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acm/course/LCS

Week 6 : LCS (Longest Common Sub-sequence)

Define

    Find a sub-sequence of 2 given sequences in which the sub-sequence’s elements are appear in both original sequences and the sub-sequence is as long as possible.
    ex: ‘aabbcc’, ‘abbccc’ => ‘abc’


What do we want to know?

    – The LCS of S1[1…i] and S2[1…j].
    – i.e. LCS[i][j]


How can we get that?

    – Find the previous number with longest LIS.
    – LCS[i][j]:
           0                            , i=0 or j=0
           LCS[i-1][j-1]+1              , S1[i]=S2[j]
           max(LCS[i-1][j],LCS[i][j-1]) , S1[i]≠S2[j]
    ex: ‘CBABCABCC’ , ‘ABCABCBA’ => ‘ABCABC’