list manipulation - Find longest monotonically increasing subsequence containing final two elements

I'm interested in finding the longest monotonically increasing subsequence of a sequence containing the final two elements. This question addresses my question without the italicized requirement. For example, given {3,4,6,7,5,8}, the function should return {3,4,5,8}, not {3,4,6,7,8}. (In fact, I only need the length of that longest subsequence, but a function returning the subsequence is fine too.)

We may assume that lst[[Length@lst-1]] < Last@lst and that the elements of lst are distinct.

EDIT: Note that this is the same problem as determining the longest increasing subsequence including the final element - given such an algorithm, apply it to Rest@lst to get the longest increasing subsequence containing the last two elements.

Answer

Using Leonid Shifrin's solution from the Q&A you mentioned:

longestSequence[{seq___, a_, b_}] := With[{list = Select[{seq}, # < a &]},
  Join[LongestCommonSequence[list, Sort@list], {a, b}]
  ]

Comments

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