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

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1 CSE 20 Lecture 13 Analysis: Counting with Pigeonhole Principle CK Cheng, May 17, 2011
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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.
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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.
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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
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5 Example 2: Handshaking Given a group of n people (n>1), each shakes hands with some (a nonzero number of) people in
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This note was uploaded on 12/11/2011 for the course CSE 20 taught by Professor Foster during the Fall '08 term at UCSD.

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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

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