Assume the following abstract data structure (ADT) implemented in Scala

Assignment:

1.Create a program that instances nodes and branches of a tree of strings as indicated in the figure above. The root node of your tree must be called root, e.g., val root =

2.Write a function size that counts the number of nodes (leaves and branches) in a tree

sizeT(tree: Tree[_]): Int = tree match {}

3.Write a function maximum that returns the maximum element in a Tree[Int]. (Note: In Scala, you can use x.max(y) or x max y to compute the maximum of two integers x and y.)

maximumT(tree: Tree[Int]): Int = tree match {}

4.Write a function depth that returns the maximum path length from the root of a tree to any leaf

depthT(tree: Tree[_]): Int = tree match {}

The instructor will:

Open a Window command line or a Linux terminal

Call scala REPL

Copy and paste your program

Execute:

println(sizeT(root))

println(maximumT(root))

println(depthT(root))

sealed trait Tree[+A] case class Leaf [A] (value: A) extends Tree[A] case class Branch [A] (left: Tree [A], right: Tree [A]) extends Tree [A] A tree Branch Left Right Branch Left Right Left Right Leaf Leaf Leaf Leaf b' I1 Value ValueValue Value