; 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)