use downloaded software DrRacket, SCHEME program .scm , R5RS language from source.

1. [3 marks] Write a function called treeReduce for trees that is analogous to the reduce function for flat lists (see Section 4.2). This function should take an operator, an initial value, and a tree as arguments and return the result of combining all nodes of the tree using the given operator. For simplicity you may assume only commutative operators are supplied. E.g.:

    (treeReduce + 0 '(1 (2 3)((4 5) 6 (7)((8 (9)) 10)))  55 

2. [3 marks] Write a function height that takes as argument an arbitrarily deeply nested list (ie a tree) and returns the maximum depth of any item in any of its sublists; the depth of an object in a list is the number of cars that can be applied to it, not necessarily in a row... (You may wish to use the built-in max function for this). E.g.:

    (height 'a)  0 (height '(a))  1 (height '(a (b) c))  2 (height '(((((a(((b)))))))))  8 

3. [3 marks] Write a function flattenTree that takes a tree as an argument and returns a list of the leaf values of the tree. E.g.:

    (flattenTree '(1 (2 3) ((4 5 6 (7)))(((8 (9))))))  (1 2 3 4 5 6 7 8 9) 

4. [5 marks] Write a function (treeMerge T1 T2) that takes two trees as arguments and merges them according to the following rules:
   • Merging two trees is done by recursing through their structure and merging their subtrees.
     • The root of T1 is merged with the root of T2
     • The first child is merged with the first child
     • Second with second... etc, etc, etc, ...
   • Merging two leaf nodes is done by multiplying their values (you may assume they are numbers).
   • Merging a leaf node with a subtree is done by scaling the subtree by the value of the leaf.
   • Merging a subtree with an empty tree, is simply the non-empty subtree.
   E.g.:

(2(3) (2 (23) (45567))) (12) (18) (28) (40) 8)(6) (4 2 ) (567) (10 (86) (42) (1218) (2840 (567) (5 (43) (21) 6(78) (2(3) (2 (23) (45567))) (12) (18) (28) (40) 8)(6) (4 2 ) (567) (10 (86) (42) (1218) (2840 (567) (5 (43) (21) 6(78)