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; amazon interview question (define (square x) (* 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 heap #f) (define (closest points k) (set! heap (make-vector k (list -1 0 0))) (do ((points points (cdr points))) ((null? points) heap) (let ((dist (+ (square (caar points)) (square (cadar points))))) (when (lt? (vector-ref heap 0) (list dist)) (vector-set! heap 0 (cons dist (car points))) (siftdown k))))) (define (siftdown len) (let loop ((parent 0)) (let ((child (+ parent parent 1))) (when (< child len) (if (and (< (+ child 1) len) ; (+ child 1) is sibling (lt? (vector-ref heap (+ child 1)) (vector-ref heap child))) (set! child (+ child 1))) ; the least child (when (lt? (vector-ref heap child) (vector-ref heap parent)) (let ((temp (vector-ref heap child))) (vector-set! heap child (vector-ref heap parent)) (vector-set! heap parent temp)) (loop child)))))) (define (lt? pt1 pt2) (not (if (negative? (car pt1)) #f (if (negative? (car pt2)) #t (< (car pt1) (car pt2)))))) (define points (let loop ((n 20) (pts (list))) (if (zero? n) pts (loop (- n 1) (cons (list (randint -1000 1000) (randint -1000 1000)) pts))))) (for-each (lambda (p) (display p) (newline)) (vector->list (closest points 10)))
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