LA 5031 Graph and Queries —— Treap名次树

　　离线做法，逆序执行操作，那么原本的删除边的操作变为加入边的操作，用名次树维护每一个连通分量的名次，加边操作即是连通分量合并操作，每次将结点数小的子树向结点数大的子树合并，那么单次合并复杂度O(n1logn2)，由于合并之后原本结点数少的子树结点数至少翻倍，所以每个结点最多被插入 logn 次，故总时间复杂度为

O(n log²n)  。

注意细节处理，代码如下：

 #include <cstdio>
 #include <cstdlib>
 #include <cstring>
 #include <algorithm>
 #include <vector>

 using namespace std;

 struct Node {
     Node *ch[];
     int r;
     int v;
     int s;
     Node(int vv): v(vv) {
         s = ;
         ch[] = ch[] = NULL;
         r = rand();
     }
     int cmp(int x) const {
         if(x == v) return -;
         return x < v ?  : ;
     }
     void maintain() {
         s = ;
         if(ch[] != NULL) s += ch[]->s;
         if(ch[] != NULL) s += ch[]->s;
     }
 };

 void rotate(Node* &o, int d) {
     Node* k = o->ch[d^]; o->ch[d^] = 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 ?  : ;
         insert(o->ch[d], x);
         if(o->ch[d]->r > o->r) rotate(o, d^);
     }
     o->maintain();
 }
 void remove(Node* &o, int x) {
     int d = o->cmp(x);
     Node* u = o;
     if(d == -) {
         if(o->ch[] != NULL && o->ch[] != NULL){
             int d2 = o->ch[]->r > o->ch[]->r ?  : ;
             rotate(o, d2);
             remove(o->ch[d2], x);
         }
         else {
             if(o->ch[] == NULL) o = o->ch[]; else o = o->ch[];
             delete u;
         }
     }
     else remove(o->ch[d], x);
     if(o != NULL) o->maintain();
 }

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

 struct cmd {
     char type;
     int x, p;
 };

 vector<cmd> cmds;

 const int maxn = 2e4 + ;
 const int maxm = 6e4 + ;
 int n, m;
 int weight[maxn], from[maxm], to[maxm], removed[maxm];

 int pa[maxn];
 int findpa(int x) {return x == pa[x] ? x : pa[x] = findpa(pa[x]);}
 long long sum;
 int cnt;
 Node* root[maxn];

 void mergetreeto(Node* &ser, Node* &to) {
     if(ser->ch[] != NULL) mergetreeto(ser->ch[], to);
     if(ser->ch[] != NULL) mergetreeto(ser->ch[], to);
     insert(to, ser->v);
     delete ser;
     ser = NULL;
 }

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

 void add_edge(int id) {
     int x = findpa(pa[from[id]]);
     int y = findpa(pa[to[id]]);
     if(x != y) {
         if(root[x]->s < root[y]->s) mergetreeto(root[x], root[y]), pa[x] = y;
         else mergetreeto(root[y], root[x]), pa[y] = x;
     }
 }

 void querycnt(int x, int k) {
     cnt++;
     sum += kth(root[findpa(x)], k);
 }

 void change_w(int x, int v) {
     int u = findpa(pa[x]);
     remove(root[u], weight[x]);
     insert(root[u], v);
     weight[x] = v;
 }

 void init() {
     cmds.clear();
     cnt = ;
     sum = ;
     memset(removed, , sizeof removed);
     for(int i = ; i < n; i++) removetree(root[i]);
 }
 int main() {
     int kase = ;
     while(scanf("%d%d", &n, &m) ==  && n) {
         for(int i = ; i <= n; i++) scanf("%d", &weight[i]);
         for(int i = ; i <= m; i++) {
             int u, v;
             scanf("%d%d", &u, &v);
             from[i] = u;
             to[i] = v;
         }
         init();
         while() {
             getchar();
             char ch;
             scanf("%c", &ch);
             cmd C;
             C.type = ch;
             C.x = C.p = ;
             if(ch == 'E') break;
             scanf("%d", &C.x);
             if(ch == 'D') removed[C.x] = ;
             if(ch == 'Q') scanf("%d", &C.p);
             if(ch == 'C') {
                 scanf("%d", &C.p);
                 swap(C.p, weight[C.x]);
             }
             cmds.push_back(C);
         }
         for(int i = ; i <= n; i++) {
             pa[i] = i;
             root[i] = new Node(weight[i]);
         }
         for(int i = ; i <= m; i++)
             if(!removed[i]) add_edge(i);

         for(int i = cmds.size()-; i >= ; i--) {
             cmd C = cmds[i];
             if(C.type == 'D') add_edge(C.x);
             if(C.type == 'C') change_w(C.x, C.p);
             if(C.type == 'Q') querycnt(C.x, C.p);
         }
         printf("Case %d: %.6lf\n", ++kase, sum/double(cnt));
     }
     return ;
 }