How can I get all possible permutations of a list with Common Lisp?

Question

I'm trying to write a Common Lisp function that will give me all possible permutations of a list, using each element only once. For example, the list '(1 2 3) will give the output ((1 2 3) (1 3 2) (2 1 3) (2 3 1) (3 1 2) (3 2 1)).

I already wrote something that kind of works, but it's clunky, it doesn't always work and I don't even really understand it. I'm not asking for code, just maybe for some guidance on how to think about it. I don't know much about writing algorithms.

Thanks, Jason

Answer 1

As a basic approach, "all permutations" follow this recursive pattern:

  all permutations of a list L is:
    for each element E in L:
      that element prepended to all permutations of [ L with E removed ]

If we take as given that you have no duplicate elements in your list, the following should do:

(defun all-permutations (list)
  (cond ((null list) nil)
        ((null (cdr list)) (list list))
        (t (loop for element in list
             append (mapcar (lambda (l) (cons element l))
                            (all-permutations (remove element list)))))))