; 1-str is a one-character-string from the set [A-Z] or [a-z]
; Word is either:
; empty
; (cons 1-str Word)
; List-of-word is either:
; (cons Word empty)
; (cons Word (List-of-word))
; word -> list-of word
; returns all possible combinations of word
(define (arrangements w)
(cond
[(empty? w) (list empty)]
[else (insert-everywhere/in-all-words (first w)
(arrangements (rest w)))]))
; 1str list-of word -> list-of word
; inserts 1-str into all positions of all words in list-of-word
(define (insert-everywhere/in-all-words a-1str a-low)
(cond
[(empty? a-low) a-low]
[else (append (insert-everywhere/in-one-word a-1str (first a-low))
(insert-everywhere/in-all-words a-1str (rest a-low)))]))
; 1str word -> list-of word
; inserts 1-str into all positions in word
(define (insert-everywhere/in-one-word a-1str a-word)
(cond
[(empty? a-word) (list (list a-1str))]
[else (create-combinations (first a-word)
(insert-everywhere/in-one-word a-1str (rest a-word)))]))
; 1-str list-of-word -> list-of-word
; create combinations of word in list-of-word
(define (create-combinations ins-ltr a-low)
(cond
[(empty? a-low) a-low]
[else (append (create-new-words ins-ltr (first a-low) empty)
(create-combinations ins-ltr (rest a-low)))]))
; 1-str word word -> list-of-word
; creates new combinations of word
(define (create-new-words l w str-w)
(cond
[(empty? w) (list (cons l str-w))]
[else (cons (create-new-word (move-letters str-w (first w))
l
(rest w))
(create-new-words l (rest w) (move-letters str-w (first w))))]))
; word 1-str word -> word
; combines two word and 1-str to form new word
(define (create-new-word l1 ins-ltr l2)
(append l1 (list ins-ltr) l2))
; word 1-str -> word
; appends 1-str to word
(define (move-letters w1 l1)
(cond
[(empty? w1) (cons l1 w1)]
[else (append w1 (list l1))]))
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