思路：
考察的点是建立AVL树以及如何判断是否为满二叉树。
建立AVL树需要搞清楚LL、LR、RR、RL四种情况如何左旋和右旋，如下：
| 类型 | BF条件 | 操作 |
|---|---|---|
| LL | BF(root)=2,BF(root->lchild)=1 | root右旋 |
| LR | BF(root)=2,BF(root->lchild)=-1 | 先root->lchild左旋，再root右旋 |
| RR | BF(root)=-2,BF(root->rchild)=-1 | root左旋 |
| RL | BF(root)=-2,BF(root->rchild)=1 | 先root->rchild右旋，再root左旋 |
接着是用bfs遍历判断是否为满二叉树：
按照层序遍历的方式（但遇到空结点也需要放入队列），将各个结点放入队列中，直到从队列拿出来的结点是空的。按照完全二叉树的定义，只有最后一层才能是有空结点，并且结点朝左排列。如果我们此时依次将队列前部的空结点全部拿出，队列应该最后是空的，此时证明是完全二叉树的。
#include<bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
typedef long long ll;struct node {int data;int height;node* lchild;node* rchild;
};int getHeight(node* tnode)
{if (tnode == NULL) return 0;else return tnode->height;
}void UpdateHeight(node* tnode)
{tnode->height = max(getHeight(tnode->lchild), getHeight(tnode->rchild)) + 1;
}int getBF(node* tnode)
{return getHeight(tnode->lchild) - getHeight(tnode->rchild);
}void L(node*& tnode)
{node* temp = tnode->rchild;tnode->rchild = temp->lchild;temp->lchild = tnode;UpdateHeight(tnode);UpdateHeight(temp);tnode = temp;
}void R(node*& tnode)
{node* temp = tnode->lchild;tnode->lchild = temp->rchild;temp->rchild = tnode;UpdateHeight(tnode);UpdateHeight(temp);tnode = temp;
}node* newnode(int v)
{node* tnode = new node;tnode->data = v;tnode->height = 1;tnode->lchild = tnode->rchild = NULL;return tnode;
}void insert(node*& root, int v)
{if (root == NULL){root = newnode(v);return;}if (v < root->data){insert(root->lchild, v);UpdateHeight(root);if (getBF(root) == 2){if (getBF(root->lchild) == 1){R(root);}else if (getBF(root->lchild) == -1){L(root->lchild);R(root);}}}else{insert(root->rchild, v);UpdateHeight(root);if (getBF(root) == -2){if (getBF(root->rchild) == -1){L(root);}else if (getBF(root->rchild) == 1){R(root->rchild);L(root);}}}
}node* create()
{int n;cin >> n;node* root = NULL;for (int i = 0; i < n; i++){int t;cin >> t;insert(root, t);}return root;
}void bfs(node* root)
{vector<int> res;queue<node*> q;node* t;q.push(root);while (!q.empty()){t = q.front();q.pop();res.emplace_back(t->data);if (t->lchild) q.push(t->lchild);if (t->rchild) q.push(t->rchild);}for (int i = 0; i < res.size(); i++)if (i == 0) cout << res[0];else cout << " " << res[i];cout << endl;
}void checkCompleteBinary(node* root)
{queue<node*> q;node* t;q.push(root);while (!q.empty()){t = q.front();q.pop();if (t == NULL) break;q.push(t->lchild);q.push(t->rchild);}while (!q.empty() && q.front() == NULL)q.pop();if (q.empty()) cout << "YES";else cout << "NO";
}int main()
{ios::sync_with_stdio(false);cin.tie(nullptr);node* root = create();bfs(root);checkCompleteBinary(root);return 0;
}
...)
