# [Haskell] Newbie : How come that cyclic recursive lists are efficient ?

Francis Girard francis.girard at free.fr
Mon Jan 24 04:38:35 EST 2005

```Hi,

The classical Hamming problem have the following solution in Haskell :

*** BEGIN SNAP
-- hamming.hs

-- Merges two infinite lists
merge :: (Ord a) => [a] -> [a] -> [a]
merge (x:xs)(y:ys)
| x == y    = x : merge xs ys
| x <  y    = x : merge xs (y:ys)
| otherwise = y : merge (x:xs) ys

-- Lazily produce the hamming sequence
hamming :: [Integer]
hamming
= 1 : merge (map (2*) hamming) (merge (map (3*) hamming) (map (5*) hamming))
*** END SNAP

I just love these algorithms that run after their tail (they make my brain
melt) but I don't know how is it that they are efficient.

Here, the hamming recursively calls itself three times. For this algorithm to
generated sequence THROUGH RECURSION (i.e. not only intermediate "local"
results) otherwise it would end up regenerating the beginning of the sequence
over and over again.

RECURSION since executing the program with GHCI runs quite smoothly and
responsively.

That Haskell manages to do that is for me "magnifique". But I need to know (if
only a little) about how it achieves this in order to know what I, as a
lambda programmer, can do, and how to compute the Big-Oh complexity of the
algorithm.

Thank you,

Francis Girard
FRANCE

```