com.jgraph.algebra

Class JGraphUnionFind

public class JGraphUnionFind extends Object

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: alpha(m,n) = min{i >= 1 | A(i, floor(m/n)) > log n} for m >= n >= 1 Which yields almost constant time for each individual operation.
Nested Class Summary
classJGraphUnionFind.Node
A class that defines the identity of a set.
Field Summary
protected Mapnodes
Maps from elements to nodes
Constructor Summary
JGraphUnionFind(Object[] elements)
Constructs a union find structure and initializes it with the specified elements.
Method Summary
booleandiffer(Object a, Object b)
Returns true if element a and element b are not in the same set.
JGraphUnionFind.Nodefind(JGraphUnionFind.Node node)
Returns the set that contains node.
JGraphUnionFind.NodegetNode(Object element)
Returns the node that represents element.
voidunion(JGraphUnionFind.Node a, JGraphUnionFind.Node b)
Unifies the sets a and b in constant time using a union by rank on the tree size.

Field Detail

nodes

protected Map nodes
Maps from elements to nodes

Constructor Detail

JGraphUnionFind

public JGraphUnionFind(Object[] elements)
Constructs a union find structure and initializes it with the specified elements.

Parameters: elements

Method Detail

differ

public boolean differ(Object a, Object b)
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.

Parameters: a the first element to compare b the second element to compare

Returns: Returns true if a and b are in the same set

See Also: getNode

find

public JGraphUnionFind.Node find(JGraphUnionFind.Node node)
Returns the set that contains node. This implementation provides path compression by halving.

getNode

public JGraphUnionFind.Node getNode(Object element)
Returns the node that represents element.

union

public void union(JGraphUnionFind.Node a, JGraphUnionFind.Node b)
Unifies the sets a and b in constant time using a union by rank on the tree size.
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