Circular Longest Increasing Subsequence

Question

How can I find the length of Longest Increasing Sub-sequence if the numbers are arranged in circular fashion. For example:

LIS of 3, 2, 1 is 3 [1, 2, 3].

P.S I know how to solve Linear LIS in O(nlogn).

Problem Source: https://www.codechef.com/problems/D2/

Update: The LIS has to be calculated by going through the circle only once. Example 2: LIS of 1, 4, 3 is 2 and that could be either of 1, 3 or 1, 4 or 3, 4.
Thanks

@TimBiegeleisen Of course not..!! What made you think so? I was learning DP from this source https://www.codechef.com/wiki/tutorial-dynamic-programming and this problem was mentioned as a practice problem in the tutorial. — bewithaman, Sep 16 '15 at 04:27
@user3518014 what would be the output of this **input:** `4, 1, 2, 2, 3`. will it be `4` or `5` ? — surajs1n, Sep 16 '15 at 07:34
You could apply `LIS` to every rotation of the array. Would be `O(n^2 log n)`. — IVlad, Sep 16 '15 at 09:08
@IVlad Yes. But i am looking for a O(nlogn) or O(n^2) solution. — bewithaman, Sep 16 '15 at 09:17
I don't understand the example given in the question, you can't shift [1,2,3] to get [3,2,1] as a subsequence. — G. Bach, Sep 16 '15 at 14:04

score 0 · Answer 1 · answered Oct 18 '16 at 05:46

The example in question is wrong. circular rotation of [1,2,3] would be [2,3,1] or [3,1,2].

In which case, we can solve it similar way as longest increasing subsequence. As:

Sort the list in ascending order.
Find min element in the original list.
Start iteration from min_index in original list and compare it with sorted list, and create intermediate array L[i][j] with same logic as longest common subsequence. i will vary from min_index to (i+n-1)%n
Finally return L[max_index][n]

Circular Longest Increasing Subsequence

1 Answers1