判断题
1.The inorder traversal sequence of an AVL tree must be in sorted (non-decreasing) order.
2.Insert 1, 2, 3, 4, 5, and 6 one by one into an initially empty AVL tree. Then the preorder traversal sequence of the resulting tree must be {4, 2, 1, 3, 5, 6}.
3.For any node in an AVL tree, the height of the left subtree must be greater than that of the right subtree.
4.For an AVL tree, the balance factors of all the non-leaf nodes are 0 iff the tree is a complete binary tree.
5.If the depth of an AVL tree with nodes { 1, 2, 3, 4 } is 3 (the depth of the root is 1), then either node 2 or node 3 must have two children.
6.任何AVL树的中序遍历结果是有序的（从小到大）。
7.将1、2、3、4、5、6顺序插入初始为空的AVL树中，当完成这6个元素的插入后，该AVL树的先序遍历结果是：4、2、1、3、5、6。
8.For any node in an AVL tree, the height of the right subtree must be greater than that of the left subtree.
9.对AVL树中的任一结点，其左子树的高度一定比其右子树的高度要高。
10.An AVL tree with the balance factors of all the non-leaf nodes being 0 must be a perfect binary tree.
11.对一棵平衡二叉树，所有非叶结点的平衡因子都是0，当且仅当该树是完全二叉树。
12.若一棵平衡二叉树的所有非叶结点的平衡因子都是0，则其必为完美二叉树。
13.If the depth of an AVL tree with nodes { 1, 2, 3, 4 } is 3 (the depth of the root is 1), then it is possible for node 4 to be the root.
14.如果由结点{ 1, 2, 3, 4 }组成的AVL树的深度是3（根结点的深度是1），则结点2或者结点3一定有两个子结点。
15.如果由结点{ 1, 2, 3, 4 }组成的AVL树的深度是3（根结点的深度是1），则结点4有可能是根结点。
选择题
1.Which of the following is TRUE for any node in an AVL tree?
B.The absolute value of the difference between the heights of left and right subtrees is no more than 1
C.The height of the left subtree is always greater than that of the right subtree
D.The height of the left subtree is always less than that of the right subtree
2.Insert key 48 into the balanced binary tree shown by the figure. Then in the resulting balanced tree, the left- and right-child of key 37 are:
B.24 and 48
C.24 and 53
D.24 and 90
3.Insert 2, 1, 4, 5, 9, 3, 6, 7 into an initially empty AVL tree. Which one of the following statements is FALSE?
B.3 and 7 are siblings
C.2 and 6 are siblings
D.9 is the parent of 7
4.If the depth of an AVL tree is 5 (the depth of an empty tree is defined to be ?1), then the minimum possible number of nodes in this tree is:
B.20
C.33
D.64
5.Insert { 9, 8, 7, 2, 3, 5, 6, 4} into an initially empty AVL tree. Which one of the following statements is FALSE?
B.2 and 5 are siblings
C.there are 2 nodes with their balance factors being -1
D.the height of the resulting AVL tree is 3
6.After inserting 28, 22, and 35 into the given AVL tree, the children of node 25 are __。
B.20 and 28
C.22 and 30
D.20 and 30
7.下列二叉搜索树中，满足平衡二叉树定义的是：
B.
C.
D.
8.在下列所示的平衡二叉树中，插入关键字48后得到一棵新平衡二叉树。在新平衡二叉树中，关键字37所在结点的左、右子结点中保存的关键字分别是：
B.24、48
C.24、53
D.24、90
9.12个结点的AVL树的最大深度是？
B.4
C.5
D.6
10.若AVL树的深度是6（空树的深度定义为-1），则该树的最少结点数是：
B.17
C.20
D.33
11.Among the following trees, which one satisfies the definition of a balanced tree?
B.
C.
D.
12.The maximum possible depth of an AVL tree with 12 nodes is:
B.4
C.5
D.6
13.Insert {88, 70, 61, 96, 120, 90} one by one into an initially empty AVL tree. Then the preorder traversal sequence of the resulting AVL tree is:
B.90,70,61,88,96,120
C.88,70,61,90,96,120
D.88,70,61,96,90,120
14.If the depth of an AVL tree is 6 (the depth of an empty tree is defined to be -1), then the minimum possible number of nodes in this tree is:
B.17
C.20
D.33
15.将 2, 1, 4, 5, 9, 3, 6, 7 顺序插入一棵初始为空的AVL树。下列句子中哪句是错的？
B.3 和 7 是兄弟
C.2 和 6 是兄弟
D.9 是 7 的父结点
16.如果AVL树的深度为5（空树的深度定义为-1），则此树最少有多少个结点？
B.20
C.33
D.64
17.如果AVL树的深度为6（空树的深度定义为-1），则此树最少有多少个结点？
B.20
C.33
D.64
18.将一系列数字顺序一个个插入一棵初始为空的AVL树。下面哪个系列的第一次旋转是"右-左"双旋？
B.6,5,4,3,2,1
C.4,2,5,6,3,1
D.3,1,4,6,5,2
19.将 1, 2, 3, 6, 5, 4 顺序一个个插入一棵初始为空的AVL树，会经历下列哪些旋转？
B.一个"右-右"旋、一个"右-左"旋、一个"左-右"旋
C.一个"右-右"旋和两个"右-左"旋
D.两个"右-右"旋和一个"左-右"旋
20.在任意一棵非空平衡二叉树（AVL 树）T1 中，删除某结点 v 之后形成平衡二叉树 T2，再将 v 插入 T2 形成平衡二叉树 T3。下列关于 T1 与 T3 的叙述中，正确的是：
- I、若 v 是 T1 的叶结点，则 T1 与 T3 可能不相同
- II、若 v 不是 T1 的叶结点，则 T1 与 T3 一定不同
- III、若 v 不是 T1 的叶结点，则 T1 与 T3 一定相同
B.仅 II
C.仅 I、II
D.仅 I、III