CS 3520 Homework 1

Due: Wednesday, August 29th, 2018 11:59pm

The following Tree datatype implements a binary tree with a number in each node and leaf:

  (define-type Tree
    (leaf [val : Number])
    (node [val : Number]
          [left : Tree]
          [right : Tree]))

Part 1 — Sum

Implement a sum function that takes a tree and returns the sum of the numbers in the tree.

Example: (sum (node 5 (leaf 6) (leaf 7))) should produce 18.

Part 2 — Negate

Implement the function negate, which takes a tree and returns a tree that has the same shape, but with all the numbers negated.

Example: (negate (node 5 (leaf 6) (leaf 7))) should produce (node -5 (leaf -6) (leaf -7)).

Part 3 — Contains?

Implement the function contains?, which takes a tree and a number and returns #t if the number is in the tree, #f otherwise.

Example: (contains? (node 5 (leaf 6) (leaf 7)) 6) should produce #t.

The second argument to the contains? function is “along for the ride.”

Part 4 — Big Leaves?

Implement the function big-leaves?, which takes a tree and returns #t if every leaf is bigger than the sum of numbers in the path of nodes from the root that reaches the leaf.

Examples: (big-leaves? (node 5 (leaf 6) (leaf 7))) should produce #t, while (big-leaves? (node 5 (node 2 (leaf 8) (leaf 6)) (leaf 7))) should produce #f (since 6 is smaller than 5 plus 2).

The big-leaves? function should be a thin wrapper on another function, perhaps bigger-leaves?, that accumulates a sum of node values.

Part 5 — Optional challenge: Sorted?

Implement the function sorted?, which takes a tree and determines whether it is sorted in the sense that the numbers increase (or stay the same) in a inorder travsersal of the tree.

Your function should run in time proportional to the size of the tree, which rules out making a list of the tree numbers using append on recursive calls. One possible solution accumulates a compound value, and another possible solution accumulates information on the way down the tree and returns more than just success or failure.


Last update: Friday, September 14th, 2018
mflatt@cs.utah.edu