The longest common subsequence problem is as follows: Given two sequences A = a1, a2, .. ., aM, and B = b1, b2, .. ., bN, find the length, k, of the longest sequence C = c1, c2, .. ., ck such that C is a subsequence (not necessarily contiguous) of both A and B. As an example, if
A = d, y, n, a, m, i, c
and
B = p, r, o, g, r, a, m, m, i, n, g,
then the longest common subsequence is a,m,i and has length 3. Give an algorithm to solve the longest common subsequence problem. Your algorithm should run in O(MN) time.
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