Exercises

Using trees

Recall the binary tree definition from class slides

datatype 'a BTree
    = EmptyBTree
    | BTNode of 'a * 'a BTree * 'a BTree

Write the following recursive functions, and deduce their types. Meta-note: in pure functional style, do not think about modifying the original tree; think about how to construct the desired result.

Write a function that...
1. ...sums the elements of a BTree.
2. ...counts the maximum depth of a BTree.
3. ...merges the elements of two BTrees. You need not worry or think about ordering, just produce a tree that has all the elements of both trees, but no more. (This is quite easy, actually; step back and think of the dumbest possible way to make a tree out of two trees.)
4. ...computes the intersection of the elements of two BTrees. In other words, consider the two trees as sets of elements; construct a list that contains only the elements found in both trees.