(a) [15 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.
Scala Programming
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 Null.
Also define a companion object for the Tree data type, with the following functions:
(a) [15 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) [5 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) [5 Points]. A polymorphic function, replace, which takes three arguments — a Tree t, a value before, and a value after — and returns t with ALL instances of before replaced with the value after.
[Hint: Model your Tree data type after the List data type]
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