MIT6_042JS10_lec10_prob

# MIT6_042JS10_lec10_prob - Massachusetts Institute of...

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Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science February 26 Prof. Albert R. Meyer revised February 21, 2010, 1416 minutes In-Class Problems Week 4, Fri. Problem 1. The table below lists some prerequisite information for some subjects in the MIT Computer Science program (in 2006). This deﬁnes an indirect prerequisite relation, , that is a strict partial order on these subjects. 18 . 01 6 . 042 18 . 01 18 . 02 18 . 01 18 . 03 6 . 046 6 . 840 8 . 01 8 . 02 6 . 001 6 . 034 6 . 042 6 . 046 18 . 03 , 8 . 02 6 . 002 6 . 001 , 6 . 002 6 . 003 6 . 001 , 6 . 002 6 . 004 6 . 004 6 . 033 6 . 033 6 . 857 (a) Explain why exactly six terms are required to ﬁnish all these subjects, if you can take as many subjects as you want per term. Using a greedy subject selection strategy, you should take as many subjects as possible each term. Exhibit your complete class schedule each term using a greedy strategy. (b) In the second term of the greedy schedule, you took ﬁve subjects including 18.03. Identify a set of ﬁve subjects not including 18.03 such that it would be possible to take them in any one term (using some nongreedy schedule). Can you ﬁgure out how many such sets there are? (c)

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MIT6_042JS10_lec10_prob - Massachusetts Institute of...

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