Is this sequence an increasing or decreasing subsequence?

Question

I have a sequence of length 1. That is,

Now can I say that the longest increasing subsequence of length 1 in the above sequence is 1. And the longest decreasing subsequence of length 1 in the above sequence is 1 ?

Yes indeed, if you remove "of length 1", because that does not make sense in combination with "longest". — trincot, Jun 12 '16 at 20:49

score 3 · Accepted Answer · answered Jun 12 '16 at 20:51

3

Degenerate sequence (i.e. a sequence of a single element) can be assigned whatever properties that you need: it is the longest increasing sequence, the longest decreasing sequence, and the longest sequence of equal elements.

This is important in situations when you define properties of sequences in terms of their sub-sequences: one-element sub-sequence gives you a base case; expanding it with another element gives you a two-element sequence.

answered Jun 12 '16 at 20:51

Sergey Kalinichenko

714,442
84
1,110
1,523

So, what will be the longest increasing and longest decreasing subsequences in this sequence `1` ? – user3243499 Jun 13 '16 at 09:43
@user3243499 The entire sequence will be both the longest increasing and the longest decreasing sub-sequence of one-element sequence `{ 1 }`. – Sergey Kalinichenko Jun 13 '16 at 10:14

Is this sequence an increasing or decreasing subsequence?

1 Answers1