Editing Longest common subsequence (section)

=== Second property ===
If ''A'' and ''B'' are distinct symbols (''A''≠''B''), then ''LCS''(X^A,Y^B) is one of the maximal-length strings in the set { ''LCS''(''X''^''A'',''Y''), ''LCS''(''X'',''Y''^''B'') }, for all strings ''X'', ''Y''.

For example, 
''LCS''("ABCDEFG","BCDGK") is the longest string among ''LCS''("ABCDEFG","BCDG") and ''LCS''("ABCDEF","BCDGK"); if both happened to be of equal length, one of them could be chosen arbitrarily.

To realize the property, distinguish two cases:
*If  ''LCS''("ABCDEFG","BCDGK") ends with a "G", then the final "K" cannot be in the LCS, hence ''LCS''("ABCDEFG","BCDGK") = ''LCS''("ABCDEFG","BCDG").
*If  ''LCS''("ABCDEFG","BCDGK") does not end with a "G", then the final "G" cannot be in the LCS, hence ''LCS''("ABCDEFG","BCDGK") = ''LCS''("ABCDEF","BCDGK").