lec13

# Lec13 - CSE 20 Lecture 13 Analysis Counting with Pigeonhole Principle CK Cheng 1 Pigeonhole Principle 5.6 6.5 Schaums Motivation The mapping of n

This preview shows pages 1–6. Sign up to view the full content.

1 CSE 20 Lecture 13 Analysis: Counting with Pigeonhole Principle CK Cheng, May 17, 2011

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

View Full Document
2 Pigeonhole Principle 5.6, 6.5 Schaum’s Motivation: The mapping of n objects to m buckets E.g. Hashing. The principle is used for proofs of certain complexity derivation.
3 Pigeonhole Principle Pigeonhole Principle: If n pigeonholes are occupied by n + 1 or more pigeons, then at least one pigeonhole is occupied by more than one pigeon. Remark: The principle is obvious. No simpler fact or rule to support or prove it. Generalized Pigeonhole Principle: If n pigeonholes are occupied by kn + 1 pigeons, then at least one pigeonhole is occupied by k + 1 or more pigeons.

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

View Full Document
4 Example 1: Birthmonth In a group of 13 people, we have 2 or more who are born in the same month. # pigeons # holes At least # born in the same month 13 12 2 or more 20 12 2 or more 121 12 11 or more 65 12 6 or more 111 12 10 or more k n +1 n k +1 or more
5 Example 2: Handshaking Given a group of n people (n>1), each shakes hands with some (a nonzero number of) people in

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/11/2011 for the course CSE 20 taught by Professor Foster during the Fall '08 term at UCSD.

### Page1 / 11

Lec13 - CSE 20 Lecture 13 Analysis Counting with Pigeonhole Principle CK Cheng 1 Pigeonhole Principle 5.6 6.5 Schaums Motivation The mapping of n

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online