MIT6_042JS10_lec27

# MIT6_042JS10_lec27 - 1 Albert R Meyer, April 12, 2010 lec...

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Unformatted text preview: 1 Albert R Meyer, April 12, 2010 lec 10M.1 Mathematics for Computer Science MIT 6.042J/18.062J Generalized Counting Rules Albert R Meyer, April 12, 2010 lec 10M.2 Pigeonhole Principle Mapping Rule: total injection from A to B implies | A | | B | . If | A | > | B | , then no total injection from A to B . Albert R Meyer, April 12, 2010 lec 10M.3 Pigeonhole Principle If more pigeons than pigeonholes, Albert R Meyer, April 12, 2010 lec 10M.4 Pigeonhole Principle then some hole must have two pigeons! Albert R Meyer, April 12, 2010 lec 10M.5 example: 5 Card Draw set of 5 cards: must have 2 with the same suit . Albert R Meyer, April 12, 2010 lec 10M.6 5 Card Draw 5 cards (pigeons) 4 suits (holes) Pigeon clip art source unknown. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse J J 10 6 2 J J 10 6 2 Image by MIT OpenCourseWare. 2 Albert R Meyer, April 12, 2010 lec 10M.7 10 Card Draw 10 cards: how many have the same suit? Albert R Meyer, April 12, 2010 lec 10M.8 10 Card Draw < 3 cards in every hole? NO! Albert R Meyer, April 12, 2010 lec 10M.9 10 Card Draw # cards with same suit 10 4 = 3 ceiling, means round up Albert R Meyer, April 12, 2010 lec 10M.10 Generalized Pigeonhole Principle If n pigeons and h holes, then some hole has pigeons.pigeons....
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## This note was uploaded on 05/27/2011 for the course CS 6.042J taught by Professor Prof.albertr.meyer during the Spring '11 term at MIT.

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MIT6_042JS10_lec27 - 1 Albert R Meyer, April 12, 2010 lec...

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