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programmingpraxis - Scheme, pasted on Dec 16:
; 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)


Output:
1
2
3
4
5
6
7
8
9
A
C
#f
1
3
#f
A
C
#f


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