; amazon interview question
(define (identity x) x)
(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 (fortune xs)
(let loop ((n 1) (x #f) (xs xs))
(cond ((null? xs) x)
((< (rand) (/ n))
(loop (+ n 1) (car xs) (cdr xs)))
(else (loop (+ n 1) x (cdr xs))))))
(define (make-set hash eql? size)
(let ((table (make-vector size (list))))
(lambda (message . args)
(if (eq? message 'random)
(let loop ((index (randint size)))
(if (pair? (vector-ref table index))
(fortune (vector-ref table index))
(loop (randint size))))
(let* ((key (car args))
(index (modulo (hash key) size))
(bucket (vector-ref table index)))
(case message
((member?)
(let loop ((bucket bucket))
(cond ((null? bucket) #f)
((eql? (car bucket) key) #t)
(else (loop (cdr bucket))))))
((insert)
(vector-set! table index
(let loop ((bucket bucket))
(cond ((null? bucket) (list key))
((eql? (car bucket) key) bucket)
(else (cons (car bucket) (loop (cdr bucket))))))))
((delete)
(vector-set! table index
(let loop ((bucket bucket))
(cond ((null? bucket) bucket)
((eql? (car bucket) key) (cdr bucket))
(else (cons (car bucket) (loop (cdr bucket))))))))
(else (error 'set "unrecognized message"))))))))
(define s (make-set identity = 7))
(s 'insert 1)
(s 'insert 2)
(s 'insert 3)
(s 'insert 4)
(s 'insert 5)
(display (s 'member? 2)) (newline)
(s 'delete 2)
(display (s 'member? 2)) (newline)
(display (s 'random)) (newline)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(define sort #f)
(define merge #f)
(let ()
(define dosort
(lambda (pred? ls n)
(if (= n 1)
(list (car ls))
(let ((i (quotient n 2)))
(domerge pred?
(dosort pred? ls i)
(dosort pred? (list-tail ls i) (- n i)))))))
(define domerge
(lambda (pred? l1 l2)
(cond
((null? l1) l2)
((null? l2) l1)
((pred? (car l2) (car l1))
(cons (car l2) (domerge pred? l1 (cdr l2))))
(else (cons (car l1) (domerge pred? (cdr l1) l2))))))
(set! sort
(lambda (pred? l)
(if (null? l) l (dosort pred? l (length l)))))
(set! merge
(lambda (pred? l1 l2)
(domerge pred? l1 l2))))
(define (uniq-c eql? xs)
(if (null? xs) xs
(let loop ((xs (cdr xs)) (prev (car xs)) (k 1) (result '()))
(cond ((null? xs) (reverse (cons (cons prev k) result)))
((eql? (car xs) prev) (loop (cdr xs) prev (+ k 1) result))
(else (loop (cdr xs) (car xs) 1 (cons (cons prev k) result)))))))
(define (first-even lt? xs)
(define (eql? a b) (if (lt? a b) #f (not (lt? b a))))
(let* ((evens (map car (filter (lambda (x) (even? (cdr x)))
(uniq-c eql? (sort lt? xs)))))
(firsts (filter (lambda (x) (member x evens)) xs)))
(if (pair? firsts) (car firsts) #f)))
(display (first-even < '(1 2 1 3 1 2 1))) (newline)
(display (first-even < '(1 2 3 4 5))) (newline)