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Computers and Technology, 10.08.2021 22:00 zel990252
Dr. Watson has been kidnaped! Sherlock Holmes was contacted by the kidnapper for ransom. Moments later he received a message from Dr. Watson's phone. The message contained three random strings. Sherlock being Sherlock, was able to deduce immediately that Dr. Watson was trying to give a hint about his location. He figured out that the longest common subsequence between the 3 words is the location. But since it was too easy for him, he got bored and asked you to find out what the actual location is. Your task is to find the longest common subsequence from the 3 given strings before it is too late. A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements. For instance, given a sequence "drew"; "d", "w", "de", "drw", "drew" are all examples of valid subsequences (there are also others), while "er", "wdre" are not. Design a dynamic programming algorithm which takes three input sequences X, Y, and Z, of lengths m, n, and p, respectively, and returns their longest common subsequence. For full marks your algorithm should run in (mnp) time. Note that W is a common subsequence of X, Y, and Z if and only if W is a subsequence of X, W is a subsequence of Y, and W is a subsequence of Z.
Required:
Describe the set of subproblems that your dynamic programming algorithm will consider.
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