UMBC CMSC641, Design & Analysis of Algorithms, Fall 1997
- 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
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
- 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.
27 Oct 1997 12:25:18 EST
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