Longest Common Non Contiguous Subsequence

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The problem of Longest Common Non Contiguous Subsequence can be modeled and solved using the optimal alignment algorithm with the following scoring:

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Or, directly compute V(n, m) with:

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Each character in the sequence S can be align with the same character in the sequence T or with a space in T (in this case no substitution is done). Since the goal is to find maximum length, character matched are valued as '1', while a space match is valued '0'.