Step by Step solution about How to resolve the algorithm Same fringe step by step in the Haskell programming language

Data Type Definition:

• Tree a is a polymorphic data type representing a binary tree with values of type a.
  • Leaf a: Represents a leaf node containing a value of type a.
  • Node (Tree a) (Tree a): Represents an internal node with links to two child trees of type Tree a.

Function Definitions:

• fringe :: Tree a -> [a]:

  • Extracts the values from the leaf nodes of a binary tree t, returning a list of a values.
  • For leaf nodes, it simply returns the single value in the leaf.
  • For internal nodes, it recursively combines the fringe values of the left and right subtrees.

• sameFringe :: (Eq a) => Tree a -> Tree a -> Bool:

  • Compares the fringe values of two binary trees t1 and t2.
  • Returns True if the fringe values are the same (as lists of a values), otherwise False.

Main Function:

• main :: IO ():
  • Defines several binary trees with different structures and values.
  • Uses mapM_ print to print the result of comparing the fringe values of the first tree a with each of the other trees [a, b, c, x, y, z].

Example:

• a is a binary tree with nodes 1, 2, 3, 4, and 5.
• sameFringe a a will return True because both trees have the same fringe values [1, 5].
• sameFringe a b will return False because the fringe values of b are different: [1, 5] vs. [1, 3].

data Tree a
  = Leaf a
  | Node (Tree a)
         (Tree a)
  deriving (Show, Eq)

fringe :: Tree a -> [a]
fringe (Leaf x) = [x]
fringe (Node n1 n2) = fringe n1 ++ fringe n2

sameFringe
  :: (Eq a)
  => Tree a -> Tree a -> Bool
sameFringe t1 t2 = fringe t1 == fringe t2

main :: IO ()
main = do
  let a = Node (Leaf 1) (Node (Leaf 2) (Node (Leaf 3) (Node (Leaf 4) (Leaf 5))))
      b = Node (Leaf 1) (Node (Node (Leaf 2) (Leaf 3)) (Node (Leaf 4) (Leaf 5)))
      c = Node (Node (Node (Node (Leaf 1) (Leaf 2)) (Leaf 3)) (Leaf 4)) (Leaf 5)
      x =
        Node
          (Leaf 1)
          (Node
             (Leaf 2)
             (Node (Leaf 3) (Node (Leaf 4) (Node (Leaf 5) (Leaf 6)))))
      y = Node (Leaf 0) (Node (Node (Leaf 2) (Leaf 3)) (Node (Leaf 4) (Leaf 5)))
      z = Node (Leaf 1) (Node (Leaf 2) (Node (Node (Leaf 4) (Leaf 3)) (Leaf 5)))
  mapM_ print $ sameFringe a <$> [a, b, c, x, y, z]