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-;;;; Weighted Quick Union Algorithm With Path Compression
-;;;; 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 Union algorithm
-;;;; by improving the way that the union-tree is constructed
-;;;; The algorithm try to reduce the deepness of the tree in
-;;;; order to optimize the find-root function
-;;;; The path compression is ensure by the find-root function
-;;;; IMPORTANT: find-root is now a destructive function ! Be aware...
-
-;;; Base functions
-
-(defun create-network (n)
-  "Build a quick-find network using a multi-dimensional dynamic vector:\n
-1st dimension = the network\n 2nd dimension = each subtree node quantities"
-  (let ((network (make-array `(2 ,n) :initial-element 1)))
-    (dotimes (id n)
-      (setf (aref network 0 id) id))
-    network))
-
-(defun find-root (network node)
-  "Find the root of a sub-tree in the network. This is a destructive version of find-root that
-include path compression"
-  (do ((id node value)
-       (value (aref network 0 node) (aref network 0 value)))
-      ((= id value) (progn (setf (aref network 0 node) id) ; Path compression
-                           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-tree network))) ; Duplicate network
-    (let* ((n1-root (find-root new-network n1))
-          (n2-root (find-root new-network n2))
-           (n1-size (aref new-network 1 n1-root))
-           (n2-size (aref new-network 1 n2-root)))
-      (if (>= n1-size n2-size) ; Check which subtree is LARGER (not deeper)
-          (progn (setf (aref new-network 0 n2-root) (aref new-network 0 n1-root)) ; Modify the second node
-                 (setf (aref new-network 1 n1-root) ; Update tree larger
-                       (+ (aref new-network 1 n1-root) (aref new-network 1 n2-root))))
-          (progn (setf (aref new-network 0 n1-root) (aref new-network 0 n2-root)) ; Otherwise modify the first node
-                 (setf (aref new-network 1 n2-root) ; Update tree larger
-                       (+ (aref new-network 1 n2-root) (aref new-network 1 n1-root)))))
-      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 the union function."
-  `(setf ,network (union_ ,network ,n1 ,n2)))
-
-