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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,142 @@ | ||
| #include<iostream> | ||
| using namespace std; | ||
|
|
||
| //定义AVL节点结构体 | ||
| struct AVLNode{ | ||
| int key; //节点关键字 | ||
| int height; //节点高度 | ||
| AVLNode *left; //左子节点 | ||
| AVLNode *right; //右子节点 | ||
| AVLNode(int k):key(k),height(1),left(NULL),right(NULL){} //构造函数 | ||
| }; | ||
|
|
||
| //获取节点高度 | ||
| int getHeight(AVLNode *node){ | ||
| if(node==NULL) return 0; | ||
| return node->height; | ||
| } | ||
|
|
||
| //获取节点平衡因子 | ||
| int getBalance(AVLNode *node){ | ||
| if(node==NULL) return 0; | ||
| return getHeight(node->left)-getHeight(node->right); | ||
| } | ||
|
|
||
| //更新节点高度 | ||
| void updateHeight(AVLNode *node){ | ||
| node->height=max(getHeight(node->left),getHeight(node->right))+1; | ||
| } | ||
|
|
||
| //左旋 | ||
| AVLNode* leftRotate(AVLNode *node){ | ||
| AVLNode *r=node->right; | ||
| AVLNode *rl=r->left; | ||
| r->left=node; | ||
| node->right=rl; | ||
| updateHeight(node); | ||
| updateHeight(r); | ||
| return r; | ||
| } | ||
|
|
||
| //右旋 | ||
| AVLNode* rightRotate(AVLNode *node){ | ||
| AVLNode *l=node->left; | ||
| AVLNode *lr=l->right; | ||
| l->right=node; | ||
| node->left=lr; | ||
| updateHeight(node); | ||
| updateHeight(l); | ||
| return l; | ||
| } | ||
|
|
||
| //插入节点 | ||
| AVLNode* insertNode(AVLNode *node,int key){ | ||
| if(node==NULL) return new AVLNode(key); | ||
| if(key<node->key) node->left=insertNode(node->left,key); | ||
| else node->right=insertNode(node->right,key); | ||
| updateHeight(node); | ||
| int balance=getBalance(node); | ||
| if(balance>1 && key<node->left->key) return rightRotate(node); | ||
| if(balance>1 && key>node->left->key){ | ||
| node->left=leftRotate(node->left); | ||
| return rightRotate(node); | ||
| } | ||
| if(balance<-1 && key>node->right->key) return leftRotate(node); | ||
| if(balance<-1 && key<node->right->key){ | ||
| node->right=rightRotate(node->right); | ||
| return leftRotate(node); | ||
| } | ||
| return node; | ||
| } | ||
|
|
||
| //查找节点 | ||
| AVLNode* searchNode(AVLNode *node,int key){ | ||
| if(node==NULL || node->key==key) return node; | ||
| if(key<node->key) return searchNode(node->left,key); | ||
| else return searchNode(node->right,key); | ||
| } | ||
|
|
||
| //删除节点 | ||
| AVLNode* deleteNode(AVLNode *node,int key){ | ||
| if(node==NULL) return node; | ||
| if(key<node->key) node->left=deleteNode(node->left,key); | ||
| else if(key>node->key) node->right=deleteNode(node->right,key); | ||
| else{ | ||
| if(node->left==NULL || node->right==NULL){ | ||
| AVLNode *temp=node->left?node->left:node->right; | ||
| if(temp==NULL){ | ||
| temp=node; | ||
| node=NULL; | ||
| } | ||
| else *node=*temp; | ||
| delete temp; | ||
| } | ||
| else{ | ||
| AVLNode *temp=node->right; | ||
| while(temp->left!=NULL) temp=temp->left; | ||
| node->key=temp->key; | ||
| node->right=deleteNode(node->right,temp->key); | ||
| } | ||
| } | ||
| if(node==NULL) return node; | ||
| updateHeight(node); | ||
| int balance=getBalance(node); | ||
| if(balance>1 && getBalance(node->left)>=0) return rightRotate(node); | ||
| if(balance>1 && getBalance(node->left)<0){ | ||
| node->left=leftRotate(node->left); | ||
| return rightRotate(node); | ||
| } | ||
| if(balance<-1 && getBalance(node->right)<=0) return leftRotate(node); | ||
| if(balance<-1 && getBalance(node->right)>0){ | ||
| node->right=rightRotate(node->right); | ||
| return leftRotate(node); | ||
| } | ||
| return node; | ||
| } | ||
|
|
||
| //中序遍历 | ||
| void inorderTraversal(AVLNode *node){ | ||
| if(node==NULL) return; | ||
| inorderTraversal(node->left); | ||
| cout<<node->key<<" "; | ||
| inorderTraversal(node->right); | ||
| } | ||
|
|
||
| //测试样例 | ||
| int main(){ | ||
| AVLNode *root=NULL; | ||
| root=insertNode(root,10); | ||
| root=insertNode(root,20); | ||
| root=insertNode(root,30); | ||
| root=insertNode(root,40); | ||
| root=insertNode(root,50); | ||
| root=insertNode(root,25); | ||
| cout<<"Inorder traversal of the AVL tree is:"<<endl; | ||
| inorderTraversal(root); | ||
| cout<<endl; | ||
| root=deleteNode(root,30); | ||
| cout<<"Inorder traversal of the AVL tree after deleting 30 is:"<<endl; | ||
| inorderTraversal(root); | ||
| cout<<endl; | ||
| return 0; | ||
| } |
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