/usr/share/gauche-0.9/0.9.5/lib/util/combinations.scm is in gauche 0.9.5-1build1.
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;;; combinations.scm - combinations and that sort of stuff.
;;;
;;; Copyright(C) 2003 by Alex Shinn (foof@synthcode.com)
;;; Copyright (c) 2003-2016 Shiro Kawai <shiro@acm.org>
;;;
;;; Permission to use, copy, modify, distribute this software and
;;; accompanying documentation for any purpose is hereby granted,
;;; provided that existing copyright notices are retained in all
;;; copies and that this notice is included verbatim in all
;;; distributions.
;;; This software is provided as is, without express or implied
;;; warranty. In no circumstances the author(s) shall be liable
;;; for any damages arising out of the use of this software.
;;;
;; Initially written by Alex Shinn.
;; Modifided by Shiro Kawai
(define-module util.combinations
(use srfi-1)
(use util.match)
(use gauche.sequence)
(export permutations permutations*
permutations-for-each permutations*-for-each
combinations combinations*
combinations-for-each combinations*-for-each
power-set-binary power-set power-set-for-each
power-set* power-set*-for-each
cartesian-product cartesian-product-for-each
cartesian-product-right cartesian-product-right-for-each)
)
(select-module util.combinations)
;;----------------------------------------------------------------
;; permuations
;;
;; return a list of k-th element is removed
(define (but-kth lis k)
(case k
[(0) (cdr lis)]
[(1) (cons (car lis) (cddr lis))]
[(2) (list* (car lis) (cadr lis) (cdddr lis))]
[(3) (list* (car lis) (cadr lis) (caddr lis) (cddddr lis))]
[else (receive (head tail) (split-at lis k)
(append! head (cdr tail)))]))
;; permute set. all elements are considered distinct.
;; the shortcut for 3 elements or less speeds up a bit.
(define (permutations set)
(match set
[() (list '())]
[(a) (list set)]
[(a b) `(,set (,b ,a))]
[(a b c)
`(,set (,a ,c ,b) (,b ,a ,c) (,b ,c ,a) (,c ,a ,b) (,c ,b ,a))]
[else
(reverse!
(fold-with-index
(lambda (ind elt acc)
(fold (lambda (subperm acc) (acons elt subperm acc))
acc
(permutations (but-kth set ind))))
'()
set))]))
;; permute set, considering equal elements, a.k.a multiset permutations
(define (permutations* set :optional (eq eqv?))
(define (rec set)
(match set
[() (list '())]
[(a) (list set)]
[(a b) (if (eq a b) (list set) `(,set (,b ,a)))]
[else
(let loop ((i 0)
(seen '())
(p set)
(r '()))
(cond [(null? p) (reverse! r)]
[(member (car p) seen eq) (loop (+ i 1) seen (cdr p) r)]
[else
(loop (+ i 1)
(cons (car p) seen)
(cdr p)
(fold (lambda (subperm r) (acons (car p) subperm r))
r
(rec (but-kth set i))))]))]))
(rec set))
;; permutations without generating entire list.
;; We use shortcut for (<= length 4) case, which boosts performace.
(define-inline (p/each3 proc x1 x2 x3)
(proc `(,x1 ,x2 ,x3)) (proc `(,x1 ,x3 ,x2))
(proc `(,x2 ,x1 ,x3)) (proc `(,x2 ,x3 ,x1))
(proc `(,x3 ,x1 ,x2)) (proc `(,x3 ,x2 ,x1)))
(define (p/each4 proc x1 x2 x3 x4)
(p/each3 (lambda (xs) (proc (cons x1 xs))) x2 x3 x4)
(p/each3 (lambda (xs) (proc (cons x2 xs))) x1 x3 x4)
(p/each3 (lambda (xs) (proc (cons x3 xs))) x1 x2 x4)
(p/each3 (lambda (xs) (proc (cons x4 xs))) x1 x2 x3))
(define (p/each* proc len xs)
(if (= len 4)
(apply p/each4 proc xs)
(let1 len1 (- len 1)
(for-each-with-index
(lambda (ind elt)
(p/each* (lambda (subperm) (proc (cons elt subperm)))
len1
(but-kth xs ind)))
xs))))
(define (permutations-for-each proc set)
(match set
[() (undefined)]
[(x) (proc set)]
[(x1 x2) (proc `(,x1 ,x2)) (proc `(,x2 ,x1))]
[(x1 x2 x3) (p/each3 proc x1 x2 x3)]
[(x1 x2 x3 x4) (p/each4 proc x1 x2 x3 x4)]
[else (p/each* proc (length set) set)]))
;; Like permutations-for-each, but considering duplications.
(define (permutations*-for-each proc set :optional (eq eqv?))
