**Due: Friday, January 13th, 2012, noon**

Be sure you have version 5.2 of Racket installed. (This is the latest version from the Racket web page.) It is installed on the tlab machines in `/usr/lcoal/bin/drracket`, or you can use your own machine. Install it via http://www.racket-lang.org.

Open DrRacket, set the language to “Use the language declared in the source” (via the Language|Choose Language menu item), put the following program into the upper window, and click “Run”

#lang plai (expt 2 100)You should see the prompt in the interactions window (a

Install `nwu-eecs-pl.plt` by using DrRacket’s “File|Install .plt file...” menu item. In the dialog box, make sure the “Web” option at the top is selected and paste this url into the box:

Wait for the

After restarting DrRacket, select the **Manage EECS 321 PL Handin Account...** menu item from DrRacket's **File** menu. Change to the **New User** panel, and pick a username and password. (Use your real name and real NetID, so that we can connect your homework submissions with you. **DON'T** use your real password.)

You will have to install `nwu-eecs-pl.plt` for DrRacket on each different filesystem that you want to have **Handin** button. However, after creating a handin account once from any machine, you can use DrRacket's **Handin** button on any other machine.

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?)])

Every problem must come with an appropriate set of test cases. At a minimum the test cases must cover every branch in each function you write.

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`.

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))`.

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”.

Impement the function `big-leaves?`, which takes a tree and returns `#t` if every leaf is bigger than (and not equal to) 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`; `(big-leaves? (node 5 (node 2 (leaf 8) (leaf 6)) (leaf 7)))` should produce `#f` (since 6 is smaller than 5 plus 2) and `(big-leaves? (node 2 (leaf 2) (leaf 2)))` should produce `#f`.

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 some information as the function traverses the tree.

Click the handin button in DrRacket to hand in your submission before the deadline. Late homework will not be accepted.

Last update: Friday, February 17th, 2012robby@eecs.northwestern.edu |