# Solution 64: Dyck Path Pattern Avoidance (UDUDUD) and Containment

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• Published on Nov 1, 2018
• Let's avoid paths with UDUDUD, while making sure that they contain DU at the center.
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• Pete Berg 8 months ago

Wait, why an= floor (n/2) ?

• Pete Berg 8 months ago

Are we comparing the number of up in the left and and the possibilites of the mid way?
Because the midway determines the possibilities for that an

• Kyro 10 months ago

usclip.net/video/4Xp4F1h0YZM/video.html

• δτ 10 months ago

What if only UDUD...DU...UD is omitted as a trivial Dyck path for each n?

• JackTheSpades 10 months ago +2

Wait, so something like U-DUU-DU-DDU-D is not valid then?
I thought the 'avoid UDUDUD' was referring to consecutive use.

@LetsSolveMathProblems That's fair. I was wondering why the subset thing was mentioned but seeing this it makes more sense now.

• LetsSolveMathProblems  10 months ago +1

Pattern containment/avoidance deals with whether we have a certain subsequence as part of the original sequence. A subsequence, by definition, does not have to be consecutive terms of the sequence. I hoped to implicitly clarify this in the problem statement (Note that the example I provided at 1:19 shows that a non-consecutive pattern must work as well because UUDUDD does not consecutively contain UUDD).

• indomit 10 months ago +3

it's 080 actually :)

• Zain Majumder 10 months ago +1

Is Dyck path the official name? I think "mountain path" is a good descriptor.

• 佐藤裕也 10 months ago +1