Chapter 4
6 points
- Tree traversals.
Give the sequence of letters for each traversal of this binary tree:
q / e r / /
c d n s
/ / a w
- (2 pts) an inorder traversal
- (2 pts) a preorder traversal
- (2 pts) a postorder traversal
10 points
- Draw an AVL tree for the following values inserted in this order. Illustrate each rotation that occurs:
65 13 16 52 28 11 20 14 87 50 26
10 points
- Draw an AVL tree for the following values inserted in this order. Illustrate each rotation that occurs: 83 12 68 55 32 6 46 57 62
10 points
- For the splay tree shown below, show how an access of node 60 is performed. Illustrate each operation that occurs:
10
20
/
15 30
/
25 40
/
35 50
60
10 points
- For the splay tree shown below, show how an access of node 75 is performed. Illustrate each operation that occurs:
80
/
40 120
/
20 60
/ /
10 30 50 70
/
45 75
10 points
- For the B+-tree where M=3 and L=5 shown below, show how an insert of value 80 is handled.
|| 12 || 50 ||
/ |
/ |
2 12 50
5 18 65
7 20 70
- 21 72
- 24 78
10 points
- For the B+-tree where M=3 and L=5 shown below, show how an insert of value 28 is handled.
|| 24 || 75 ||
/ |
/ |
/ |
|| 10 || 16 || || 41 || 50 || || 82 || 90 ||
| / / | |
/ | | | | | | |
2 10 16 24 41 50 75 82 90
5 11 18 26 42 65 78 83 92
7 14 20 30 45 70 80 86 93
- 21 33 47 72 81
35
- points
- A B+-tree is to be stored on disk whose block size is 3096 bytes. The data records to be stored are 36 bytes, and their key is 4 bytes. Determine the values for M and L for the B+-tree. Assume pointers are 4 bytes each.
8 points
- For the problem above, how many levels are needed to store 8,600,000 records?
8 points
- If a binary tree has N nodes, how many null child pointers will it have? Explain your reasoning.
8 points
- In a perfect binary tree (one filled at every level), what does adding another level do to the number of nodes in the tree?
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