[Haskell-cafe] Hints for Euler Problem 11

[Jules Bean]

> I came up with this function to try to extract the main diagonal.
> 
>  > getDiag :: [[a]] -> [a]
>  > getDiag = map (head . head) . iterate (tail . map tail)
> 
> The problem is, this function doesn't work unless I have an infinite
> grid.
> 
> Could anyone provide me with some hints to lead me in the right direction?

I think Dan's hint is pretty good, but a hint for this *specific* part 
of the problem, rather than the whole thing.

'head' and 'tail' blow up on empty lists. So any kind of solution 
involving iterate and similar with them tends to eventually blow up on 
finite lists.

(take 1) and (drop 1) are rather similar functions, but they simply give 
[] on [] instead of blowing up. Then, on a finite list, you just keep 
getting []s after a while, which you can trim with takeWhile (not . null).

Another approach is to replace iterate with an unfoldr; an unfoldr is 
rather like a 'general iterate' which 'knows when to stop' : it stops 
when your unfolding function gives Nothing.

Jules