mxUnionFind.java

/**
 * $Id: mxUnionFind.java,v 1.2 2009-11-24 12:00:28 gaudenz Exp $
 * Copyright (c) 2007, Gaudenz Alder
 */
package com.mxgraph.analysis;

import java.util.Hashtable;
import java.util.Map;

/**
 * Implements a union find structure that uses union by rank and path
 * compression. The union by rank guarantees worst case find time of O(log N),
 * while Tarjan shows that in combination with path compression (halving) the
 * average time for an arbitrary sequence of m >= n operations is
 * O(m*alpha(m,n)), where alpha is the inverse of the Ackermann function,
 * defined as follows:
 * <code>alpha(m,n) = min{i >= 1 | A(i, floor(m/n)) > log n} for m >= n >= 1</code>
 * Which yields almost constant time for each individual operation.
 */
public class mxUnionFind
{

	/**
	 * Maps from elements to nodes
	 */
	protected Map<Object, Node> nodes = new Hashtable<Object, Node>();

	/**
	 * Constructs a union find structure and initializes it with the specified
	 * elements.
	 * 
	 * @param elements
	 */
	public mxUnionFind(Object[] elements)
	{
		for (int i = 0; i < elements.length; i++)
		{
			nodes.put(elements[i], new Node());
		}
	}

	/**
	 * Returns the node that represents element.
	 */
	public Node getNode(Object element)
	{
		return nodes.get(element);
	}

	/**
	 * Returns the set that contains <code>node</code>. This implementation
	 * provides path compression by halving.
	 */
	public Node find(Node node)
	{
		while (node.getParent().getParent() != node.getParent())
		{
			Node t = node.getParent().getParent();
			node.setParent(t);
			node = t;
		}

		return node.getParent();
	}

	/**
	 * Unifies the sets <code>a</code> and <code>b</code> in constant time
	 * using a union by rank on the tree size.
	 */
	public void union(Node a, Node b)
	{
		Node set1 = find(a);
		Node set2 = find(b);

		if (set1 != set2)
		{
			// Limits the worst case runtime of a find to O(log N)
			if (set1.getSize() < set2.getSize())
			{
				set2.setParent(set1);
				set1.setSize(set1.getSize() + set2.getSize());
			}
			else
			{
				set1.setParent(set2);
				set2.setSize(set1.getSize() + set2.getSize());
			}
		}
	}

	/**
	 * Returns true if element a and element b are not in the same set. This
	 * uses getNode and then find to determine the elements set.
	 * 
	 * @param a The first element to compare.
	 * @param b The second element to compare.
	 * @return Returns true if a and b are in the same set.
	 * 
	 * @see #getNode(Object)
	 */
	public boolean differ(Object a, Object b)
	{
		Node set1 = find(getNode(a));
		Node set2 = find(getNode(b));

		return set1 != set2;
	}

	/**
	 * A class that defines the identity of a set.
	 */
	public class Node
	{

		/**
		 * Reference to the parent node. Root nodes point to themselves.
		 */
		protected Node parent = this;

		/**
		 * The size of the tree. Initial value is 1.
		 */
		protected int size = 1;

		/**
		 * @return Returns the parent node
		 */
		public Node getParent()
		{
			return parent;
		}

		/**
		 * @param parent The parent node to set.
		 */
		public void setParent(Node parent)
		{
			this.parent = parent;
		}

		/**
		 * @return Returns the size.
		 */
		public int getSize()
		{
			return size;
		}

		/**
		 * @param size The size to set.
		 */
		public void setSize(int size)
		{
			this.size = size;
		}
	}
}