判斷題
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樹的中序遍歷結果是有序的（從小到大）。
7.將1、2、3、4、5、6順序插入初始為空的AVL樹中，當完成這6個元素的插入后，該AVL樹的先序遍歷結果是：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.對AVL樹中的任一結點，其左子樹的高度一定比其右子樹的高度要高。
10.An AVL tree with the balance factors of all the non-leaf nodes being 0 must be a perfect binary tree.
11.對一棵平衡二叉樹，所有非葉結點的平衡因子都是0，當且僅當該樹是完全二叉樹。
12.若一棵平衡二叉樹的所有非葉結點的平衡因子都是0，則其必為完美二叉樹。
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.如果由結點{ 1, 2, 3, 4 }組成的AVL樹的深度是3（根結點的深度是1），則結點2或者結點3一定有兩個子結點。
15.如果由結點{ 1, 2, 3, 4 }組成的AVL樹的深度是3（根結點的深度是1），則結點4有可能是根結點。
選擇題
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.下列二叉搜索樹中，滿足平衡二叉樹定義的是：
B.
C.
D.
8.在下列所示的平衡二叉樹中，插入關鍵字48后得到一棵新平衡二叉樹。在新平衡二叉樹中，關鍵字37所在結點的左、右子結點中保存的關鍵字分別是：
B.24、48
C.24、53
D.24、90
9.12個結點的AVL樹的最大深度是？
B.4
C.5
D.6
10.若AVL樹的深度是6（空樹的深度定義為-1），則該樹的最少結點數是：
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.將 2, 1, 4, 5, 9, 3, 6, 7 順序插入一棵初始為空的AVL樹。下列句子中哪句是錯的？
B.3 和 7 是兄弟
C.2 和 6 是兄弟
D.9 是 7 的父結點
16.如果AVL樹的深度為5（空樹的深度定義為-1），則此樹最少有多少個結點？
B.20
C.33
D.64
17.如果AVL樹的深度為6（空樹的深度定義為-1），則此樹最少有多少個結點？
B.20
C.33
D.64
18.將一系列數字順序一個個插入一棵初始為空的AVL樹。下面哪個系列的第一次旋轉是"右-左"雙旋？
B.6,5,4,3,2,1
C.4,2,5,6,3,1
D.3,1,4,6,5,2
19.將 1, 2, 3, 6, 5, 4 順序一個個插入一棵初始為空的AVL樹，會經歷下列哪些旋轉？
B.一個"右-右"旋、一個"右-左"旋、一個"左-右"旋
C.一個"右-右"旋和兩個"右-左"旋
D.兩個"右-右"旋和一個"左-右"旋
20.在任意一棵非空平衡二叉樹（AVL 樹）T1 中，刪除某結點 v 之后形成平衡二叉樹 T2，再將 v 插入 T2 形成平衡二叉樹 T3。下列關於 T1 與 T3 的敘述中，正確的是：
- I、若 v 是 T1 的葉結點，則 T1 與 T3 可能不相同
- II、若 v 不是 T1 的葉結點，則 T1 與 T3 一定不同
- III、若 v 不是 T1 的葉結點，則 T1 與 T3 一定相同
B.僅 II
C.僅 I、II
D.僅 I、III