Step by Step solution about How to resolve the algorithm Shortest common supersequence step by step in the Haskell programming language

The provided Haskell code defines a function scs that takes two lists of elements of type a (which must be instances of the Eq typeclass) as input and returns a new list that is the shortest common subsequence (SCS) of the two input lists.

Here's how the code works:

• The scs function takes two lists, xss and yss, as input.

• It first checks if either list is empty. If xss is empty, it returns yss. If yss is empty, it returns xss.

• If neither list is empty, it compares the first elements of the two lists (x and y).

• If x and y are equal, it means they are part of the SCS, so it prepends x to the result of calling scs recursively on the tails of xss and yss (i.e., xs and ys).

• If x and y are not equal, it means they are not part of the SCS. So, it calculates two possible SCSs: us by calling scs recursively on xs and yss, and vs by calling scs recursively on xss and ys.

• It then chooses the shorter of us and vs as the SCS and prepends the first element of the chosen list (x or y) to it.

• Finally, it returns the calculated SCS.

When you run the code with the input lists "abcbdab" and "bdcaba", it calculates and prints the SCS, which is "abcd".

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"