Homework 6

Background: 18.1, 18.2, 12.

Due October 23rd:

• 6.1: Last time, you created a binary search tree from the letters of the word ``algorithm.'' Do it again, and annotate the tree with the number of credits the splay analysis would assign to each node. Now splay on ``m.'' What is the depth of the resulting tree? Where are the credits now?
• 6.2: Use the amortized analysis template to argue that we can satisfy a sequence of n operations to a heap (initially empty) in amortized time for inserts and O(1) amortized time for delete-max.
• 6.3: Give worst-case bounds for executing min, max, min, max, min, max, ... k times on a balanced binary search tree and a splay tree. Which is asymptotically more efficient if ?
• 6.4: CLR Exercise 12.2-2 (pg 226).
• 6.5: CLR Exercise 12.2-6 (pg 226).
• 6.6: CLR Exercise 12.3-1 (pg 231).
• 6.7: When a hash table fills up, it is often necessary to expand it (especially with open addressing). Let's say that we start off with a table of size m=101 and every time we reach , we set and then reinsert all the items into the new table. Argue that the amortized time to insert a single item into the hash table over a sequence of n insertions is . Use the uniform-hashing assumption if you need it.