;;;; Quick Find Algorithm
;;;; This algorithm solve dynamic connectivity
;;;; problem by providing a way to find if there
;;;; is a path between two nodes in a dynamic graph


;;; Base functions

(defun create-network (n)
  "Build a quick-find network using a dynamic vector"
  (let ((nodes (make-array n :fill-pointer 0)))
    (dotimes (id n)
      (vector-push id nodes))
    nodes))

;; Link two nodes in the network
(defun union_ (network n1 n2)
  "Link two nodes in the quick-find network. union_ represent the union operation of the Quick Find Algorithm"
  (let ((v-n1 (elt network n1))
        (v-n2 (elt network n2))
        (new-network (copy-seq network)))
    (dotimes (n (length new-network))
      (if (= (elt new-network n) v-n2) (setf (elt new-network n) v-n1)))
    new-network))

;;; Macro definitions

(defmacro connected (network n1 n2)
  " Return t if there is a path between n1 and n2, nil otherwise. connected represent the find operation of the Quick Find Algorithm"
    `(= (elt ,network ,n1) (elt ,network ,n2)))

(defmacro nunion_ (network n1 n2)
  "A consed version of union_"
  `(setq ,network (union_ ,network ,n1 ,n2)))