【PTA】【数据结构与算法】B-树和B+树

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.Among the following statements, which one does NOT satisfy the definition of a B tree of order m?
选项
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
2.B+树不同于B树的特点之一是:
选项
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
3.After deleting 9 from the 2-3 tree given in the figure, which one of the following statements is FALSE?

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选项
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
4.Which of the following statements concerning a B+ tree of order M is TRUE?
选项
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
5.A B+ tree of order 3 with 21 numbers has at most __ nodes of degree 3.
选项
A 1
B 2
C 3
D 4
6.一棵有21个数字的、度为3的B+树最少有 __ 个度为2的结点。
选项
A 0
B 1
C 2
D 3
7.Which one of the following is NOT true about B+ trees and AVL trees: they are both __。
选项
A balanced binary trees
B fit for sequential searches
C fit for random searches
D fit for range searches
8.Given a 2-3 tree as shown in the figure, after inserting 7 with splitting strategy, what is (are) the key(s) in the root?

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选项
A 4
B 6
C 8
D 4 and 6
9.Given a 2-3 tree as shown in the figure, after inserting 18 with splitting strategy, where will the key 15 be?

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选项
A in the root alone
B in the root with key 20
C alone in a node on the second level (the leaves are on the first level)
D in a node with key 11 on the second level (the leaves are on the first level)
10.The minimum number of keys in a B tree with order 3 and height 5 is __.
选项
A 15
B 31
C 62
D 242
11.After inserting 0 into the 2-3 tree given in the figure, how many of the following statements are FALSE?

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(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.
选项
A 0
B 1
C 2
D 3
12.下面关于B-和B+树的叙述中,不正确的是( )。
选项
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
13.m阶B-树是一棵( )。
选项
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
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