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

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 :

Tillmann Rendel 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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