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see CLRS intro to algorithms 3ed chapter 15, which discusses the two types of DP approaches: top down recursive, and bottom up iterative. The bottom-up approach builds a table starting from the simplest solutions, and that's the approach that is necessary here.
Magic Spells
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Exactly! i had never solved LCS non recursively. Quite interesting.
see CLRS intro to algorithms 3ed chapter 15, which discusses the two types of DP approaches: top down recursive, and bottom up iterative. The bottom-up approach builds a table starting from the simplest solutions, and that's the approach that is necessary here.