Programming Praxis: Flavius Josephus

;; Programming Praxis
;; http://programmingpraxis.com/2009/02/19/flavius-josephus
;; Flavius Josephus
;; Written in Scheme (Guile 2.0)
;; (josephus 41 3) ->
;;   (2 5 8 11 14 17 20 23 26 29 32 35 38 0 4 9 13 18 22 27 31 36 40 6 12 19 25
;;   33 39 7 16 28 37 10 24 1 21 3 34 15 30)

(define (josephus n m)
  (let loop ((s (apply circular-list (iota n)))
             (n n)
             (res '()))
    (if (= 1 n) (reverse (cons (car s) res))
      (let* ((x (drop s (- m 2)))   ;; element preceding the element to remove
             (y (cadr x)))          ;; element to remove
        (set-cdr! x (cddr x))   ;; remove element from circular list
        (loop (cdr x) (1- n) (cons y res))))))