I'm trying to make a pattern that's easy to preceive by human but hard to write out by Mathematica when I came across this problem. (Check the original problem herehere)
Let's check this simple case:
I've got a list {5,1,2,1,2,1,2,1,2,4,3,3,3,3,3,3,10} and I would like to find out all the recurrence period and the sequence before and after them. So, if you have a brief match with your brain, you can know there are two possible matchs:{5,1,2,1,2,1,2,1,2,4,3,3,3,3,3,3,10} and {5,1,2,1,2,1,2,1,2,4,3,3,3,3,3,3,10}.
It's okay if I only want to find out one of them, using the following code will work as desired:
Replace[{5, 1, 2, 1, 2, 1, 2, 1, 2, 4, 3, 3, 3, 3, 3, 3, 10},
{Shortest[pre___, 3], Longest[Repeated[Shortest[rep__, 1], {2, Infinity}]], Shortest[inc___, 2]}
:> {{pre}, {rep}, {inc}}]
(*{{5}, {1, 2}, {4, 3, 3, 3, 3, 3, 3, 10}}*)
But If I want to find out all of them, it's not quite direct as the following code which simply change Replace to ReplaceList will not work:
r1=
ReplaceList[{5, 1, 2, 1, 2, 1, 2, 1, 2, 4, 3, 3, 3, 3, 3, 3, 10},
{Shortest[pre___, 3], Longest[Repeated[Shortest[rep__, 1], {2, Infinity}]], Shortest[inc___, 2]}
:> {{pre}, {rep}, {inc}}]
The result is incredibly long and included all the possible match and ignored all the Shortest or Longest:
r2 = ReplaceList[{5, 1, 2, 1, 2, 1, 2, 1, 2, 4, 3, 3, 3, 3, 3, 3, 10},
{pre___, Repeated[rep__, {2, Infinity}], inc___} :> {{pre}, {rep}, {inc}}]
Sort@r1==Sort@r2
(*True*)
This is, of course, not the desired result, but how can I set the pattern-matcher to do this work? And are there any reason that ReplaceList will ignore all these Shortest and Longest? Any help or any other approach other than my way is appreciated. But of course, the final goal is to solve this using ReplaceList or similar functions.
