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
1 #include <iostream> 2 #include <cstring> 3 #include <cstdlib> 4 #include <ctime> 5 #include <cstdio> 6 using namespace std; 7 8 struct Node 9 { 10 Node* ch[2]; 11 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 12 bool operator < (const Node& rhs) 13 { 14 return (r<rhs.r); 15 } 16 int cmp(int x) 17 { 18 if (x==v) return -1; 19 return x<v?0:1; 20 } 21 void maintain() 22 { 23 s=1; 24 if (ch[0]!=NULL) s+=ch[0]->s; 25 if (ch[1]!=NULL) s+=ch[1]->s; 26 } 27 Node (int v):v(v) //结构体的构造函数 28 { 29 ch[0]=ch[1]=NULL; 30 r=rand(); 31 s=1; 32 } 33 }; 34 35 void rotate(Node* &o,int d) 36 { 37 Node* k=o->ch[d^1]; 38 o->ch[d^1]=k->ch[d]; 39 k->ch[d]=o; 40 o->maintain(); 41 k->maintain(); 42 o=k; 43 } 44 45 void insert(Node* &o,int x) 46 { 47 if (o==NULL) 48 o=new Node(x); 49 else 50 { 51 //int d=o->cmp(x); //不用cmp 52 int d=(x < o->v ? 0 : 1); 53 insert(o->ch[d],x); 54 if (o->ch[d]->r > o->r) 55 rotate(o,d^1); 56 } 57 o->maintain(); 58 } 59 60 void remove(Node* &o,int x) 61 { 62 int d=o->cmp(x); 63 if (d==-1) 64 { 65 Node *u=o; 66 if ((o->ch[0]!=NULL) && (o->ch[1]!=NULL)) 67 { 68 int d2=(o->ch[0]->r > o->ch[1]->r ? 1 : 0); 69 rotate(o,d2); 70 remove(o->ch[d2],x); 71 } 72 else 73 { 74 if (o->ch[0]==NULL) 75 o=o->ch[1]; 76 else 77 o=o->ch[0]; 78 delete u; 79 } 80 } 81 else 82 remove(o->ch[d],x); 83 if (o!=NULL) 84 o->maintain(); 85 } 86 87 int kth(Node* o,int k) 88 { 89 if ((o==NULL)||(k<=0)||(k > o->s)) 90 return 0; 91 int s=(o->ch[1]==NULL ? 0 : o->ch[1]->s); 92 if (k==s+1) 93 return o->v; 94 else if (k<=s) 95 return kth(o->ch[1],k); 96 else 97 return kth(o->ch[0],k-s-1); 98 99 } 100 101 int _find(Node* o,int x) 102 { 103 while (o!=NULL) 104 { 105 int d=o->cmp(x); 106 if (d==-1) 107 return 1; 108 else 109 o=o->ch[d]; 110 } 111 return 0; 112 } 113 114 int main() 115 { 116 //freopen("in.txt","r",stdin); 117 118 int n,m,opr,x; 119 srand(time(0)); 120 cin>>n; 121 Node* root=new Node(0); 122 for (int i=1;i<=n;i++) 123 { 124 cin>>opr>>x; 125 if (opr==1) 126 { 127 insert(root,x); 128 } 129 else if (opr==2) 130 { 131 if (!_find(root,x)) 132 cout<<"Not Found,Operation Failed"<<endl; 133 else 134 remove(root,x); 135 } 136 } 137 cout<<"-----------------"<<endl; 138 cin>>m; 139 for (int i=1;i<=m;i++) 140 { 141 cin>>x; 142 if (_find(root,x)) 143 cout<<"Found"<<endl; 144 else 145 cout<<"Not Found"<<endl; 146 } 147 cout<<"-----------------"<<endl; 148 cin>>m; 149 for (int i=1;i<=m;i++) 150 { 151 cin>>x; 152 int ans=kth(root,x); 153 cout<<x<<"th: "<<ans<<endl; 154 } 155 }
PS：发现一个画图论图形的神器：GraphViz