The   shortest common supersequence   is a problem closely related to the   longest common subsequence,   which you can use as an external function for this task.



Task

Given two strings 



u


{\displaystyle u}

 and 



v


{\displaystyle v}

, find the shortest possible sequence 



s


{\displaystyle s}

, which is the shortest common super-sequence of 



u


{\displaystyle u}

 and 



v


{\displaystyle v}

 where both 



u


{\displaystyle u}

 and 



v


{\displaystyle v}

 are a subsequence of 



s


{\displaystyle s}

. Defined as such, 



s


{\displaystyle s}

 is not necessarily unique.

Demonstrate this by printing 



s


{\displaystyle s}

 where 



u
=


{\displaystyle u=}

“abcbdab” and 



v
=


{\displaystyle v=}

“bdcaba”.



Also see

 Wikipedia: shortest common supersequence 


USING: combinators io kernel locals math memoize sequences ;
 
MEMO:: scs ( x y -- seq )
    {
        { [ x empty? ] [ y ] }
        { [ y empty? ] [ x ] }
        { [ x first y first = ]
          [ x rest y rest scs x first prefix ] }
        { [ x y rest scs length x rest y scs length <= ]
          [ x y rest scs y first prefix ] }
        [ x rest y scs x first prefix ]
    } cond ;
 
"abcbdab" "bdcaba" scs print