UMBC CMSC641, Design & Analysis of Algorithms, Fall 1997

Old News

• Thursday, 10/1/97: Some clarifications on Test 1 (previously sent out by email):

  • Question 1: Do not worry about expanding and contracting the array R. Assume that the array R is infinite. (This makes the question easier.)

  • Question 3: Where the question says LINK, I meant UNION and that the union-by-rank heuristic is used.

  • Somebody asked what n is in Questions 2 and 3. Here, n is the total number of elements in the disjoint set union data structure, which is the same as the number of MakeSet operations. This notation is the same as the one in the textbook.

  • Also, for Question 2, you may modify the disjoint set union data structure as you see fit. You can have auxiliary data structures if you want. Make sure that you adequately describe any changes to the "standard" data structure and justify their effects on the running time of the operations. (I.e., you can change anything you want as long as the total running time for m operations is still O(m log* n).

  • Question 2, again: Since MakeSet is not the only operation that creates a set (Insert does this as well), it is no longer the case that n is equal to the number of MakeSet operations. For this question, assume that log* m = Theta(log* n). That is, you can show that your modifications cause m Disjoint Set Union operations to run in O(m log* m) time instead of O(m log* n). The value of m has to be ridiculously larger than n in order for (m log* m) to be larger than (m log* n).

• Monday 9/29/97: Correction on Homework 4. In Exercise 22.3-4, where the question says "UNION" replace the word with "LINK".

• Wednesday 9/24/97: Homework 4 assigned.

• Wednesday 9/17/97: Homework 3 assigned.

• Friday 9/12/97: Whoops, I meant alpha GREATER than 1/2 for the third question of Homework 2 and for parts c through E.

• Wednesday 9/10/97: Homework 2 assigned.

• Monday 9/8/97: Some clarifications on HW1. Question #2 is only one exercise, 18.1-3. I did not assign 18.1-1 through 18.1-3. For Question #3, your algorithm will need to read the entire sequence of numbers before deciding whether there is a way to sort the sequence using two stacks.

• Thursday 9/4/97: Good news: we have a bigger room, CP206, which holds 65. The class is now open again for registration for up to 50 students (32 slots are available). This should be enough slots for everyone. You shouldn't need my permission for normal registration.

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