CS 5510 Homework 1

Due: Thursday, September 1st, 2011 10:45am

The following Tree datatype implements binary trees with numbers 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

Impement 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?

Impement 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?

Impement 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, say bigger-leaves? that accumulates a sum of node values.

Part 5 – Optional challenge: Sorted?

Impement 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. Instead, you must accumulate information both on the way down the tree and from one banch to the other.