MIT6_042JS10_lec27

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Page1 / 7

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online