1066 Root of AVL Tree (25)（25 分）

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.

 

 

 

Now given a sequence of insertions, you are supposed to tell the root of the resulting AVL tree.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (<=20) which is the total number of keys to be inserted. Then N distinct integer keys are given in the next line. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print the root of the resulting AVL tree in one line.

Sample Input 1:

5

88 70 61 96 120

Sample Output 1:

70

Sample Input 2:

7

88 70 61 96 120 90 65

Sample Output 2:

88

 

题意：

给出AVL树的插入顺序，要求构建AVL树，并输出根结点的值。

 

思路：

AVL模板题，原理不赘述。详见《算法笔记》。

需要引起注意的是，若操作会改变结点的地址，则要

引用传值。如insert()，leftRotation()，rightRotation()操作。而updateHeight()操作只是改变了结点的数据域，并未改变结点的地址，所以无需加引用（当然，加引用也没关系）。

 

代码：

#include 
          
           #include 
           
            using namespace std;struct Node{    int val;    int height;//以该结点为根结点的子树高度    Node *lchild,*rchild;    Node(int v):val(v),height(1),lchild(nullptr),rchild(nullptr){}};int getHeight(Node* pNode){    if(pNode==nullptr) return 0;    else return pNode->height;}int getBalancedFactor(Node* pNode){    return getHeight(pNode->lchild)-getHeight(pNode->rchild);}void updateHeight(Node* pNode){    pNode->height=max(getHeight(pNode->lchild),getHeight(pNode->rchild))+1;}void leftRotation(Node* &pNode){    Node* temp=pNode->rchild;    pNode->rchild=temp->lchild;    temp->lchild=pNode;    updateHeight(pNode);    updateHeight(temp);    pNode=temp;}void rightRotation(Node* &pNode){    Node* temp=pNode->lchild;    pNode->lchild=temp->rchild;    temp->rchild=pNode;    updateHeight(pNode);    updateHeight(temp);    pNode=temp;}void insert(Node* &root,int val){    if(root==nullptr){        root=new Node(val);        return;    }    if(val < root->val){        insert(root->lchild,val);        updateHeight(root);        if(getBalancedFactor(root)==2){            if(getBalancedFactor(root->lchild)==1){
        //LL型                rightRotation(root);            }else if(getBalancedFactor(root->lchild)==-1){
        //LR型                leftRotation(root->lchild);                rightRotation(root);            }        }    }else{        insert(root->rchild,val);        updateHeight(root);        if(getBalancedFactor(root)==-2){            if(getBalancedFactor(root->rchild)==-1){
        //RR型                leftRotation(root);            }else if(getBalancedFactor(root->rchild)==1){
        //RL型                rightRotation(root->rchild);                leftRotation(root);            }        }    }}int main(){    int n,val;    Node* root=nullptr;    scanf("%d",&n);    for(int i=0;i
            
             val);    return 0;}