Problem Statement

Create a routine that, given a set of strings representing directory paths and a single character directory separator, will return a string representing that part of the directory tree that is common to all the directories. Test your routine using the forward slash '/' character as the directory separator and the following three strings as input paths: Note: The resultant path should be the valid directory '/home/user1/tmp' and not the longest common string '/home/user1/tmp/cove'. If your language has a routine that performs this function (even if it does not have a changeable separator character), then mention it as part of the task.

Let's start with the solution:

(defun common-directory-path (&rest paths)
  (do* ((pathnames (mapcar #'(lambda (path) (cdr (pathname-directory (pathname path)))) paths)) ; convert strings to lists of subdirectories
     (rem pathnames (cdr rem))
     (pos (length (first rem))) ) ; position of first mismatched element
    ((null (cdr rem)) (make-pathname :directory (cons :absolute (subseq (first pathnames) 0 pos)))) ; take the common sublists and convert back to a pathname
  (setq pos (min pos (mismatch (first rem) (second rem) :test #'string-equal))) )) ; compare two paths