Scala language (functional lang.)

Problem 3 [35 Points). Define a polymorphic Tree data type, where a Tree is either a Node with a left subtree, a value, and a right subtree; or it is a Leaf with just a value. [11 Points] Also define a companion object for the Tree data type, with the following functions: (a) [12 Points). Three polymorphic functions -- inOrder, preOrder, and postOrder -- to traverse the tree in-order, pre-order, and post-order. Each function takes a tree and returns a list with the contents of the tree when traversed in that order. (b) [6 Points). A polymorphic function, search, which takes two arguments - a Tree and a key and returns a boolean result based on whether the key is found in the tree. (c) [6 Points). A polymorphic function, replace, which takes three arguments - a Tree t, a value before, and a value after and returns a variant of t with ALL instances of before replaced with the value after. Problem 3 [35 Points). Define a polymorphic Tree data type, where a Tree is either a Node with a left subtree, a value, and a right subtree; or it is a Leaf with just a value. [11 Points] Also define a companion object for the Tree data type, with the following functions: (a) [12 Points). Three polymorphic functions -- inOrder, preOrder, and postOrder -- to traverse the tree in-order, pre-order, and post-order. Each function takes a tree and returns a list with the contents of the tree when traversed in that order. (b) [6 Points). A polymorphic function, search, which takes two arguments - a Tree and a key and returns a boolean result based on whether the key is found in the tree. (c) [6 Points). A polymorphic function, replace, which takes three arguments - a Tree t, a value before, and a value after and returns a variant of t with ALL instances of before replaced with the value after