Created: Sat 12 Sep 2009
Wed 16 Sep 2009
Wed 23 Sep 2009
- Please review the course syllabus and make sure that you understand the course policies for grading, late homework, and academic honesty.
- On the first page of your solution write-up,
you must make explicit which problems are to be graded for
"regular credit", which problems are to be graded for "extra credit",
and which problems you did not attempt.
Please use a table something like the following
where "RC" is "regular credit", "EC" is "extra credit", and "NA"
is "not applicable" (not attempted). Failure to do so will result
in an arbitrary set of problems being graded for regular
credit, no problems being graded for extra credit, and a five percent
- You must also write down with whom you worked on the assignment. If this
changes from problem to problem, then you should write down this
information separately with each problem.
Required: 4 of the following 5 problems.
Points: 20 pts per problem
Unless otherwise indicated, problems are from Introduction to Algorithms by Cormen, Leiserson, Rivest, and Stein. The edition (2nd or 3rd) will be indicated if the numbering differs.
- Problem 3-3
- Problem 3-4
- Solve the following recurrences and justify your result. (These are in problem 4.3 of the 3rd edition of CLRS. They do not appear in the 2nd edition.
- (a) T(n) = 4T(n/3) + n lg n.
- (b) T(n) = T(n - 2) + 1 / lg n
- Solve the following recurrences and justify your result.
- (a) T(n) = 3T(n/3 - 2) + n/2
This is 4-3 d in the 3rd edition of CLRS.
- (b)4-4 j in the 2nd edition of CLRS or
4-3 j in the 3rd edition of CLRS. (They are the same.)
- Derive an asymptotically tight bound on the following recurrence.
Hint: This problem has a five line solution.
You'll need to think "out of the box."
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