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Implementation of disjoint-set data structure
//package gr.forth.ics.util;
/**
* Implementation of disjoint-set data structure, providing merge(merge)/find operations, in
* order to be able to track whether two elements belong in the same set or not, and
* to efficiently merge two sets.
*
* <p>The set that contains a particular element {@code e} (of type {@code Partition}
* is accessed by {@code e.find()}.
* Note that the returned set is merely an element itself, which is used as a representative of
* the set. So, if two elements have the same representative, they belong to the same set.
* Otherwise, they belong to different sets. Note that the elements of a particular set cannot be
* queried directly. Thus, perhaps confusingly, a {@code Partition} represents both a single
* element <em>and</em> potentially a set of elements, in the particular partition happens
* to be chosen as the representative of its set.
*
* <p>A <em>partition</em> is initially {@link #singleton(Object) created as a singleton}.
* It accepts an arbitrary (user-defined) value (of type {@code <E>})
* that is permanently associated with the created partition, and can be accessed by {@link #value()}.
* A created partition is independent from any other created partition. This means that the return value
* of {@link #find()} is unique, and method {@link #areMerged(Partition, Partition)}
* always returns false when given such a partition as an argument.
*
* <p>A partition {@code p1} may be <em>merged</em> with another partition {@code p2} by
* {@code p1.merge(p2);} (or, equivalently, {@code p2.merge(p1);}). From that point on,
* this invariant is created: {@code p1.find() == p2.find()} which remains true regardless of
* other future merge operations. Similarly, {@code areMerged(p1, p2)} will always return {@code true}.
*
* <p>All methods throw {@code NullPointerException} if given {@code null} arguments.
*
* @param <E> the type of the arbitrary (user-defined) element associated with a partition
* @author Andreou Dimitris, email: jim.andreou (at) gmail (dot) com
* @see <a href="http://en.wikipedia.org/wiki/Disjoint-set_data_structure">
* Disjoint-set data structure article on Wikipedia</a>
*/
public class Partition<E> {
private Partition<?> parent;
private int rank;
private final E value;
private Partition(E value) {
this.value = value;
this.parent = this;
}
/**
* Creates a partition of a singleton set, containing only itself. The created
* partition is permanently associated with the specified value, which can
* be accessed by {@linkplain #value()}.
*
* @param <E> the type of the user-defined value
* @param value the value to associate with the created partition
* @return the created partition
*/
public static <E> Partition<E> singleton(E value) {
return new Partition<E>(value);
}
/**
* Returns the value associated with this partition upon creation.
*
* @return the value associated with this partition upon creation
*/
public E value() {
return value;
}
/**
* Merges this partition with another one. This has the following implications:
* <ul>
* <li>{@code this.find() == other.find()} will be true, forever
* <li>{@code Partition.areMerged(this, other)} will return true, forever
* </ul>
* @param other the partition to merge this partition with
* @return a partition representing the merged partitions. It will be either equal to either
* {@code this.find()} or {@code other.find()}, i.e. one representative of the partitions
* which will be elected to represent the union
*/
public Partition<?> merge(Partition<?> other) {
Partition<?> root1 = other.find();
Partition<?> root2 = find();
if (root1.rank < root2.rank) {
root1.parent = root2;
return root2;
} else if (root1.rank > root2.rank) {
root2.parent = root1;
return root1;
} else {
root2.parent = root1;
root1.rank++;
return root1;
}
}
/**
* Returns the unique representative of the set that this element belongs to. The
* returned instance can be compared with the representative of another element,
* to check whether the two elements belong to the same set (when the two
* representatives will be identical)
*
* @return the unique representative of the set that this partition belongs to
*/
public Partition<?> find() {
//A single-pass path compressing algorithm
Partition<?> current = this;
Partition<?> last = this;
while (current.parent != current) {
last.parent = current.parent; //initially a no-op
last = current;
current = current.parent;
}
return current;
}
/**
* Checks whether the two elements have been merged.
*
* <p>Equivalent to {@code partition1.find() == partition2.find()}.
* @param partition1 the first element
* @param partition2 the second element
* @return whether the two partitions have been merged
*/
public static boolean areMerged(Partition<?> partition1, Partition<?> partition2) {
return partition1.find() == partition2.find();
}
}
package gr.forth.ics.util;
import junit.framework.TestCase;
/**
*
* @author Andreou Dimitris, email: jim.andreou (at) gmail (dot) com
*/
public class PartitionTest extends TestCase {
public PartitionTest(String testName) {
super(testName);
}
public void testValue() {
Partition<String> p = Partition.singleton("test");
assertEquals("test", p.value());
}
public void testFind() {
Partition<String> p1 = Partition.singleton("a");
assertSame(p1, p1.find());
}
public void testUnionWithEqualRank() {
Partition<String> p1 = Partition.singleton("a");
Partition<String> p2 = Partition.singleton("b");
assertNotSame(p1.find(), p2.find());
p1.merge(p2);
assertSame(p1.find(), p2.find());
}
public void testUnionWithLessRank() {
Partition<?> pSmall = Partition.singleton("a");
Partition<?> pBig = Partition.singleton("b").merge(Partition.singleton("c"));
Partition<?> pAll = pSmall.merge(pBig);
//the small is attached to the big
assertSame(pSmall.find(), pBig);
assertSame(pBig.find(), pBig);
assertSame(pAll, pBig);
}
public void testUnionWithMoreRank() {
Partition<?> pSmall = Partition.singleton("a");
Partition<?> pBig = Partition.singleton("b").merge(Partition.singleton("c"));
Partition<?> pAll = pBig.merge(pSmall);
//the small is attached to the big
assertSame(pSmall.find(), pBig);
assertSame(pBig.find(), pBig);
assertSame(pAll, pBig);
}
}
