AVL树

AVL树是一种自平衡二叉查找树。它的平衡因子等于它的左子树的高度减去它的右子树的高度。只有平衡因子等于1，0，-1的结点是平衡的，不平衡的结点需要通过旋转来保持平衡。因此，在AVL树中任何结点的两个子树的高度差的最大值为1。

google到了一篇代码很简洁易懂的文章，将其中的代码整理了一下：

  1 //AVL Tree
  2 #include 
  3 #include 
  4 using namespace std;
  5 
  6 typedef int Type;
  7 
  8 struct avl_node{
  9     Type data;
 10     avl_node *lchild, *rchild;
 11 }*root;
 12 
 13 
 14 class avlTree{
 15 public:
 16     avlTree(){
 17         root=NULL;
 18     }
 19 
 20     ~avlTree(){
 21         delete_tree(root);
 22     }
 23 
 24     void delete_tree(avl_node *node){
 25         if(node->lchild!=NULL){
 26             delete_tree(node->lchild);
 27         }
 28         if(node->rchild!=NULL){
 29             delete_tree(node->rchild);
 30         }
 31         delete node;
 32         node=NULL;
 33     }
 34 
 35     //get height of a node
 36     //the height of one single node is 1 (not 0)
 37     int height(avl_node* node){
 38         if(node==NULL) return 0;
 39         int left_h=height(node->lchild);
 40         int right_h=height(node->rchild);
 41         return max(left_h,right_h)+1;
 42     }
 43     
 44     //get difference of height of the node's left tree and right tree
 45     //node will not be NULL
 46     //calculated by left-right
 47     int diff(avl_node* node){
 48         int left_h=height(node->lchild);
 49         int right_h=height(node->rchild);
 50         return left_h-right_h;
 51     }
 52     
 53     avl_node* RR_rotation(avl_node* head){
 54         avl_node* temp=head->rchild;
 55         head->rchild=temp->lchild;
 56         temp->lchild=head;
 57         return temp;
 58     }
 59     
 60     avl_node* LL_rotation(avl_node* head){
 61         avl_node* temp=head->lchild;
 62         head->lchild=temp->rchild;
 63         temp->rchild=head;
 64         return temp;
 65     }
 66     
 67     avl_node* LR_rotation(avl_node* head){
 68         head->lchild=RR_rotation(head->lchild);
 69         return LL_rotation(head);
 70     }
 71     
 72     avl_node* RL_rotation(avl_node* head){
 73         head->rchild=LL_rotation(head->rchild);
 74         return RR_rotation(head);
 75     }
 76     
 77     //recursively check and keep the tree balanced
 78     avl_node* balance(avl_node* head){
 79         int bal_factor=diff(head);
 80         //balance factor==2
 81         if(bal_factor>1){
 82             if(diff(head->lchild)>0){
 83                 head=LL_rotation(head);
 84             }
 85             else{
 86                 head=LR_rotation(head);
 87             }
 88         }
 89         //balance factor=-2
 90         else if(bal_factor<-1){
 91             if(diff(head->rchild)>0){
 92                 head=RL_rotation(head);
 93             }
 94             else{
 95                 head=RR_rotation(head);
 96             }
 97         }
 98         return head;
 99     }
100     
101     avl_node* insert(avl_node* root, Type value){
102         if(root==NULL){
103             root=new avl_node;
104             root->data=value;
105             root->lchild=NULL;
106             root->rchild=NULL;
107             return root;
108         }
109         else if(valuedata){
110             root->lchild=insert(root->lchild,value);
111             root=balance(root);
112         }
113         else if(value>root->data){
114             root->rchild=insert(root->rchild,value);
115             root=balance(root);
116         }
117         return root;
118     }
119     
120     //an interesting way to display the tree horizontally
121     void display(avl_node* cur, int level){
122         if(cur!=NULL){
123             display(cur->rchild, level+1);
124             cout<<endl;
125             if(cur==root){
126                 cout<<"Root-> ";
127             }
128             for(int i=0;i){
129                 cout<<"        ";
130             }
131             cout<data;
132             display(cur->lchild, level+1);
133         }
134     }
135     
136     void preorder(avl_node* cur){
137         if(cur==NULL) return;
138         cout<data<<" ";
139         preorder(cur->lchild);
140         preorder(cur->rchild);
141     }
142     
143     void inorder(avl_node* cur){
144         if(cur==NULL) return;
145         inorder(cur->lchild);
146         cout<data<<" ";
147         inorder(cur->rchild);
148     }
149     
150     void postorder(avl_node* cur){
151         if(cur==NULL) return;
152         postorder(cur->lchild);
153         postorder(cur->rchild);
154         cout<data<<" ";
155     }
156 };
157 
158 
159 
160 //for testing
161 int main()
162 {
163     int choice;
164     Type item;
165     avlTree avl;
166     while (1)
167     {
168         cout<<"\n---------------------"<<endl;
169         cout<<"AVL Tree Implementation"<<endl;
170         cout<<"\n---------------------"<<endl;
171         cout<<"1.Insert Element into the tree"<<endl;
172         cout<<"2.Display Balanced AVL Tree"<<endl;
173         cout<<"3.InOrder traversal"<<endl;
174         cout<<"4.PreOrder traversal"<<endl;
175         cout<<"5.PostOrder traversal"<<endl;
176         cout<<"6.Exit"<<endl;
177         cout<<"Enter your Choice: ";
178         cin>>choice;
179         switch(choice)
180         {
181             case 1:
182                 cout<<"Enter value to be inserted: ";
183                 cin>>item;
184                 root = avl.insert(root, item);
185                 break;
186             case 2:
187                 if (root == NULL)
188                 {
189                     cout<<"Tree is Empty"<<endl;
190                     continue;
191                 }
192                 cout<<"Balanced AVL Tree:"<<endl;
193                 avl.display(root, 1);
194                 break;
195             case 3:
196                 cout<<"Inorder Traversal:"<<endl;
197                 avl.inorder(root);
198                 cout<<endl;
199                 break;
200             case 4:
201                 cout<<"Preorder Traversal:"<<endl;
202                 avl.preorder(root);
203                 cout<<endl;
204                 break;
205             case 5:
206                 cout<<"Postorder Traversal:"<<endl;
207                 avl.postorder(root);
208                 cout<<endl;
209                 break;
210             case 6:
211                 exit(1);
212                 break;
213             default:
214                 cout<<"Wrong Choice"<<endl;
215         }
216     }
217     return 0;
218 }

 

测试结果和原文请见：http://www.sanfoundry.com/cpp-program-implement-avl-trees/

 

转载于:https://www.cnblogs.com/NoviScl/p/7055863.html