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From: Austin Obyrne <austin.obyrne@hotmail.com>
Newsgroups: comp.lang.ada
Subject: Re: My Invention of "Bug Sort".
Date: Thu, 21 Jun 2012 04:50:34 -0700 (PDT)
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Date: 2012-06-21T04:50:34-07:00
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On Thursday, June 21, 2012 8:23:12 AM UTC+1, Manuel Collado wrote:
> El 21/06/2012 7:13, Simon Wright escribi=F3:
> > "Jeffrey R. Carter"<ggsub@pragmada.co.cc>  writes:
> >
> >>> 2 ) In "O(N log N)" do I assume log to the base 'e' or what.
> >>
> >> In "Big-O" notation, log is understood to be to the base 2.
> >
> > Isn't there a constant factor between log2(x) and ln(x)? Which is taken
> > up in the O?
> >
> >     N =3D e**x =3D 2**y
> >
> > Taking natural logs,
> >
> >     ln N =3D x =3D y.ln 2
>=20
> Yes. In "Big-O" notation, the base for log() is irrelevant.
>=20
>    O(log N) =3D O(ln N)
>=20
> Both expressions denote exactly the same set of functions.
>=20
> --=20
> Manuel Collado - http://lml.ls.fi.upm.es/~mcollado

---------------


This is surprising to me - is it right?

<<Yes. In "Big-O" notation, the base for log() is irrelevant.=20

   << O(log N) =3D O(ln N)=20

<< Both expressions denote exactly the same set of functions.=20

In general,

A change of base in logarithms:

Log(base(a)M =3D Log (base(b))M / Log (base(b))'a'.

Applying that,In particular here,

Ln of N =3D Log2N / Ln 2


Unless it is true that there is some constant incorporated in O that verifi=
es this, then

N(Ln N) /=3D  N(Log2 N)

Which is it?

On face value it appears totally incorrect arithmetically, I'm surprised th=
at such an anomaly would be acceptable.=20

Austin O'Byrne