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 


scs :: Eq a  => [a] -> [a] -> [a]
scs [] ys = ys
scs xs [] = xs
scs xss@(x:xs) yss@(y:ys)
  | x == y = x : scs xs ys
  | otherwise = ws
      where
      us = scs xs yss
      vs = scs xss ys
      ws  | length us < length vs = x : us
          | otherwise = y : vs
 
main = putStrLn $ scs "abcbdab" "bdcaba"