找出一组对象所有的全排列

下午无聊，到论坛闲逛。发现一个朋友提到面试时的一个问题“打印A、B、C、D、E的所有排列组合”，一时手痒，就写了一个。内存占用有些大，不过这个好说，只要将生成排列的结果用stream表示就可以了，stream是按需求值的，或者说惰性求值的。代码如下：

#lang racket/base

;; get all permutations of [0 .. (- n 1)],
;; return as a list
(define (permutation n)
  ;; get all permutations of [0 .. (- i 1), (+ i 1) .. (- n 1)]
  ;; return as a list
  (define (permutation/without i n)
    (let ((temp-last (- n 1)))
      (map (lambda (temp-permutation)
             (map (lambda (x)
                    (if (eqv? x i)
                        temp-last
                        x))
                  temp-permutation))
           (permutation temp-last))))

  (if (or (= n 1) (< n 1)) ;; base case
      '((0))
      (for/fold ((result '())) ((i n))
        (foldl (lambda (irest result)
                     (cons (cons i irest)
                           result))
               result
               (permutation/without i n)))))

;; print out all the permutations of ABCDE
(define (print-result)
  (let ((elements #(A B C D E)))
    (for-each (lambda (indexes)
                (for-each (lambda (i)
                            (printf "~a" (vector-ref elements i)))
                          indexes)
                (printf "~n"))
              (permutation 5))))