CSE 2320 Section 501/571 Fall 1999

**Homework 3**

Due: October 26, 1999, in class (October 27, 1999, 5:00pm for -10%)

Due: October 26, 1999, in class (October 27, 1999, 5:00pm for -10%)

- 1.
- Show the hash table
*H*after inserting the keys 30, 79, 8, 39, 11, 60, 16, 14, 19, 17, 44, 18 (in this order).*H*has*m*=13 slots and uses collision resolution by open addressing and the double hashing function , where and , . Show all computations of hash table indices, including collisions. - 2.
- Show the binary-search tree whose post-order traversal is 1, 3, 5, 4,
2, 6, 9, 11, 13, 12, 10, 8, 7. Also, show the preorder traversal of your
tree.
- 3.
- Show the Red-Black trees that result after each successive insertion
of the keys 30, 79, 8, 39, 11, 60, 16, 14, 19, 17 (in this order) into an
initially empty Red-Black tree.
- 4.
- Show the Red-Black trees that result after each successive deletion
of the keys 13, 40, 95, 42, 70, 27, 5, 26, 49, 69 (in this order) from the
following Red-Black tree.

- 5.
- Show the B-trees that result after each successive insertion of the
keys X, F, A, Y, T, H, I, G, Q, W, U, S, R, J, D, E, B, Z, C, V (in this
order) into an initially empty B-tree with minimum degree
*t*= 3. - 6.
- Show the B-trees that result after each successive deletion of the
keys J, O, H, X, T, R, S, F, C, K, P, G, E, L, I (in this order) from the
following B-tree with minimum degree
*t*= 2. When you have a choice between a left or right sibling, always choose the left sibling. Always try Case 2a (predecessor) before Case 2b (successor).