(define (rec proc set)
(match set
[() (undefined)]
[(a) (proc set)]
[(a b) (cond [(eq a b) (proc set)] [else (proc set) (proc `(,b ,a))])]
[else
(let loop ((i 0)
(seen '())
(p set))
(cond [(null? p)]
[(member (car p) seen eq) (loop (+ i 1) seen (cdr p))]
[else (rec (lambda (subperm) (proc (cons (car p) subperm)))
(but-kth set i))
(loop (+ i 1) (cons (car p) seen) (cdr p))]))]))
(rec proc set))
;;----------------------------------------------------------------
;; combinations
;;
(define (combinations set n)
(define (rec set tail)
(cond [(null? tail) (list set)]
[(eq? (cdr set) tail) (map list set)]
[else (fold-right (cut acons (car set) <> <>)
(rec (cdr set) (cdr tail))
(rec (cdr set) tail))]))
(cond [(not (positive? n)) (list '())]
[(list-tail set n #f) => (cut rec set <>)]
[else '()]))
(define (combinations* set n :optional (eq eqv?))
(define (rec set n)
(if (not (positive? n))
(list '())
(let loop ((p set)
(seen '())
(r '()))
(cond [(null? p) (reverse! r)]
[(member (car p) seen eq) (loop (cdr p) seen r)]
[else
(loop (cdr p)
(cons (car p) seen)
(fold (cut acons (car p) <> <>)
r
(rec (lset-difference eq (cdr p) seen) (- n 1))))]
))))
(rec set n))
(define (combinations-for-each proc set n)
(if (not (positive? n))
(proc '())
(pair-for-each
(lambda (pr)
(combinations-for-each
(lambda (sub-comb) (proc (cons (car pr) sub-comb)))
(cdr pr)
(- n 1)))
set)))
(define (combinations*-for-each proc set n :optional (eq eqv?))
(define (rec proc set n)
(if (not (positive? n))
(proc '())
(let loop ((p set)
(seen '()))
(cond [(null? p)]
[(member (car p) seen eq) (loop (cdr p) seen)]
[else
(rec (lambda (sub-comb) (proc (cons (car p) sub-comb)))
(lset-difference eq (cdr p) seen)
(- n 1))
(loop (cdr p) (cons (car p) seen))]))))
(rec proc set n))
;;----------------------------------------------------------------
;; power sets (all subsets of any size of a given set)
;;
;; the easy binary way
(define (power-set-binary set)
(if (null? set)
(list '())
(let ((x (car set))
(rest (power-set-binary (cdr set))))
(append rest (map (^s (cons x s)) rest)))))
;; use combinations for nice ordering
(define (power-set set)
(let ((size (length set)))
(let loop ((i 0))
(if (> i size)
'()
(append! (combinations set i)
(loop (+ i 1)))))))
;; also ordered
(define (power-set-for-each proc set)
(let ((size (length set)))
(let loop ((i 0))
(if (> i size)
'()
(begin
(combinations-for-each proc set i)
(loop (+ i 1)))))))
;; w/o duplicate entry
(define (power-set* set . maybe-eq)
(let ((size (length set)))
(let loop ((i 0))
(if (> i size)
'()
(append! (apply combinations* set i maybe-eq)
(loop (+ i 1)))))))
(define (power-set*-for-each proc set . maybe-eq)
(let ((size (length set)))
(let loop ((i 0))
(if (> i size)
'()
(begin
(apply combinations*-for-each proc set i maybe-eq)
(loop (+ i 1)))))))
;;----------------------------------------------------------------
;; cartesian product (all combinations of one element from each set)
;;
(define (cartesian-product lol)
(if (null? lol)
(list '())
(let ((l (car lol))
(rest (cartesian-product (cdr lol))))
(append-map!
(lambda (x)
(map (lambda (sub-prod) (cons x sub-prod)) rest))
l))))
(define (cartesian-product-for-each proc lol)
(if (null? lol)
(proc '())
(for-each
(lambda (x)
(cartesian-product-for-each
(lambda (sub-prod)
(proc (cons x sub-prod)))
(cdr lol)))
(car lol))))
;; The above is left fixed (it varies elements to the right first).
;; Below is a right fixed product which could be defined with two
;; reverses but is short enough to warrant the performance gain of a
;; separate procedure.
;;(define (cartesian-product-right lol)
;; (map reverse (cartesian-product (reverse lol))))
(define (cartesian-product-right lol)
(if (null? lol)
(list '())
(let ((l (car lol))
(rest (cartesian-product-right (cdr lol))))
(append-map!
(lambda (sub-prod)
(map (^x (cons x sub-prod)) l))
rest))))
(define (cartesian-product-right-for-each proc lol)
(if (null? lol)
(proc '())
(cartesian-product-right-for-each
(lambda (sub-prod)
(for-each (^x (proc (cons x sub-prod))) (car lol)))
(cdr lol))))
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