[Haskell-cafe] Re: appending an element to a list

[Abhay Parvate]

I think I would like to make another note: when we talk about the complexity
of a function, we are talking about the time taken to completely evaluate
the result. Otherwise any expression in haskell will be O(1), since it just
creates a thunk.
And then the user of the program is to be blamed for running the program,
since that is what caused evaluation of those thunks :)


Abhay

2008/5/31 Martin Geisler <mg at daimi.au.dk>:

> Tillmann Rendel <rendel at daimi.au.dk> writes:
>
> Hi! (Cool, another guy from DAIMI on haskell-cafe!)
>
> > Another (n - 1) reduction steps for the second ++ to go away.
> >
> >         last ("o" ++ "l")
> > A)  ~>  last ('o' : "" ++ "l"))
> > L)  ~>  last ("" ++ "l")
> > A)  ~>  last ("l")
> > L)  ~>  'l'
> >
> > And the third and fourth ++ go away with (n - 2) and (n - 3) reduction
> > steps. Counting together, we had to use
> >
> >   n + (n - 1) + (n - 2) + ... = n!
> >
> > reduction steps to get rid of the n calls to ++, which lies in O(n^2).
> > Thats what we expected of course, since we know that each of the ++
> > would need O(n) steps.
>
> I really liked the excellent and very clear analysis! But the last
> formula should be:
>
>   n + (n - 1) + (n - 2) + ... = n * (n+1) / 2
>
> which is still of order n^2.
>
> --
> Martin Geisler
>
> VIFF (Virtual Ideal Functionality Framework) brings easy and efficient
> SMPC (Secure Multi-Party Computation) to Python. See: http://viff.dk/.
>
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