in reply to Mutually Exclusive Elements

I'm not sure about your requirements. I wrote a solution that produces

[1,2,3] [3,4,7] [3,6,9]

This seems more consistent with your stated requirements than your example results. 4 & 8 are equally common -- they appear twice in the arrays. 4 occurs before 8 in $b, thus the elements appear in $b's order of insertion.

At any rate, my algorithm was:

  1. Traverse all the arrays, counting how many of each element appear.
  2. Sort the results in order of ascending frequency and assign it to @frequency.
  3. Take the last of these (i.e. most frequent, or tied for most frequent, and thus common to all) and assign it to $common.
  4. Die with an error message if $common < the number of arrays -- there wasn't really an element common to all.
  5. Start building the results for each array:
    1. First, assign $common.
    2. Then, for each element in @frequency, test if that element is present in the current array. If it is, assign it to the results for this array. Do this X-1 times (assigning $common took care of one element.)
    3. Sort this array's results.
  6. Push an arrayref for this array's results on your final results array.

Updated: my unstated assumption in the above was that that code would be in a subroutine to be called like so:

my ($a_, $b_, $c_) = mutually_exclusive($X, $a, $b, $c);