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Separately, we have distributed an answer sheet. You may use the space on the exam booklet for whatever temporary work you find useful, but you MUST enter your answers into the answer sheet. Only the answer sheet will be graded. Each problem that requires an answer has been numbered. Place your answer at the corresponding number in the answer sheet.
Note that any procedures or code fragments that you write will be judged not only on correct function, but also on clarity and good programming practice.
The answer sheet asks for your section number and tutor. For your reference, here is the table of section numbers.
Section Time Instructor Tutor R01 MTWRF 10 AM Ben Vandiver Ben Vandiver
Part 1: (18 points)
For each of the following expressions you are to (1) draw the box and pointer diagram corresponding to the list or pair structure created, and (2) write the printed result of evaluating the last expression in the sequence.
(define a (list 1 (cons 2 nil) 3)) a
Question 1: Draw box and pointer for a
Question 2: Printed result
(define x (list 1 2)) (define y (list 3 (list 4))) (define z (append x y)) z
Question 3: Draw box and pointer for z
Question 4: Printed result
(define y (list 42 17 54)) (define z (cons 7 (cdr y))) z
Question 5: Draw box and pointer for z
Question 6: Printed result
Part 3: (30 points)
Ben Bitdiddle (a common character in 6.001 with no connection to your instructor) is implementing a rating tracking system for people playing the card game Spades. This tracking system maintains a count of wins and losses for each player. His first job is to implement a player abstraction that wraps up the player’s name, number of wins, and number of losses. He’s managed to implement the selectors, but the constructor continues to elude him. Help Ben Bitdiddle out by completing the constructor in such a way that the contract is preserved (ie the selectors return the appropriate values).
(define (makeplayer name wins losses) INSERT1)
(define (playername player) (first player))
(define (playerwins player) (second player))
(define (playerlosses player) (third player))
; example usage: (define p (makeplayer "Ben" 5 3))
(playername p) ;Value: "Ben" (playerwins p) ;Value: 5 (playerlosses p) ;Value: 3
Question 8: What expression should be used for INSERT1?
———–ABSTRACTION BARRIER————–
The number of primary interest to the players (and Ben) is their win ratio, which is the ratio of wins to total games.
(define (playerwinratio player) INSERT2)
Question 9: What expression should be used for INSERT2?
Finally, given a list of players who have only played each other, for every win counted by one player there should be a loss counted by another. Thus, the total number of wins must equal the total number of losses. We can use this fact to check to see if anyone is cheating and misreporting their won/loss record.
Ben is writing a procedure called checkrecords which takes a list of players and returns 0 if the number of wins equals the number of losses, returns a positive number if there are more wins than losses, and a negative number if there are more losses than wins. Help him finish the procedure.
(define (checkrecord listofplayers) (if (null? listofplayers) INSERT (+ INSERT (checkrecord (cdr listofplayers)))))
Question 10: What expression should be used for INSERT3?
Question 11: What expression should be used for INSERT4?
Part 5: (20 points)
For each of the following expressions or sequences of expressions, state the value returned as the result of evaluating the final expression in each set, or indicate that the evaluation results in an error. If the expression does not result in an error, also state the “type” of the returned value, using the notation from lecture. If the result is an error, state in general terms what kind of error (e.g. you might write “error: wrong type of argument to procedure”). If the evaluation returns a built in procedure, write primitive procedure, and its type. If the evaluation returns a usercreated procedure, write compound procedure, and also indicate its type using the notation we introduced in class. You may assume that evaluation of each sequence takes place in a newly initialized Scheme system.
For example, for the expression 88 your answer would be Value: 88 Type: number
((lambda (a b) (a b)) (lambda (c) (* 2 c))
Question 16: Value
Question 17: Type
(lambda (m n) (if m (* 2 n) (/ 2 n)))
Question 18: Value
Question 19: Type
(let ((x <) (y 10) (z 20)) (z y x))
Question 20: Value
Question 21: Type
(define (double x) (* 2 x)) (define (check y) (if (< (double y) 10) "yip" (if (> (double y) 6) "yay" "yuck"))) check
Question 22: Value
Question 23: Type
(define three (lambda (a b c) (* a b c))) (three (three 1) (three 2) (three 3))
Question 24: Value
Question 25: Type
