1123. Is It a Complete AVL Tree(AVL树旋转、判断完全二叉树)

Is It a Complete AVL Tree (30)
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

题目说明：根据AVL树的插入规则，输入一段数字，根据输入的数字构建 AVL树。然后，根据层序遍历输出对应的数字，之后再判断这棵AVL树是否是完全二叉树。
分析要点：这道题首先要解决的问题是引起AVL树不平衡的插入的四种情况（设结点A为不平衡结点）：
1.新插入的结点在A的左子树的左子树。
2.新插入的结点在A的左子树的右子树。
3.新插入的结点在A的右子树的左子树。