[plt-scheme] HtDP newbie question, 12.4.2

OK, now I can celebrate....
   
  In the solution I posted before, I accidentally put "(cons empty empty)" instead of "empty" in Helper #3, which added an unnecessary list to each word.
   
  Thanks again, cooke
   
  FINAL SOLUTION:
   
  ;MAIN FUNCTION: arrangements: word --> list of words
  (define (arrangements a-word)
  (cond [(empty? a-word) (cons empty empty)]
        [else (insert-everywhere/in-all-words (first a-word) (arrangements (rest
 a-word)))]))
   
  ;HELPER #1: insert-everywhere/in-all-words : letter, list of words --> list of words
  (define (insert-everywhere/in-all-words s low)
  (cond
    [(empty? (rest low)) (insert-everywhere/one-word s (first low))]
    [else (append (insert-everywhere/one-word s (first low)) (insert-everywhere/in-all-words s (rest low)))]))
  
  ;HELPER #2: insert-everywhere/one-word : letter, word --> list of words
  ;NOTE: this function just adds the last word to Helper #3
  (define (insert-everywhere/one-word letter a-word)
  (append (list (append a-word (list letter))) (insert-everywhere-except-last-letter letter a-word)))
   
  ;HELPER #3: insert-everywhere-except-last-letter : letter, word --> list of words
  (define (insert-everywhere-except-last-letter letter a-word)
  (cond
    [(empty? a-word) empty]
    [(empty? (rest a-word)) (cons (list letter (first a-word)) empty)]
    [else (cons (cons letter a-word) (add-first-letter (first a-word) (insert-everywhere-except-last-letter letter (rest a-word))))]))
   
  ;HELPER #4 : add-first-letter : letter, list of words --> list of words
  (define (add-first-letter letter low)
  (cond 
    [(empty? (rest low)) (cons (append (list letter) (first low)) empty)]
    [else (cons (append (list letter) (first low)) (add-first-letter letter (rest low)))]))

  ;test
(arrangements (list 'd 'a 'r 'e))
  ;result
  (list
 (list 'e 'r 'a 'd)
 (list 'd 'e 'r 'a)
 (list 'e 'd 'r 'a)
 (list 'e 'r 'd 'a)
 (list 'a 'e 'r 'd)
 (list 'd 'a 'e 'r)
 (list 'a 'd 'e 'r)
 (list 'a 'e 'd 'r)
 (list 'e 'a 'r 'd)
 (list 'd 'e 'a 'r)
 (list 'e 'd 'a 'r)
 (list 'e 'a 'd 'r)
 (list 'r 'e 'a 'd)
 (list 'd 'r 'e 'a)
 (list 'r 'd 'e 'a)
 (list 'r 'e 'd 'a)
 (list 'a 'r 'e 'd)
 (list 'd 'a 'r 'e)
 (list 'a 'd 'r 'e)
 (list 'a 'r 'd 'e)
 (list 'r 'a 'e 'd)
 (list 'd 'r 'a 'e)
 (list 'r 'd 'a 'e)
 (list 'r 'a 'd 'e))

       
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