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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
(in-package :com.lisp-algo.union-find)
(defclass quick-union ()
((nw-size
:initarg :network-size
:initform 10
:accessor network-size)
(nw
:initarg nil
:accessor network)))
(defmethod initialize-instance :after ((algo quick-union) &key)
"Build a quick-find network using a dynamic vector"
(with-slots ((n nw-size) (nw nw)) algo
(let ((nodes (make-array n :fill-pointer 0)))
(dotimes (id n)
(vector-push id nodes))
(setf nw nodes))))
(defun quick-union-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)))
(defmethod union ((algo quick-union) n1 n2)
"Connect to sub-tree together. union represent the union operation on the Quick Union algorithm"
(with-slots ((network nw)) algo
(let ((new-network (copy-seq network)))
(setf (elt new-network (quick-union-find-root new-network n1))
(quick-union-find-root new-network n2))
(setf network new-network))))
(defmethod connected ((algo quick-union) n1 n2)
"Return true if n1 and n2 are connected and nil otherwise. connection represent
the find operation on the Quick Union algorithm"
(with-slots ((network nw)) algo
(= (quick-union-find-root network n1) (quick-union-find-root network n2))))
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