){
            fa[u] = v;
            mergeto(root[u], root[v]);
        }
        else{
            fa[v] = u;
            mergeto(root[v], root[u]);
        }
    }
}

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+1) return kth(o->ch[1], k);
    else return kth(o->ch[0], k-s-1);
}

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

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

void read(){
    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]);
    c = 0;
    memset(removed, 0, sizeof(removed));
    while(1){
        char type;
        int X, K, V;
        scanf(" %c", &type);
        if(type == 'E') break;
        scanf("%d", &X);
        if(type == 'D') removed[X] = 1;
        else if(type == 'Q') scanf("%d", &K);
        else{
            scanf("%d", &V);
            K = weight[X];
            weight[X] = V;
        }
        commands[c++] = Command(type, X, K);
    }
}

void build(){
    for(int i = 1; i <= N; i++){
        fa[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]) addEdge(i);
}

void solve(){
    query_tot = query_cnt = 0;
    for(int i = c-1; i >= 0; i--){
        if(commands[i].type == 'D') addEdge(commands[i].x);
        else if(commands[i].type == 'Q') query(commands[i].x, commands[i].p);
        else change_weight(commands[i].x, commands[i].p);
    }
    printf("Case %d: %.6lf
", kase++, (double)query_tot / query_cnt);
}

int main()
{
    kase = 1;
    while(scanf("%d%d", &N, &M) == 2){
        if(!N && !M) return 0;
        read();
        build();
        solve();
    }
    return 0;
}