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The longest common subsequence (LCS) problem is the problem of finding the longest subsequence common to all sequences in a set of sequences (often just two sequences). It differs from problems of finding common substrings: unlike substrings, subsequences are not required to occupy consecutive positions within the original sequences. The longest common subsequence problem is a classic computer science problem, the basis of data comparison programs such as the diff utility, and has applications in bioinformatics. It is also widely used by revision control systems such as Git for reconciling multiple changes made to a revision-controlled collection of files. == Complexity == For the general case of an arbitrary number of input sequences, the problem is NP-hard. When the number of sequences is constant, the problem is solvable in polynomial time by dynamic programming (see ''Solution'' below). Assume you have sequences of lengths . A naive search would test each of the subsequences of the first sequence to determine whether they are also subsequences of the remaining sequences; each subsequence may be tested in time linear in the lengths of the remaining sequences, so the time for this algorithm would be : For the case of two sequences of ''n'' and ''m'' elements, the running time of the dynamic programming approach is O(''n'' × ''m''). For an arbitrary number of input sequences, the dynamic programming approach gives a solution in : There exist methods with lower complexity,〔 〕 which often depend on the length of the LCS, the size of the alphabet, or both. Notice that the LCS is not necessarily unique; for example the LCS of "ABC" and "ACB" is both "AB" and "AC". Indeed, the LCS problem is often defined to be finding ''all'' common subsequences of a maximum length. This problem inherently has higher complexity, as the number of such subsequences is exponential in the worst case, even for only two input strings. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「longest common subsequence problem」の詳細全文を読む スポンサード リンク
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