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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)
;;; Base functions
(defun qu-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 qu-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 qu-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 (qu-find-root new-network n1))
(qu-find-root new-network n2))
new-network))
;;; Macro definitions
(defmacro qu-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"
`(= (qu-find-root ,network ,n1) (qu-find-root ,network ,n2)))
(defmacro qu-nunion (network n1 n2)
"A destructive version of union_"
`(setf ,network (qu-union ,network ,n1 ,n2)))
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