Hello Guys,

Can you share your thoughts on the following question:

Given a string, we have to find the longest non-overlapping repeating subsequence. For example, If we have a string like "abdead", then here the answer is "ad" because longest repeating subsequence is "ad" which is non-overlapping.

My initial thought on this question is that we can use the concept of longest common subsequence but we need to manage the non-overlapping part.

Thanks in advance!

Split the string into two strings $$$s_1,s_2$$$ such that $$$s=s_1s_2$$$ in all possible ways (there are $$$n-1$$$ ways) and then find the LCS of those two strings. The largest such LCS is the solution. The complexity is $$$O(n^3)$$$. It can probably be done faster though.

Thanks @ivan110sic, seems like a good approach. But is there any other way possible which is better than O(n^3)?

You can use ternary search for the split, and it'll be $$$O(n^2log(n))$$$

You

cannotuse ternary search. For example for`s = "sxyaatxysaaxyt"`

the LCSs for subsequent splits are`1 2 3 3 4 5 4 5 4 3 3 2 1`

.However, there is $$$O(n^2)$$$ algorithm for finding the optimal split.

@moonsoon, Can you please share the algorithm to find the optimal split. I tried reading the article you mentioned, But I am not able to understand the algorithm.

if s = "abcadbcd" then longest non onverlapping repeating subsequence is abcd, but with your approach there donot exist a spliting of s in which LCS of s1 and s2 is abcd. please correct me if i am wrong

No, you need to find the longest subsequence which has the form $$$ss$$$ for some string $$$s$$$, not two identical non-overlapping subsequences.

I think I miss understood the meaning of non overlapping.

My understanding is no character of subsequence1 should be at the same position as any character of subsequence2

What I expect everyone is taking non overlapping meaning: subsequence1 should end before subsequence2 starts

For each suffix run z-algorithm. O(n^2) update: only works for segments

But, Z-algorithm will find the longest substring, not the subsequence right??