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a03sol

# a03sol - Question 2 Part(a(define—struct Line(slope...

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Unformatted text preview: ;; Question 2: ;; Part (a) (define—struct Line (slope intercept)) ;; A Line = (make—Line (union Num Symbol) Num) ;; Part (b) ;; helper function ;; compute—slope: Posn Posn —> Num ;; Purpose: ;; compute the slope between two points, assuming it is defined ;; Examples: (check—expect (compute—slope (make—posn 0 0) (make—posn 3 3)) 1) (check—expect (compute—slope (make—posn 3 4) (make—posn 5 7)) 3/2) (define (compute—slope p1 p2) (/ (- (posn-y p1) (posn-y p2)) (- (posn-x p1) (posn-x p2)))) ;; Tests: (check—expect (compute—slope (make—posn —2 4) (make—posn 3 —7)) —11/5) (check—expect (compute—slope (make—posn 7 6) (make—posn 9 6)) 0) ;; two—points—>Line: Num Num —> Line ;- Purpose: create a Line structure u ‘1 (i.e., calculate slope and intercept) ;; based on the given points (Posn's) ;; if the line is non—vertical, the intjécept is the , a. c ;; y—intercept. If the line is vertical, ;; is the x—intercept ;; Examples: ;? //: (check—expect (‘ ”' ﬂ (two—points—>Line (make—posn>p 0) (Gake—losn —2 —2)) (make—Line 1 0)) (check—expect - (two—points—>Line (make—posn 3 4) ( e—posn 5 5)) (make—Line 1/2 5/2)) (define (two—points—>Line p1 p2) (cond ;; check for vertical line [(= (posn—x p1) (posn—x p2)) (make—Line ‘undefined (posn—x pl))] ;; non—vertical [else (make—Line (compute—slope p1 p2) (- (posn-y p1) (* (compute-slope P1 p2) (posn-x p1))))])) ;; Tests: ;; test vertical (check—expect (two—points—>Line (make—posn 4 3) (make—posn 4 7)) (make—Line ‘undefined 4)) ;; test negative slope (check—expect (two—points—>Line (make—posn —2 4) (make—posn 3 —7)) (make—Line —11/5 —2/5)) This document is for the exclusive use of j65lu. ;; test horizontal (check—expect (two—points—>Line (make—posn 7 6) (make—poem 9 6)) (make—Line 0 6)) ;; Part (c) ;; perp—Line: Posn Line —> Line ;; Purpose: ;; Produce a new Line which is perpendicular (i.e., at 90 degrees) ;; to the given Line, which passes through the given point ;; Examples: (check—expect (perp—Line (make—posn 3 2) (make—Line l 0)) (make—Line —1 5)) ;; Definition (define (perp—Line point line) (cond [(equal? (Line—slope line) 'undefined) (make—Line 0 (posn—y point))] [(= (Line—slope line) 0) (make—Line 'undefined (posn—x point))] [else (make—Line (— (/ l (Line—slope line))) \\\\{ (— (posn—y point) (* (posn—x p int) —/} l (Line—slope line))))))])) ;; Tests a (check—expect (perp—Line (make—posn 3 4) f e— i 'undefined 6)) (make—Line o 4)) /‘ (check—expect (perp—Line (make—posn 7 8 (mag Line 0 4)) (make—Line 'un \fine (3) (check—expect (perp—Line (ma —}osn b 9 (make—Line 5/11 69/+l)) (check—expect (perp—Line (make—posn 0 0) (make—Line 'undefined 0)) (make—Line 0 0)) ) (make—Line —11/5 —2/5)) This document is for the exclusive use of j65lu. ;; Question 3 ;; Part (a) (define—struot Card (suit rank)) ;; A Card=(make—Card Symbol Num) - Part (b) ;; better—Card: Card Card —> Card ;; Purpose: ;; Given two cards return the card either with higher suit value ;; or, if they are the same suit, the higher card value a. d ;; Examples: (check—expect (better—Card (make—Card ‘spades l) (make—Card ‘diamonds 13)) (make—Card 'spades 1)) ;; Tests Case 3 (check—expect (better—Card (make—Card ‘olubs 3) (make—Card ‘olubs 4)) (make—Card 'olubs 4)) ;; Tests Case 2 (define (better—Card o1 o2) (oond ;; if the suits are the same [(symbol=? (Card—suit o1) (Card—suit o2)) (oond [(> (Card—rank o1) (Card—rank o2)) cl] ;; Case 1 [else o2])] ;\$\Case L ;; if the suits are different _ Cas 3 [(symbol=? (Card—suit o1) ‘spades) o1) [(symbol=? (Card—suit o2) ‘spades) r'] a. ;; Case 4 [(symbol=? (Card—suit o1) ‘hearts) o ] ,; Case 5 [(symbol=? (Card—suit o2) ‘hearts) aziiu ,; Case 6 [(symbol=? (Card—suit o1) ‘diﬁmonds o1]!, ,; Case 7 ' ,; Case 8 [ l 21)) e2? ° > K ;; test Case 1 (check—expect (better—Card (make—Cai ‘hearts 3) (make—Card ‘hearts 2)) (make—Card 'hearts 3)) ;; test Case 3 (check—expect (better—Card (make—Card ‘spades l) (make—Card ‘hearts 13)) (make—Card 'spades 1)) ;; test Case 4 (check—expect (better—Card (make—Card ‘olubs l3) (make—Card 'spades 1)) (make—Card 'spades 1)) ;; test