Better explanation for LCS

[nvmnghia]

Hi, I've been always NOT understanding LCS & DP in general. In the LCS explanation, these sentences

If we throw A, our LCS length will be dp[i - 1][j] (since we have prefixes S[1..i - 1] and T[1..j]). If we try to throw B character, we will have prefixes S[1..i] and T[1..j - 1] so the length of LCS will be dp[i][j - 1].

seem to claim that dp[i][j] = dp[i - 1][j] = dp[i][j - 1], which is not the case.

Can we have a better explanation?

[Rastrian]

A = prefix S (1th array)
B = prefix T (2th array)

Its just for represent each values, in the same text he also said based on this: As we are looking for the Longest common subsequence, we will pick the maximum value from dp[i][j - 1] and dp[i - 1][j].

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