[Haskell-cafe] Programming Chalenges: The 3n+1 problem

[Luke Palmer]

On Thu, Apr 14, 2011 at 4:29 AM, Dmitri O.Kondratiev <dokondr at gmail.com>wrote:

> 3n+1 is the first, "warm-up" problem at Programming Chalenges site:
>
> http://www.programming-challenges.com/pg.php?page=downloadproblem&probid=110101&format=html
>
> (This problem illustrates Collatz conjecture:
>
> http://en.wikipedia.org/wiki/3n_%2B_1#Program_to_calculate_Collatz_sequences
> )
>
> As long as the judge on this site takes only C and Java solutions, I
> submitted in Java some add-hock code (see at the end of this message) where
> I used recursion and a cache of computed cycles. Judge accepted my code and
> measured  0.292 sec with best overall submissions of 0.008 sec to solve the
> problem.
>
> *** Question: I wonder how to implement cache for this problem in Haskell?
> At the moment, I am not so much interested in the speed of the code, as in
> nice implementation.
>

This is the exact problem data-memocombinators was written to solve.
http://hackage.haskell.org/packages/archive/data-memocombinators/0.4.1/doc/html/Data-MemoCombinators.html

For this problem, it is too slow to memoize everything; you have to use a
bounded memo table.  That's why I use a combinator-based memo approach as
opposed to the type-directed approach used in eg. MemoTrie.  The memo table
you need is something like

    switch (<10^6) integral id

Luke
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