[racket] Looking for feedback on code style
This means that even function add1 cannot always be concidered to be O(1).
It may depend on the representation of numbers. In this sense I agree with
you.
Jos
> -----Original Message-----
> From: users-bounces at racket-lang.org
> [mailto:users-bounces at racket-lang.org] On Behalf Of Stephen Bloch
> Sent: 13 September 2010 21:44
> To: users at racket-lang.org
> Subject: Re: [racket] Looking for feedback on code style
>
>
> On Sep 13, 2010, at 3:07 PM, David Van Horn wrote:
>
> >> In fact, ANY method to do this (even with a vector) takes
> Omega(n log
> >> n) time. It needs to be able to produce any of n!
> different answers,
> >> so it needs to make at least log(n!) decisions, which is
> Theta(n log n).
> >> Otherwise there wouldn't be enough leaves on the decision tree.
> >
> > Doesn't it make n decisions? 1 decision for each element
> (the decision being, where does the element go in the shuffled list)?
>
> Each of these is an n-way decision, which takes log(n) bits
> to specify. Any algorithm that solves this problem MUST
> generate at least n log(n) random bits of information, and
> therefore MUST take at least n log(n) time (ignoring parallelism).
>
> Ryan Culpeper points out:
> > I think the discrepancy comes from the fact that each of
> those decisions takes O(log n) bits, but we customarily
> pretend that "indexes" are O(1).
>
> Exactly. As long as your n fits into a machine word, and you
> have at least n cells of truly-random-access memory, you can
> treat array indexing and random-number-generation as taking O(1) time.
>
> > Is this right? Does complexity analysis have a notation for
> distinguishing "true" complexity from "for up to k bits" complexity?
>
> Not exactly a "notation" AFAIK, but people do routinely talk
> about whether the computational model allows bit operations
> in O(1) time, or integer operations in O(1) time, or whatever.
>
>
> Stephen Bloch
> sbloch at adelphi.edu
>
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