uvalive 5031 Graph and Queries 名次树+Treap

题意：给你个点m条边的无向图，每个节点都有一个整数权值。你的任务是执行一系列操作。操作分为3种。。。

思路：本题一点要逆向来做，正向每次如果删边，复杂度太高。逆向到一定顺序的时候添加一条边更容易。详见算法指南P235。

 #include<cstdlib>

 struct Node
 {
     Node *ch[]; // 左右子树
     int r; // 随机优先级
     int v; // 值
     int s; // 结点总数
     Node(int v):v(v)
     {
         ch[] = ch[] = NULL;
         r = rand();
         s = ;
     }
     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 ?  : ); // 不要用cmp函数，因为可能会有相同结点
         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);
     int ret = ;
     if(d == -)
     {
         Node* u = o;
         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();
 }

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

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

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

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

 // 名次树相关
 Node* root[maxn]; // Treap

 int kth(Node* o, int k)   // 第k大的值
 {
     if(o == NULL || k <=  || k > o->s) 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-);
 }

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

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

 // 主程序相关
 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 = ;
     while(scanf("%d%d", &n, &m) ==  && n)
     {
         for(int i = ; i <= n; i++) scanf("%d", &weight[i]);
         for(int i = ; i <= m; i++) scanf("%d%d", &from[i], &to[i]);
         memset(removed, , sizeof(removed));

         // 读命令
         int c = ;
         for(;;)
         {
             char type;
             int x, p = , v = ;
             scanf(" %c", &type);
             if(type == 'E') break;
             scanf("%d", &x);
             if(type == 'D') removed[x] = ;
             if(type == 'Q') scanf("%d", &p);
             if(type == 'C')
             {
                 scanf("%d", &v);
                 p = weight[x];
                 weight[x] = v;
             }
             commands[c++] = (Command)
             {
                 type, x, p
             };
         }

         // 最终的图
         for(int i = ; i <= n; i++)
         {
             pa[i] = i;
             if(root[i] != NULL) removetree(root[i]);
             root[i] = new Node(weight[i]);
         }
         for(int i = ; i <= m; i++) if(!removed[i]) add_edge(i);

         // 反向操作
         query_tot = query_cnt = ;
         for(int i = c-; i >= ; 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 ;
 }