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Permute Fucntion (Scheme)

From: "andrew cooke" <andrew@...>

Date: Tue, 14 Aug 2007 22:53:01 -0400 (CLT)

":";exec snow -- "$0" "$@"

(package* permute/v1.0.0
  (provide: (define (permute lst))))

; generates a list of all permutations
; assumes all values in original list are unique (under equal?)
(define (permute lst)
  (case (length lst)
    ((0) '())
    ((1) (list lst))
    (else (flat-map (lambda (head)
                      (map (lambda (perm) (cons head perm))
                           (permute (except head lst))))
                    lst))))

(define (flat-map f lst) (flat-map-acc f lst '()))
(define (flat-map-acc f lst acc)
  (if (null? lst)
      acc
      (flat-map-acc f (cdr lst) (append acc (f (car lst))))))

; this does not attempt to keep any kind of ordering
(define (except x lst) (except-acc x lst '()))
(define (except-acc x lst acc)
  (if (null? lst)
      acc
      (let ((head (car lst))
            (tail (cdr lst)))
        (if (equal? x head)
            (append acc tail)
            (except-acc x tail (cons head acc))))))


(test*
 (define (dup x) (list x x))
 (expect* (equal? '() (flat-map dup '())))
 (expect* (equal? '(1 1) (flat-map dup '(1))))
 (expect* (equal? '(1 1 2 2) (flat-map dup '(1 2)))))

(test*
 (expect* (equal? '() (except 0 '())))
 (expect* (equal? '() (except 1 '(1))))
 (expect* (equal? '(2) (except 1 '(1 2))))
 (expect* (equal? '(3 2 1) (except 0 '(1 2 3))))
 (expect* (equal? '(2 3) (except 1 '(1 2 3))))
 (expect* (equal? '(1 3) (except 2 '(1 2 3))))
 (expect* (equal? '(2 1) (except 3 '(1 2 3)))))

(test*
 (expect* (equal? '() (permute '())))
 (expect* (equal? '((1)) (permute '(1))))
 (expect* (equal? '((1 2)(2 1)) (permute '(1 2))))
 (expect* (equal? '((1 2 3)(1 3 2)(2 1 3)(2 3 1)(3 2 1)(3 1 2))
                  (permute '(1 2 3)))))

Improved Permutation Function (Start of List Library)

From: "andrew cooke" <andrew@...>

Date: Wed, 15 Aug 2007 12:07:38 -0400 (CLT)

":";exec snow -- "$0" "$@"

; library of list-related functions

(package* ac-lists/v1.0.0
  (provide:
      ; abstract the typical patter used to recurse over lists
      (define-syntax acl-list-process
        (syntax-rules (null?)
          ((_ ((null? list) null-body)
              ((head tail) body))
           (if (null? list)
               null-body
               (let ((head (car list))
                     (tail (cdr list)))
                 body)))))
    (define (acl-filter pred lst))
    (define (acl-filter-acc pred lst acc))
    (define (acl-except x lst))
    (define (acl-flat-map fun lst))
    (define (acl-flat-map-acc fun lst acc))
    (define (acl-permute lst))
    ))

; remove all values that match predicate from a list
(define (acl-filter pred lst) (reverse (acl-filter-acc pred lst '())))
(define (acl-filter-acc pred lst acc)
  (acl-list-process
   ((null? lst) acc)
   ((head tail) (if (pred head)
                    (acl-filter-acc pred tail acc)
                    (acl-filter-acc pred tail (cons head acc))))))

(test*
 (define (one? x) (= 1 x))
 (expect* (equal? '() (acl-filter one? '())))
 (expect* (equal? '() (acl-filter one? '(1))))
 (expect* (equal? '(2) (acl-filter one? '(2))))
 (expect* (equal? '(2 3) (acl-filter one? '(2 1 3)))))

; exclude instances of a particular value
(define (acl-except x lst) (acl-filter (lambda (y) (equal? x y)) lst))

(test*
 (expect* (equal? '() (acl-except 0 '())))
 (expect* (equal? '() (acl-except 1 '(1))))
 (expect* (equal? '(2) (acl-except 1 '(1 2))))
 (expect* (equal? '(1 2 3) (acl-except 0 '(1 2 3)))))

; map with append instead of cons
(define (acl-flat-map fun lst) (reverse (acl-flat-map-acc fun lst '())))
(define (acl-flat-map-acc fun lst acc)
  (acl-list-process
   ((null? lst) acc)
   ((head tail) (acl-flat-map-acc fun tail (append (fun head) acc)))))

(test*
 (define (dup x) (list x x))
 (expect* (equal? '() (acl-flat-map dup '())))
 (expect* (equal? '(1 1) (acl-flat-map dup '(1))))
 (expect* (equal? '(1 1 2 2) (acl-flat-map dup '(1 2)))))

; a list of all permutations
; assumes all values in original list are unique (under equal?)
(define (acl-permute lst)
  (define (perm-rest x)
    (define (cons-x rest) (cons x rest))
    (let ((rest (acl-except x lst)))
      (map cons-x (acl-permute rest))))
  (acl-list-process
   ((null? lst) '())
   ((head tail) (if (null? tail)
                    (list lst)
                    (acl-flat-map perm-rest lst)))))

(test*
 (expect* (equal? '() (acl-permute '())))
 (expect* (equal? '((1)) (acl-permute '(1))))
 (expect* (equal? '((1 2)(2 1)) (acl-permute '(1 2))))
 (expect* (equal? '((1 3 2)(1 2 3)(2 3 1)(2 1 3)(3 2 1)(3 1 2))
                  (acl-permute '(1 2 3)))))

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