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; chutes and ladders (define rand #f) (define randint #f) (let ((two31 #x80000000) (a (make-vector 56 -1)) (fptr #f)) (define (mod-diff x y) (modulo (- x y) two31)) ; generic version ; (define (mod-diff x y) (logand (- x y) #x7FFFFFFF)) ; fast version (define (flip-cycle) (do ((ii 1 (+ ii 1)) (jj 32 (+ jj 1))) ((< 55 jj)) (vector-set! a ii (mod-diff (vector-ref a ii) (vector-ref a jj)))) (do ((ii 25 (+ ii 1)) (jj 1 (+ jj 1))) ((< 55 ii)) (vector-set! a ii (mod-diff (vector-ref a ii) (vector-ref a jj)))) (set! fptr 54) (vector-ref a 55)) (define (init-rand seed) (let* ((seed (mod-diff seed 0)) (prev seed) (next 1)) (vector-set! a 55 prev) (do ((i 21 (modulo (+ i 21) 55))) ((zero? i)) (vector-set! a i next) (set! next (mod-diff prev next)) (set! seed (+ (quotient seed 2) (if (odd? seed) #x40000000 0))) (set! next (mod-diff next seed)) (set! prev (vector-ref a i))) (flip-cycle) (flip-cycle) (flip-cycle) (flip-cycle) (flip-cycle))) (define (next-rand) (if (negative? (vector-ref a fptr)) (flip-cycle) (let ((next (vector-ref a fptr))) (set! fptr (- fptr 1)) next))) (define (unif-rand m) (let ((t (- two31 (modulo two31 m)))) (let loop ((r (next-rand))) (if (<= t r) (loop (next-rand)) (modulo r m))))) (init-rand 19380110) ; happy birthday donald e knuth (set! rand (lambda seed (cond ((null? seed) (/ (next-rand) two31)) ((eq? (car seed) 'get) (cons fptr (vector->list a))) ((eq? (car seed) 'set) (set! fptr (caadr seed)) (set! a (list->vector (cdadr seed)))) (else (/ (init-rand (modulo (numerator (inexact->exact (car seed))) two31)) two31))))) (set! randint (lambda args (cond ((null? (cdr args)) (if (< (car args) two31) (unif-rand (car args)) (floor (* (next-rand) (car args))))) ((< (car args) (cadr args)) (let ((span (- (cadr args) (car args)))) (+ (car args) (if (< span two31) (unif-rand span) (floor (* (next-rand) span)))))) (else (let ((span (- (car args) (cadr args)))) (- (car args) (if (< span two31) (unif-rand span) (floor (* (next-rand) span)))))))))) (define chutes '((16 . 6) (47 . 26) (49 . 11) (56 . 53) (62 . 19) (64 . 60) (87 . 24) (93 . 73) (95 . 75) (98 . 78))) (define ladders '((1 . 38) (4 . 14) (9 . 31) (21 . 42) (28 . 84) (36 . 44) (51 . 67) (71 . 91) (80 . 100))) (define (game) (let loop ((ps '(0))) (let* ((die (randint 6 0)) (p (+ (car ps) die))) (cond ((= 100 (car ps)) (cdr (reverse ps))) ((< 100 p) (loop (cons (car ps) ps))) ((or (assoc p chutes) (assoc p ladders)) => (lambda (x) (loop (cons (cdr x) ps)))) (else (loop (cons p ps))))))) (define (games n) (let loop ((n n) (gs '())) (if (zero? n) gs (loop (- n 1) (cons (length (game)) gs))))) (define (compete k n) (let loop ((n n) (gs '())) (if (zero? n) gs (loop (- n 1) (cons (apply min (games k)) gs))))) (define (stats k n) (let ((gs (compete k n))) (values (apply min gs) (apply max gs) (exact->inexact (/ (apply + gs) n))))) (call-with-values (lambda () (stats 1 5000)) (lambda (mn mx av) (display mn) (display " ") (display mx) (display " ") (display av) (newline))) (call-with-values (lambda () (stats 2 2000)) (lambda (mn mx av) (display mn) (display " ") (display mx) (display " ") (display av) (newline))) (call-with-values (lambda () (stats 3 2000)) (lambda (mn mx av) (display mn) (display " ") (display mx) (display " ") (display av) (newline))) (call-with-values (lambda () (stats 4 2000)) (lambda (mn mx av) (display mn) (display " ") (display mx) (display " ") (display av) (newline))) (call-with-values (lambda () (stats 5 1000)) (lambda (mn mx av) (display mn) (display " ") (display mx) (display " ") (display av) (newline)))
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