CS61A, MT2, Spring 2001CS61A Spring 2001MT2Professor Brian Harvey and Professor Dan GarciaProblem #1Consider the following definitions:> (define c (cons '() '(lets (go) bears)))> (define a (append '() '(lets (go) bears)))> (define 1 (list '() '(lets (go) bears)))(a) What will Scheme print in response to the following expressions? If an expression produces an errormessage, you may just write "error"; you don't have to provide the exact text of the message. If the value ofan expression is a procedure, just write "procedure"; you don't have to show the form in which Scheme printsprocedures. Also, draw a box and pointer diagram for the value produced by each expression.> c> a> 1(b) What will Scheme print in response to the following expressions? Do not draw the box and pointerdiagrams for them.> (cdr c)> (cdr a)> (cdr 1)Problem #2As you already know, lists are made out of pairs. Suppose we want to use an OOP version of pairs to makelists in proper object-oriented style. Louis Reasoner gives the following implementation of OOP pairs:(define-class (pair the-car the-cdr) (method (length) (if (null? the-cdr) 1 CS61A, MT2, Spring 2001 CS61A Spring 2001 MT2 Professor Brian Harvey and Professor Dan Garcia 1(+ 1 (ask the-cdr 'length)))))(a) Happy with his implementation, Louis interacts the following way with his pairs (fill in the blanks):> (define (new-cons a b) (instantiate pair a b))> (define (new-cdr p) (ask p 'the-cdr))> (define my-list (new-cons 3 '()))> (ask my-list 'length)________________________________________________> (define other-list (new-cdr my-list))> (ask other-list 'length)________________________________________________(b) Reimplement OOP-style lists so that the examples in part (a) return 1 and 0 as they should. You maycreate or modify classes, methods, and/or procedures as needed. You must use OOP style.Problem #3(a) Complete the definition below for the lock class. When a lock is instantiated, it must be given a PIN. Youcan close a lock at any time, but you may only open it if you have the secret PIN (matching the one givenwhen it was created). You cannot open or close a lock twice in a row. (An attempt to open an already-openlock with the wrong PIN should complain about the PIN rather than about the openness.) Each lock isinitially closed.> (define my-lock (instantiate lock '1234))> (ask my-lock 'open 1234)(lock opens)> (ask my-lock 'open 1234)(lock is open already!)> (ask my-lock 'open 3424)(sorry wrong pin)> (ask my-lock 'close)(lock closes)> (ask my-lock 'close)(lock is closed already!)(define-class ( ) (method (open pin) (cond ( '(sorry wrong pin)) ( '(lock is open already!)) (else CS61A, MT2, Spring 2001Problem #2 2'(lock opens)))) (method (close) (cond ( '(lock is closed already!)) (else '(lock closes)))))(b) Define a class smart-lock which has the same features as lock with one small exception: If you try to opena smart-lock three times with a wrong PIN (the three trials need not be consecutive), it will disallow anyfuture open attempts, even if you eventually pass in the correct PIN:Use the proper object-oriented programming style.> (define my-smart-lock (instantiate smart-lock '1234))okay> (ask my-smart-lock 'open 3423) ; first wrong attempt(sorry wrong pin)> (ask my-smart-lock 'open 4532) ; second wrong attempt(sorry wrong pin)> (ask my-smart-lock 'open 1234) ; (opening and closing(lock opens)> (ask my-smart-lock 'close) ; between wrong attempts)(lock closes)> (ask my-smart-lock 'open 2923) ; third wrong attempt(sorry wrong pin)> (ask my-smart-lock 'open 8623) ; now lock is shut down(lock shut down)> (ask my-smart-lock 'open 1234) ; correct PIN but too late(lock shut down)> (ask my-smart-lock 'close) ; closing unaffected(lock is closed already!)Problem #4This question is about binary trees, as defined in SICP:Constructor: (make-tree entry left right) Selectors: (entry tree) (left-branch tree) (right-branch tree)We'll call a binary tree full if all leaves are at the same depth, and there are no missing nodes. Your goal is totake a tree that is not full and fill it.(a) Write make-filler, which takes a nonnegative integer as its argument. If the argument is zero, it shouldreturn the empty list. Otherwise, it should return a full binary tree, with zeros in every entry, and with the CS61A, MT2, Spring 2001Problem #3 3number of levels specified by the argument. Some examples will help make this clear (showing pictures oftrees rather than the representation as printed by Scheme):> (make-filler 1)0> (make-filler 2) 0 / \0 0> (make-filler 3) 0 / \ 0 0 /\ /\0 0 0 0(b) Now we can write fill, which takes in a tree and returns a filled version of that tree.For example:Someone has written depth for us; it returns the maximum depth of the tree. (The depth of a tree with only aroot node is zero.) We've given you the procedure below as a starter. You write fill-help.(define (fill tree) (fill-help tree (depth tree)))Problem #5We are going to design a data-directed Adventure game program. (Later, in project 3, you'll work on adifferent object-oriented design for an Adventure game.) Note -- this explanation is a lot longer than theprogram you have to write! Don't get scared.In an Adventure game, you move around through a sort of maze with rooms connected by passageways. Hereis a typical interaction (the user types the bold text):> (adventure)You are at the entrance to a cave. There is a tunnel heading east.Your move? eastYou are in a large cavern. The walls are glowing faintly. There are tunnels to the east and south. There is awand lying on the ground.Your move? wave wandThere is a puff of smoke. You are now in a small room with golden walls. A flask containing a green potionis on the floor. There are doors to the north and south. CS61A, MT2, Spring 2001Problem #4 4... and so on. The game is data-directed because the program will not have specific information about therooms; instead, we'll use put to set up the rooms, like this:(put 'entrance 'description "You are at the entrance ... heading east.")(put 'entrance 'east (lambda () (visit 'cavern)))(put 'cavern 'description "You are in a large cavern. ... on the ground.")(put 'cavern 'east (lambda () (visit 'torture-chamber)))(put 'cavern 'south (lambda () (visit 'lecture-hall)))(put 'wand 'wave (lambda () (visit 'gold-room)))You are given the following procedures:(define (adventure) (visit
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