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-;;;; Quick Union 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.
-;;;; It is an improved version of the Quick Find algorithm
-;;;; It optimize the union function
-
-
-;;; 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))
-
-(defun find-root (network node)
-  "Find the root of a sub-tree in the network."
-  (do ((id node value)
-       (value (elt network node) (elt network value)))
-      ((= id value) id)))
-
-(defun union_ (network n1 n2)
-  "Connect to sub-tree together. union represent the union operation on the Quick Union algorithm"
-  (let ((new-network (copy-seq network)))
-    (setf (elt new-network (find-root new-network n1))
-          (find-root new-network n2))
-    new-network))
-
-
-;;; Macro definitions
-
-(defmacro connected (network n1 n2)
-  "Return true if n1 and n2 are connected and nil otherwise. connection represent
-the find operation on the Quick Union algorithm"
-  `(= (find-root ,network ,n1) (find-root ,network ,n2)))
-
-(defmacro nunion_ (network n1 n2)
-  "A destructive version of union_"
-  `(setf ,network (union_ ,network ,n1 ,n2)))
-