57 lines
2.4 KiB
Common Lisp
57 lines
2.4 KiB
Common Lisp
;;;; Weighted Quick Union Algorithm
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;;;; This algorithm solve dynamic connectivity
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;;;; problem by providing a way to find if there
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;;;; is a path between two nodes in a dynamic graph.
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;;;; It is an improved version of the Quick Union algorithm
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;;;; by improving the way that the union-tree is constructed
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;;;; The algorithm try to reduce the deepness of the tree in
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;;;; order to optimize the find-root function
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(in-package :com.lisp-algo.union-find)
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;;; Base functions
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(defun wqu-create-network (n)
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"Build a quick-find network using a multi-dimensional dynamic vector:\n
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1st dimension = the network\n 2nd dimension = each subtree node quantities"
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(let ((network (make-array `(2 ,n) :initial-element 1)))
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(dotimes (id n)
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(setf (aref network 0 id) id))
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network))
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(defun wqu-find-root (network node)
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"Find the root of a sub-tree in the network."
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(do ((id node value)
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(value (aref network 0 node) (aref network 0 value)))
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((= id value) id)))
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(defun wqu-union-union (network n1 n2)
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"Connect to sub-tree together. union represent the union operation on the Quick Union algorithm"
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(let ((new-network (copy-tree network))) ; Duplicate network
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(let* ((n1-root (wqu-find-root new-network n1))
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(n2-root (wqu-find-root new-network n2))
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(n1-size (aref new-network 1 n1-root))
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(n2-size (aref new-network 1 n2-root)))
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(if (>= n1-size n2-size) ; Check which subtree is LARGER (not deeper)
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(progn (setf (aref new-network 0 n2-root) (aref new-network 0 n1-root)) ; Modify the second node
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(setf (aref new-network 1 n1-root) ; Update tree larger
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(+ (aref new-network 1 n1-root) (aref new-network 1 n2-root))))
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(progn (setf (aref new-network 0 n1-root) (aref new-network 0 n2-root)) ; Otherwise modify the first node
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(setf (aref new-network 1 n2-root) ; Update tree larger
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(+ (aref new-network 1 n2-root) (aref new-network 1 n1-root)))))
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new-network)))
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;;; Macro definitions
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(defmacro wqu-connected (network n1 n2)
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"Return true if n1 and n2 are connected and nil otherwise. connection represent
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the find operation on the Quick Union algorithm"
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`(= (wqu-find-root ,network ,n1) (wqu-find-root ,network ,n2)))
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(defmacro wqu-nunion (network n1 n2)
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"A destructive version of the union function."
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`(setf ,network (wqu-union ,network ,n1 ,n2)))
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