# CS5343 Assignment #4 solution

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## 1. Tree traversals.

Give the sequence of letters for each traversal of this binary tree:

q
/ \
e r
/ \ / \
c d n s
/ /
a w

a. (2 pts) an inorder traversal
b. (2 pts) a preorder traversal
c. (2 pts) a postorder traversal

10 points
2. 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
3. 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
4. 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
5. 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
6. 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
9 21 72
10 24 78

10 points
7. 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
9 21 33 47 72 81
35

10 points
8. 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
9. For the problem above, how many levels are needed to store 8,600,000 records?

8 points
10. If a binary tree has N nodes, how many null child pointers will it have? Explain your reasoning.

8 points
11. 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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