Dear monks,
A holiday ponderance.

Given a hash consisting of key integers > value integers, remove the fewest number of key/value pairs such that all remaining pairs are "nested" (loosely used!! see examples). Integers may only appear once in the hash. Note that there are equally optimal solutions in some (many?) cases, and not all need be returned. A solution which loops through left to right and removes non-nested pairs as they are encountered (using some look-ahead to detect this) is simple, but AFAIKT not guaranteed to remove the fewest number of pairs? I may be wrong on this, in which case this question is pointless. Of course this is not Perl specific- but Perl is what I'm using, and perhaps there some nice hash-foo which will work!

Some trivial examples with letters, to show possible input patterns: 

1. a b B c A C <- bad
2. a b B A c C <- ok
3. a b c C B A <- ok
4. a b A B c C <- bad
5. a b B c C A d e E D <- ok
6. a A b B c C <- ok

[download]
'solved'
1. a b B A (removed cC) or- b B c C (removed aA)
4. remove aA or bB

Some play data. 

 %k = ( 0 => 8,
        3 => 5,
        7 => 9,
        10 => 100,
        11 => 99, 
        15 => 25,
        16 => 26,
        17 => 27,
        35 => 40,
        36 => 39,
        37 => 38,
        60 => 80,
        65 => 75, 
        66 => 76,
        67 => 74);

[download]

Happy qw/Holidays Christmas Festivus Kwanzaa yet-another-day-of-meditation-with-no-otherwise-special-meaning/

P.S. Over-caffeinated monks- this is honestly not homework, or a final exam question, or even class related, so don't bother pointing out the fact its sounds like such. :) Thank you.

In reply to (non) nested pairs by xipho

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