1123 Is It a Complete AVL Tree （30 分）--PAT甲级

1123 Is It a Complete AVL Tree （30 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 output the level-order traversal sequence of the resulting AVL tree, and to tell if it is a complete binary tree.
Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (≤ 20). 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, insert the keys one by one into an initially empty AVL tree. Then first print in a line the level-order traversal sequence of the resulting AVL tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line. Then in the next line, print YES if the tree is complete, or NO if not.
Sample Input 1:

5
88 70 61 63 65

Sample Output 1:

70 63 88 61 65
YES

Sample Input 2:

8
88 70 61 96 120 90 65 68

Sample Output 2:

88 65 96 61 70 90 120 68
NO

平衡二叉树的基本操作，主要是插入时的旋转方式。参考算法笔记。
LL：根平衡因子为2，左子树为1，对根进行右旋；
LR：根平衡因子为2，左子树为-1，先对左子树进行左旋，再对根进行右旋；
RR：根平衡因子为-2，右子树为-1，对根进行左旋；
RL：根平衡因子为-2，右子树为1，先对右子树进行右旋，再对根进行左旋。
用队列层序输出时，判断第一个无孩子结点之后输出的结点是否有孩子，用来判断是否是完全二叉树。

#include
#include
#include
using namespace std;
const int maxn = 10010;
struct node{
    int val;
    int height;
    node* left;
    node* right;
};

node* newNode(int v){
    node* root = new node;
    root->val=v;
    root->height=1;
    root->left=root->right=NULL;
    return root;
}
int getHeight(node *root){
    if(root==NULL) return 0;
    return root->height;
}
int getBalance(node* root){//获取平衡因子
    return getHeight(root->left) - getHeight(root->right);
}
void updateHeight(node* &root){//更新树高
    root->height = max(getHeight(root->left),getHeight(root->right))+1;
}
void leftRotate(node* &root){
    node* temp=root->right;
    root->right=temp->left;
    temp->left=root;
    updateHeight(root);
    updateHeight(temp);
    root=temp;
}
void rightRotate(node* &root){
    node* temp=root->left;
    root->left=temp->right;
    temp->right=root;
    updateHeight(root);
    updateHeight(temp);
    root=temp;
}
void insertNode(node* &root,int v){
    if(root==NULL){
        root=newNode(v);
        return;
    }
    if(root->val > v){
        insertNode(root->left,v);
        updateHeight(root);
        if(getBalance(root)==2){
            if(getBalance(root->left)==1){
                rightRotate(root);
            }
            else if(getBalance(root->left)==-1){
                leftRotate(root->left);
                rightRotate(root);
            }
        }
    }
    else {
        insertNode(root->right,v);
        updateHeight(root);
        if(getBalance(root)==-2){
            if(getBalance(root->right)==-1){
                leftRotate(root);
            }
            else if(getBalance(root->right)==1){
                rightRotate(root->right);
                leftRotate(root);
            }
        }
    }
}


int main()
{
    int n;
    scanf("%d",&n);
    node* root=NULL;
    for(int i=0;i<n;i++){
        int t;
        scanf("%d",&t);
        insertNode(root,t);
    }
  //  inorder(root);
    queue<node*>q;
    q.push(root);
    bool flag=true;
    bool havechild=true;
    while(!q.empty()){
        int sum=q.size();
        for(int i=0;i<sum;i++){
            node* now=q.front();
            if(now->left!=NULL) {
                q.push(now->left);
                if(!havechild) flag=false;
            }
            else havechild=false;
            if(now->right!=NULL) {
                q.push(now->right);
                if(!havechild) flag=false;
            }
            else havechild=false;
            if(now==root) printf("%d",now->val);
            else printf(" %d",now->val);
            q.pop();
        }
    }
    printf("\n");
    if(flag) printf("YES\n");
    else printf("NO\n");
    return 0;
}