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The LCS problem gets two strings and returns their longest common subsequence.

For example:

LCS on the strings: elephant and eat is 3, as the whole string eat is a subsequence in elephant - indices 0,6,7 or 2,6,7

Another example:

LCS on the strings: elephant and olives is 2, as their longest common subsequence is le

The question is, whether there is an algorithm that does not only returns the most optimal solution, but that can return the K best solutions?

SomethingSomething
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1 Answers1

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There is an algorithm to return all the optimal solutions (I think this is what you asked).

As in Wikipedia:

Using the dynamic programming algorithm for two strings, the table is constructed, then backtracked from the end to the beginning recursively, with the added computation that if either of (i, j-1) or (i-1, j) could be the point preceding the current one, then both paths are explored. This leads to exponential computation in the worst case.

There can be an exponential number of these optimal sequences in the worst case!

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    Thank you. I actually wanted the best K solutions - i.e. if the best solution is a subsequence of length (N) and there are subsequences of length (N-1), I want to know about them too – SomethingSomething Nov 19 '17 at 14:46