数据结构与算法（周测9-B树与B+树）

由于博主太菜，题目集还不完整，有待更新。

判断题

1.m阶B树的根结点最多有m棵子树。

    
T
    
F

2.In a B+ tree, leaves and nonleaf nodes have some key values in common.

    
T
    
F

3.A 2-3 tree with 12 leaves may have at most 10 nonleaf nodes.

    
T
    
F

选择题

1.下列叙述中，不符合m阶B树定义要求的是：

    A.叶结点之间通过指针链接

    B.根结点最多有m棵子树

    C.所有叶结点都在同一层上

    D.各结点内关键字均升序或降序排列

2.Among the following statements, which one does NOT satisfy the definition of a B tree of order m?

    A.All the leaf nodes are linked by pointers

    B.The root has at most m subtrees

    C.All the leaf nodes are on the same level

    D.Inside each node, the keys are arranged in sorted order

3.B+树不同于B树的特点之一是：

    A.能支持顺序查找

    B.结点中含有关键字

    C.根结点至少有两个分支

    D.所有叶结点都在同一层上

4.After deleting 9 from the 2-3 tree given in the figure, which one of the following statements is FALSE?

    A.the root is full

    B.the second key stored in the root is 6

    C.6 and 8 are in the same node

    D.6 and 5 are in the same node

5.Which of the following statements concerning a B+ tree of order M is TRUE?

    A.the root always has between 2 and M children

    B.not all leaves are at the same depth

    C.leaves and nonleaf nodes have some key values in common

    D.all nonleaf nodes have between ⌈M/2⌉ and M children

6.下列关于M阶B+树的说法，哪一句是对的？

    A.根结点一定有2到M个孩子

    B.不是所有的叶结点都有同样的深度

    C.叶结点和非叶结点中存的有一些键值是一样的

    D.所有非叶结点都有⌈M/2⌉到M个孩子

10.Which one of the following is NOT true about B+ trees and AVL trees: they are both __。

    A.balanced binary trees

    B.fit for sequential searches

    C.fit for random searches

    D.fit for range searches

13.高度为 5 的 3 阶 B 树含有的关键字个数至少是：

    A.15

    B.31

    C.62

    D.242

14.The minimum number of keys in a B tree with order 3 and height 5 is __.

    A.15

    B.31

    C.62

    D.242

15.After inserting 0 into the 2-3 tree given in the figure, how many of the following statements are FALSE?

• (S1) The tree grows higher;
• (S2) 2 and 4 are in the same interior node;
• (S3) the root node still contains 9 only;
• (S4) the interior node containing 12 keeps unchanged.

    A.0

    B.1

    C.2

    D.3

16.在图中给定的 2-3 树中插入 0，以下描述有几句是错误的？

• (S1) 树变高了；
• (S2) 2 和 4 在同一个内部结点里；
• (S3) 根结点仍然只包含 9；
• (S4) 包含 12 的那个内部结点没有改变。

    A.0

    B.1

    C.2

    D.3

17.下面关于B-和B+树的叙述中，不正确的是（ ）。

    A.B-树和B+树都是平衡的多叉树

    B.B-树和B+树都可用于文件的索引结构

    C.B-树和B+树都能有效地支持顺序检索

    D.B-树和B+树都能有效地支持随机检索

18.m阶B-树是一棵（ ）。

    A.m叉排序树

    B.m叉平衡排序树

    C.m-1叉平衡排序树

    D.m+1叉平衡排序树

19.To sort N records by merge sort, the worst-case time complexity is:

    A.O(logN)

    B.O(N)

    C.O(NlogN)

    D.O(N²)

20.To sort N records by merge sort, the space complexity is:

    A.O(logN)

    B.O(N)

    C.O(NlogN)

    D.O(N²)