Treap实现山寨set

treap插入、删除、查询时间复杂度均为O(logn)

treap树中每个节点有两种权值：键值和该节点优先值

如果只看优先值，这棵树又是一个堆

treap有两种平衡方法：左旋&右旋

insert 插入

remove 删除

_find 查找

kth 返回root为根的树中第k大的元素

 #include <iostream>
 #include <cstring>
 #include <cstdlib>
 #include <ctime>
 #include <cstdio>
 using namespace std;

 struct Node
 {
     Node* ch[];
     int r,v,s;    //r:随机优先级，v:值，s:以本节点为根的子树的结点总数
     bool operator < (const Node& rhs)
     {
         return (r<rhs.r);
     }
     int cmp(int x)
     {
         if (x==v) return -;
         return x<v?:;
     }
     void maintain()
     {
         s=;
         if (ch[]!=NULL) s+=ch[]->s;
         if (ch[]!=NULL) s+=ch[]->s;
     }
     Node (int v):v(v)        //结构体的构造函数
     {
         ch[]=ch[]=NULL;
         r=rand();
         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=o->cmp(x);        //不用cmp
         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);
     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();
 }

 int kth(Node* o,int k)
 {
     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-);

 }

 int _find(Node* o,int x)
 {
     while (o!=NULL)
     {
         int d=o->cmp(x);
         if (d==-)
             return ;
         else
             o=o->ch[d];
     }
     return ;
 }

 int main()
 {
     //freopen("in.txt","r",stdin);

     int n,m,opr,x;
     srand(time());
     cin>>n;
     Node* root=new Node();
     for (int i=;i<=n;i++)
     {
         cin>>opr>>x;
         if (opr==)
         {
             insert(root,x);
         }
         else if (opr==)
         {
             if (!_find(root,x))
                 cout<<"Not Found,Operation Failed"<<endl;
             else
                 remove(root,x);
         }
     }
     cout<<"-----------------"<<endl;
     cin>>m;
     for (int i=;i<=m;i++)
     {
         cin>>x;
         if (_find(root,x))
             cout<<"Found"<<endl;
         else
             cout<<"Not Found"<<endl;
     }
     cout<<"-----------------"<<endl;
     cin>>m;
     for (int i=;i<=m;i++)
     {
         cin>>x;
         int ans=kth(root,x);
         cout<<x<<"th: "<<ans<<endl;
     }
 }

PS：发现一个画图论图形的神器：GraphViz