解析：这题我学了一天AVL树的调整，建好了树，又用了一个多小时尝试各种方法判断是否为完全二叉树，最后败在了输出层次遍历上。。

解题步骤：

• 建立AVL树，其中涉及AVL树的四种调整
• 输出层次遍历，用队列输出，不能用stack！
• 判断一棵树是否为完全二叉树，可以给每个节点编号，比如某个节点编号为id，它左儿子为2*id,右儿子为2*id+1，如果最大的编号为n，即为完全二叉树。（这也是完全二叉树的一个性质）

代码示例：

#include<iostream>
#include<cstdio>
#include<queue>
using namespace std;
typedef struct AVLNode *position;
typedef position AVLTree;
int maxid = -1;
struct AVLNode{
    int data;
    AVLTree left;
    AVLTree right;
    int h;
};
int GetHight(AVLTree A){
    if(A == NULL)	return -1;
    return A->h;
}
//左单旋
AVLTree SLR(AVLTree A){
    AVLTree B = A->left;
    A->left = B->right;
    B->right = A;
    A->h = max(GetHight(A->left),GetHight(A->right))+1;
    B->h = max(GetHight(B->left),GetHight(B->right))+1;
    return B;
} 
//右单旋
AVLTree SRR(AVLTree A){
    AVLTree B = A->right;
    A-> right = B->left;
    B->left = A;
    A->h = max(GetHight(A->left),GetHight(A->right))+1;
    B->h = max(GetHight(B->left),GetHight(B->right))+1;
    return B;
}
//左右双旋
AVLTree DLRR(AVLTree A){
    AVLTree B = A->left;
    A->left = SRR(B);
    return SLR(A);
}
//右左双旋 
AVLTree DRLR(AVLTree A){
    AVLTree B = A->right;
    A->right = SLR(B);
    return SRR(A);
}
AVLTree Insert(AVLTree T,int x){
    if(T == NULL){
        T = new AVLNode();
        T->data = x;
        T->left = NULL;
        T->right = NULL;
        T->h = 0;
    }else if(x < T->data){
        T->left = Insert(T->left,x);
        if(GetHight(T->left) - GetHight(T->right) == 2)
            if(x < T->left->data)	T = SLR(T);
            else T = DLRR(T);
    }else if(x > T->data){
        T->right = Insert(T->right,x);
        if(GetHight(T->left)-GetHight(T->right) == -2)
            if(x > T->right->data)	T = SRR(T);
            else	T = DRLR(T);
    }
    T->h = max(GetHight(T->left),GetHight(T->right))+1;
    return T;
}
void printTree(AVLTree T){
    if(!T)	return;
    queue<AVLTree> q;
    q.push(T);
    int cnt = 0;
    while(q.size()){
        AVLTree a = q.front();
        q.pop();
        if(cnt == 0)	printf("%d",a->data);
        else	printf(" %d",a->data);
        cnt++;
        if(a->left)	q.push(a->left);
        if(a->right)	q.push(a->right);
    } 
    printf("\n");
}
void solve(AVLTree T,int id){
    maxid = max(id,maxid);
    if(T->left)	solve(T->left,id<<1);
    if(T->right)	solve(T->right,id<<1|1);
    return;
}
bool judge(AVLTree T,int n){
    solve(T,1);
    if(maxid != n)	return false;
    return true;
}
int main()
{
    int n,x;
    scanf("%d",&n);
    AVLTree T = NULL;
    for(int i = 0;i < n;i++){
        scanf("%d",&x);
        T = Insert(T,x);
    }
    if(n == 0)	puts("NO");
    else{
        printTree(T);
        if(judge(T,n))	puts("YES");
        else puts("NO");
    }
    
    return 0;
}