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; majority voting (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 (shuffle x) (do ((v (list->vector x)) (n (length x) (- n 1))) ((zero? n) (vector->list v)) (let* ((r (randint n)) (t (vector-ref v r))) (vector-set! v r (vector-ref v (- n 1))) (vector-set! v (- n 1) t)))) (define (partition xs) (let ((x (car xs))) (let loop ((xs (cdr xs)) (lt '()) (ge '())) (cond ((null? xs) (values lt x ge)) ((< (car xs) x) (loop (cdr xs) (cons (car xs) lt) ge)) (else (loop (cdr xs) lt (cons (car xs) ge))))))) (define (select k xs) (if (<= (length xs) k) (error 'select "out of range") (let loop ((k k) (xs (shuffle xs))) (let-values (((lt x ge) (partition xs))) (cond ((< k (length lt)) (loop k lt)) ((< (length lt) k) (loop (- k (length lt) 1) ge)) (else x)))))) (define (majority1 xs) (let ((goal (/ (length xs) 2))) (let loop ((xs xs) (counts (list))) (cond ((null? xs) #f) ((assoc (car xs) counts) => (lambda (x) (let ((n (+ (cdr x) 1))) (if (< goal n) (car x) (loop (cdr xs) (cons (cons (car x) n) counts)))))) (else (loop (cdr xs) (cons (cons (car xs) 1) counts))))))) (display (majority1 '(A B A B A))) (newline) (display (majority1 '(A A A C C B B C C C B C C))) (newline) (display (majority1 '(A B C A B A))) (newline) (define (majority2 xs) (let ((goal (floor (/ (length xs) 2)))) (confirm (select goal xs) xs goal))) (define (confirm cand xs goal) (let loop ((xs xs) (k 0)) (cond ((< goal k) cand) ((null? xs) #f) ((equal? cand (car xs)) (loop (cdr xs) (+ k 1))) (else (loop (cdr xs) k))))) (display (majority2 '(1 2 1 2 1))) (newline) (display (majority2 '(1 1 1 3 3 2 2 3 3 3 2 3 3))) (newline) (display (majority2 '(1 2 3 1 2 1))) (newline) (define (mjrty zs) (let loop ((cand #f) (k 0) (xs zs)) (cond ((null? xs) (confirm cand zs (/ (length zs) 2))) ((zero? k) (loop (car xs) 1 (cdr xs))) ((equal? cand (car xs)) (loop cand (+ k 1) (cdr xs))) (else (loop cand (- k 1) (cdr xs)))))) (display (mjrty '(A B A B A))) (newline) (display (mjrty '(A A A C C B B C C C B C C))) (newline) (display (mjrty '(A B C A B A))) (newline)
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