Scheme tree map

Question

Write n analogous function (maptree f t) that returns a tree made by applying the function f to each entry of the binary tree t. (Just like map) Since the tree is a data abstraction, only the followings are allowed to operate on trees:(entry t) (right-branch t) （left-branch t) (make=tree entry left right), and (empty-tree? t). You may use the predefined constant the-empty-tree.

Example:

(define tree 
(make-tree 10 (make-tree 5 the-empty-tree the-empty-tree)
          (make-tree 12 the-empty-tree the-empty-tree)))


tree

(10 (5 () ())(12 () ()))

(maptree square tree)

(100 (25 () ())(144 () ()))

Also, have a look at http://stackoverflow.com/q/19122833/1281433. It discusses tree mapping at a relatively high level that should help you develop an answer to this question. — Joshua Taylor, Oct 10 '13 at 20:44

score 1 · Answer 1 · answered Apr 12 '13 at 15:32

Like this:

(define (maptree func tree)
  (if (empty-tree? tree)
      the-empty-tree
      (make-tree (func (entry tree))
                 (maptree func (left-branch  tree)) 
                 (maptree func (right-branch tree)))))

When a data structure is recursively defined, then a function's implementation may be naturally recursive. In this case, perform the function on one tree item and then recurse on the left and right subtrees.

score 0 · Answer 2 · answered Apr 12 '13 at 13:52

This seems like a homework question. A good starting point would be to make your way down the tree recursively while rebuilding the tree. Check to see if the left and right are empty, and if not call your map function again on each branch.

Start at the top (the first entry) and make a new tree, with the function f applied to entry and a check if the left and right branches are the-empty-tree or not. If not, call the function again on each branch.

Scheme tree map

2 Answers2