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;;;; 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)))
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