## License Plates

### May 16, 2017

; license plates

(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 licenses (make-vector 17576 (list)))

(define (hash license) (define (c->i c) (- (char->integer (char-upcase c)) 65)) (let loop ((cs (string->list license)) (e 2) (s 0)) (if (negative? e) s (loop (cdr cs) (- e 1) (+ (* 26 s) (c->i (car cs)))))))

(define (adjoin license) (when (not (license? license)) (vector-set! licenses (hash license) (cons (substring license 3 6) (vector-ref licenses (hash license))))))

(define (license? license) (member (substring license 3 6) (vector-ref licenses (hash license))))

(define (start-list half-license) (sort string<? (vector-ref licenses (hash half-license))))

(define (create-random-data n) (define (i->c i) (integer->char (+ i 65))) (define (i->d i) (integer->char (+ i 48))) (set! licenses (make-vector 17576 (list))) (do ((n n (- n 1))) ((zero? n)) (adjoin (list->string (cons (i->c (randint 26)) (cons (i->c (randint 26)) (cons (i->c (randint 26)) (cons (i->d (randint 10)) (cons (i->d (randint 10)) (list (i->d (randint 10))))))))))))

(display (license? "PLB123")) (newline) (display (length (start-list "PLB"))) (newline) (display (start-list "PLB")) (newline)

(display (apply max (map length (vector->list licenses)))) (newline) (display (length (filter zero? (map length (vector->list licenses))))) (newline) (display (apply + (map length (vector->list licenses)))) (newline)

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In Python

MUMPS V1

MUMPS V1

Using SQLite.