Beefy Boxes and Bandwidth Generously Provided by pair Networks
Clear questions and runnable code
get the best and fastest answer

comment on

( #3333=superdoc: print w/replies, xml ) Need Help??
Quite an interesting technique, and as a disclaimer I really do like it. That being said, this technique will not always get you the fastest iterator. The holy grail of iterators for combinatorial structures is a constant amortized time (CAT) algorithm, meaning that any N successive calls to the iterator takes O(N) time. This is as good as it gets.

Your technique is great as the iterator algorithm mirrors the easy-to-understand recursive algorithm. And kudos for noting (and fixing) the double-recursion. However, your algorithm's running time for iterating through all (N choose K) combinations is proportional to (N+2 choose K+1), so it is not CAT. For a detailed analysis of this and many other interesting iteration algorithms, see section 4.3 of the book Combinatorial Generation by Frank Ruskey. The book does give a CAT iterator for generating combinations, and I believe your general technique of mirroring the recursive algorithm inherently cannot achieve CAT running time (unless you memoize, which defeats the whole purpose of iterating to save memory).

I guess it's a matter of what you want to trade -- (sometimes small) factors of running time, or readability of the algorithm. Although for iteration problems like this, I usually just refer to Ruskey's book and find a pre-packaged CAT algorithm ;)


In reply to Re: Recursively-generated Iterators by blokhead
in thread Recursively-generated Iterators by Roy Johnson

Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post; it's "PerlMonks-approved HTML":

  • Are you posting in the right place? Check out Where do I post X? to know for sure.
  • Posts may use any of the Perl Monks Approved HTML tags. Currently these include the following:
    <code> <a> <b> <big> <blockquote> <br /> <dd> <dl> <dt> <em> <font> <h1> <h2> <h3> <h4> <h5> <h6> <hr /> <i> <li> <nbsp> <ol> <p> <small> <strike> <strong> <sub> <sup> <table> <td> <th> <tr> <tt> <u> <ul>
  • Snippets of code should be wrapped in <code> tags not <pre> tags. In fact, <pre> tags should generally be avoided. If they must be used, extreme care should be taken to ensure that their contents do not have long lines (<70 chars), in order to prevent horizontal scrolling (and possible janitor intervention).
  • Want more info? How to link or How to display code and escape characters are good places to start.
Log In?

What's my password?
Create A New User
Domain Nodelet?
and the web crawler heard nothing...

How do I use this? | Other CB clients
Other Users?
Others pondering the Monastery: (9)
As of 2022-12-01 16:09 GMT
Find Nodes?
    Voting Booth?