acm/course/LCS

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