[Haskell-cafe] A tale of Project Euler

[Olivier Boudry]

On 11/27/07, Sebastian Sylvan <sebastian.sylvan at gmail.com> wrote:
>
> That is indeed a nice and clear version that's pretty fast. It's
> basically the same as the C version except "backwards" (i.e. examine a
> number and work backwards through its divisors, rather than filling in
> a "map" of all multiples of a known prime).
> Let me suggest the following slight modification (primeFactors in your
> version doesn't actually return prime factors - it returns prime
> factors *or* a list of just the number itself),
>
> primes :: [Integer]
> primes = 2 : filter (null . primeFactors) [3,5..]
>
> primeFactors :: Integer-> [Integer]
> primeFactors n = factor n primes
>     where
>         factor m (p:ps) | p*p > m        = []
>                         | m `mod` p == 0 = p : factor (m `div` p) (p:ps)
>                         | otherwise      = factor m ps
>
>
> This is roughly 35% faster on my machine with GHC 6.7.20070730 too,
> but the point wasn't to make it faster, but clearer.
> --
> Sebastian Sylvan
> +44(0)7857-300802
> UIN: 44640862
>

Great remark, it's even simpler like this.

By the way I just found the article I stole this algorithm from:
http://www.haskell.org/haskellwiki/99_questions/31_to_41 last one in problem
35.

Cheers,

Olivier.
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