Case 5 (check—expect (better—Card (make—Card ‘hearts 3) (make—Card ‘diamonds 13)) (make—Card 'hearts 3)) ;; test Case 6 (check—expect (better—Card (make—Card ‘diamonds 13) (make—Card ‘hearts 3)) (make—Card 'hearts 3)) ;; test Case 7 (check—expect (better—Card (make—Card ‘diamonds 13) (make—Card ‘olubs 1)) (make—Card 'diamonds 13)) ;; test Case 8 (check—expect (better—Card (make—Card ‘olubs 1) (make—Card ‘diamonds 13)) (make—Card 'diamonds 13)) This document is for the exclusive use of j65lu. ;; Part (c) ;; Define some cards for testing various functions ;; Define some cards (as constants) to make examples/testing easier (define cardl (make—Card 'spades 3)) (define card2 (make—Card 'spades 4)) (define card3 (make—Card 'spades 5)) (define card4 (make—Card 'diamonds 3)) (define card5 (make—Card 'clubs 3)) ;; helpers: ;; same—suit?: Card Card Card —> Boolean ;; Purpose: ;; Given three cards, return true if and only if they ;; are the same suit ;; Examples: (check—expect (same—suit? cardl card2 card3) true) (check—expect (same—suit? cardl card3 card4) false) (define (same—suit? c1 c2 c3) (and (symbol=? (Card—suit c1) (Card—suit c2)) (s 0-3)”) ;; Tests: ;; Try all other positions of one non suited c rd\\\\_// (check—expect (same—suit? cardl card4 ca 3) fal.e) (check—expect (same—suit? card4 card3 ca 1) .alse ;; Try with three different suits (check—expect (same—suit? cardl cardﬁ cardéu fa se) 1:? (Card-suit c2) (Card-suit ;; all—same—num?: Num Num Num>f> gooeean ;; Purpose: ;; Returns true if all three numb: s ar the same, false otherwise '; Examples: (define (all—same—num? numl num2 num3) (and (= numl num2) (= numl num3))) ;; Tests: (check—expect (all—same—num? 3 4 3) false) (check—expect (all—same—num? 4 3 3) false) (check—expect (all—same—num? 2 3 4) false) ;; consecutive—num?: Num Num Num —> Boolean ;; Purpose: ;; Returns true if all three numbers are consecutive, false otherwise ;; Examples: (check—expect (consecutive—num? 6 7 8) true) (check—expect (consecutive—num? 2 4 6) false) ;; Definition (define (consecutive—num? numl num2 num3) (and (= (— (max numl num2 num3) (min numl num2 num3)) 2) (= (— (max numl num2 num3) 1) (/ (+ numl num2 num3) 3)))) This document is for the exclusive use of j65lu. ;; Tests: (check—expect (consecutive—mum? 1 2 3) true) (check—expect (consecutive—num? 1 3 2) true) (check—expect (consecutive—num? 2 1 3) true) (check—expect (consecutive—num? 2 3 1) true) (check—expect (consecutive—num? 3 2 1) true) (check—expect (consecutive—num? 3 1 2) true) (check—expect (consecutive—num? 3 4 6) false) (check—expect (consecutive—num? 3 5 6) false) (check—expect (consecutive—num? 6 3 4) false) ;; two—same—num? Num Num Num —> Boolean ;; Purpose: ;; Produce true if (at least) two of the numbers are the same ;; and false otherwise ;; Examples: (check—expect (two—same—nmn? 1 1 3) true) (check—expect (two—same—num? 1 2 3) false) ;; Definition (define (two—same—num? numl num2 num3) (or (= numl num2) (= numl num3) (= num2 num3))) ;; Tests: \\\:\\\é> (check—expect (two—same—nmn? 1 1 1) true) _ j (check—expect (two—same—nmn? 1 3 1) true) (check—expect (two—same—num? 3 1 1) true' ;; Purpose: _ ;; Given 3 cards, output the Zest lag: va.ue ;; straight—flush, flush, str ight, t ree of—a—kind, pair, high—card ;; Examples: o (check—expect (hand—value 0ardl care card3) ‘straight—flush) (check—expect (hand—value 0ardl 0ard4 card5) ‘three—of—a—kind) ;; Definition (define (hand—value 01 02 03) (00nd [(and (same—suit? 01 02 03) (consecutive—num? (Card—rank 01) (Card—rank 02) (Card—rank 03))) ‘straight—flush] [(same—suit? 01 02 03) ‘flush] [(0onse0utive—num? (Card—rank 01) (Card—rank 02) (Card—rank 03)) ‘straight] [(all—same—num? (Card—rank 01) (Card—rank 02) (Card—rank 03)) ‘three—of—a—kind] [(two—same—num? (Card—rank 01) (Card—rank 02) (Card—rank 03)) ‘pair] [else 'high—0ard])) ;; Tests (check—expect (hand—value 0ardl 0ard2 (make—Card 'spades 13)) ‘flush) (check—expect (hand—value 0ardl 0ard4 card3) ‘pair) (check—expect (hand—value 0ard5 0ard3 0ard2) ‘straight) (check—expect (hand—value 0ard1 0ard2 (make—Card '0lubs 13)) 'high—0ard) ;; hand—value: Card Card Card —> ?:mbo1 ,Jiu This document is for the exclusive use of j65lu. ...
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