Checking if lists share one or more elements in Racket

Question

I have two lists, lst1 and lst2. I want to define a function to check if they share some elements. For example:

• (share-some-elements? '(a b) '(a c)) ⇒ true
• (share-some-elements? '(a b) '(d e f)) ⇒ false
• (share-some-elements? '(a b) '(a b d e)) ⇒ true

I have an implementation:

(define (share-some-elements? lst1 lst2)
  (ormap (λ (x) (member x lst1)) lst2))

Which checks if each element in lst2 is a member of lst1, and returns true if any of them is.

My questions are:

1. What are the other ways of doing this?
2. How can I extend this to support any number of lists? ie.
   • (all-share-some-elements? '(a b) '(a c) '(a d)) ⇒ true
   • (all-share-some-elements? '(a b) '(a c) '(b d)) ⇒ false
   • (all-share-some-elements? '(a b) '(a c) '(b d a)) ⇒ true

There is a similar question on how to do this on two lists in python: Checking if two lists share at least one element, which doesn't quite answer my questions.

Answer 1

Both questions can be solved using a single procedure that takes a variable number of arguments. Assuming that at least one list is passed, we have:

(define (all-share-some-elements? . lists)
  (not (null? (apply set-intersect lists))))

Explanation:

• We apply set-intersect on all the lists.
• If after the intersection the result is non-empty, then the lists share at least one element in common.

Using your examples:

(all-share-some-elements? '(a b) '(a c))
=> #t
(all-share-some-elements? '(a b) '(d e f))
=> #f
(all-share-some-elements? '(a b) '(a b d e))
=> #t

(all-share-some-elements? '(a b) '(a c) '(a d))
=> #t
(all-share-some-elements? '(a b) '(a c) '(b d))
=> #f
(all-share-some-elements? '(a b) '(a c) '(b d a))
=> #t