adjacency matrix/Floyd/Warshall in lisp

Question

Apparently my teacher believes that even if we don't have time to learn stuff (nor enough examples) we should move on, so I now need to know how to make Floyd-Warshall's and Warshall's algorithms in clisp.

As I did with prolog, my problem is to generate the adjacency matrix from the graph, in this case it would be a list of lists, e.g.:

((A B) (A C) (A D) (B C) (C D))

That should generate:

((0 1 1 1) (1 0 1 9) (1 1 0 1) (1 9 1 0))

I've got this:

(defun floyd(graph)
    (setf l (length graph)) 
    (setf mat (matrix l graph))
)

(defun matrix(l graph)
    (setf matrix (make-array (list l l)))
    (dotimes (i l)
        (dotimes (j l)
            (if (= i j)
                (setf (aref matrix i j) 0)
                (setf (aref matrix i j) ???)
            )
        )
    )
    matrix
)

Any help is greatly appreciated.

Also, and kind of off-topic: If I could solve my own question, should I reply myself for the sake of having an answered question?

Answer 1

I converted the Wikipedia pseudo-code into Common Lisp with type declarations. The return type declaration is non-standard, I used SBCL. I guess this won't run but it might give you an idea how Lisp code is supposed to look like.

(defparameter *n* 5)
(defparameter *path*
  (make-array (list *n* *n*)
          :element-type '(unsigned-byte 64)))


(defun floyd-warshall (path)
  (declare (type (simple-array (unsigned-byte 64) 2) path)
       (values (simple-array (unsigned-byte 64) 2) &optional))
  (destructuring-bind (y x) (array-dimensions path)
    (unless (= y x)
      (break "I expect a square matrix, not ~ax~a." x y))
    (macrolet ((p (j i)
         `(aref path ,j ,i)))
      (dotimes (k x)
    (dotimes (i x)
      (dotimes (j x)
        (setf (p j i)
          (min (p j i) (+ (p k i)
                  (p j k)))))))))
  path)

Note 1: If you have a 3D volume image you should have your indices like this (aref vol k j i) where k indexes z, j y and i the x-direction. That way in SBCL and presumably all other implementations the slices are consecutive in memory.

Note 2: macrolet can save quite a lot of typing. Also look at the implementation of with-arrays in this beautiful library: git://github.com/nikodemus/raylisp.git/objects/box.lisp