[racket] FW: q about code for partitions

Sorry, forgot to post the following to the users list.

Hi,
count partitions, much faster and exact.
You may want to put the hash or part of it within function p such as to
avoid spllling much memory.
Jos

#lang racket

(require math/number-theory)

(define p-hash (make-hash '((0 . 1))))

(define (p n)
 (hash-ref! p-hash n
  (λ ()
   (+
    (let loop ((k 1) (m (sub1 n)) (s 0))
     (if (< m 0) s
      (loop (add1 k) (- m (add1 (* 3 k))) (if (odd? k) (+ s (p m)) (- s (p
m))))))
    (let loop ((k -1) (m (- n 2)) (s 0))
      (if (< m 0) s
       (loop (sub1 k) (+ m (* 3 k) -2) (if (odd? k) (+ s (p m)) (- s (p
m))))))))))

(time (for ((n (in-range 0 1000))) (p n)))
(time (for ((n (in-range 0 1000))) (partitions n)))
(void (time (p 10000)))

(for/and ((n (in-range 0 1000))) (= (partitions n) (p n)))

(read-line)

; results with racket:
; cpu time: 16 real time: 16 gc time: 0
; cpu time: 8845 real time: 8845 gc time: 111
; cpu time: 577 real time: 578 gc time: 0
; #t