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From: dewar@cs.nyu.edu (Robert Dewar)
Subject: Re: Teaching sorts [was Re: What's the best language to start with?]
Date: 1996/08/17
Message-ID: <dewar.840305735@schonberg>#1/1
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distribution: inet
references: <4umeot$re2@hil-news-svc-2.compuserve.com>
 <dewar.839831192@schonberg> <4v2fb9$lpj@news.utdallas.edu>
 <4v2qkd$40f@news1.mnsinc.com>
organization: Courant Institute of Mathematical Sciences
newsgroups: comp.lang.c,comp.lang.c++,comp.unix.programmer,comp.lang.ada
Date: 1996-08-17T00:00:00+00:00
List-Id: <comp.lang.ada>


"Wrong order.  An O(n) program where n=1,000 that takes 1 second to
complete should be able to finish n=2,000 in 2 seconds, not the other
way around.  In other words, you can't derive time complexity by
timing an algorithm, *especially* with only two samples."

This statement is wrong (big-O seems to be generating a lot of confusion).
big-O notation is about asymptotic behavior. If you know an algorithm
is O(N) and you know that the time for n=1000 is one second, you know
ABSOLUTELY NOTHING about the time for n=2000, NOTHING AT ALL!

For example, suppose the behavior of an algorithm is

  for n up to 1000, time is 1 second
  for n greater than 1000, time is 1000*n seconds

that's clearly O(N), but the time for 2000 items will be 2_000_000 seconds.

A good reference for big-O notation is Mike Feldman's data structure book.
It emphasizes big-O more than some other books at this level, and has a
clear explanation and some nice examples. If everyone reads this we will
have a clearer discussion here (and avoid things like O(2N) :-)
Of  course what it has to do with the origins of the thread is obscure :-)