org.jheaps.tree.PairingHeap Maven / Gradle / Ivy
/*
* (C) Copyright 2014-2016, by Dimitrios Michail
*
* JHeaps Library
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.jheaps.tree;
import java.io.Serializable;
import java.util.Comparator;
import java.util.NoSuchElementException;
import org.jheaps.AddressableHeap;
import org.jheaps.MergeableAddressableHeap;
import org.jheaps.annotations.ConstantTime;
import org.jheaps.annotations.LogarithmicTime;
/**
* Pairing heaps. The heap is sorted according to the {@linkplain Comparable
* natural ordering} of its keys, or by a {@link Comparator} provided at heap
* creation time, depending on which constructor is used.
*
*
* This implementation provides amortized O(log(n)) time cost for the
* {@code insert}, {@code deleteMin}, and {@code decreaseKey} operations.
* Operation {@code findMin}, is a worst-case O(1) operation. The algorithms are
* based on the pairing heap
* paper. Pairing heaps are very efficient in practice, especially in
* applications requiring the {@code decreaseKey} operation. The operation
* {@code meld} is amortized O(log(n)).
*
*
* All the above bounds, however, assume that the user does not perform
* cascading melds on heaps such as:
*
*
* d.meld(e);
* c.meld(d);
* b.meld(c);
* a.meld(b);
*
*
* The above scenario, although efficiently supported by using union-find with
* path compression, invalidates the claimed bounds.
*
*
* Note that the ordering maintained by a pairing heap, like any heap, and
* whether or not an explicit comparator is provided, must be consistent
* with {@code equals} if this heap is to correctly implement the
* {@code AddressableHeap} interface. (See {@code Comparable} or
* {@code Comparator} for a precise definition of consistent with
* equals.) This is so because the {@code AddressableHeap} interface is
* defined in terms of the {@code equals} operation, but a pairing heap performs
* all key comparisons using its {@code compareTo} (or {@code compare}) method,
* so two keys that are deemed equal by this method are, from the standpoint of
* the pairing heap, equal. The behavior of a heap is well-defined even
* if its ordering is inconsistent with {@code equals}; it just fails to obey
* the general contract of the {@code AddressableHeap} interface.
*
*
* Note that this implementation is not synchronized. If
* multiple threads access a heap concurrently, and at least one of the threads
* modifies the heap structurally, it must be synchronized externally.
* (A structural modification is any operation that adds or deletes one or more
* elements or changing the key of some element.) This is typically accomplished
* by synchronizing on some object that naturally encapsulates the heap.
*
* @param
* the type of keys maintained by this heap
* @param
* the type of values maintained by this heap
*
* @author Dimitrios Michail
*
* @see CostlessMeldPairingHeap
* @see FibonacciHeap
*/
public class PairingHeap implements MergeableAddressableHeap, Serializable {
private final static long serialVersionUID = 1;
/**
* The comparator used to maintain order in this heap, or null if it uses
* the natural ordering of its keys.
*
* @serial
*/
private final Comparator comparator;
/**
* The root of the pairing heap
*/
private Node root;
/**
* Size of the pairing heap
*/
private long size;
/**
* Used to reference the current heap or some other pairing heap in case of
* melding, so that handles remain valid even after a meld, without having
* to iterate over them.
*
* In order to avoid maintaining a full-fledged union-find data structure,
* we disallow a heap to be used in melding more than once. We use however,
* path-compression in case of cascading melds, that it, a handle moves from
* one heap to another and then another.
*/
private PairingHeap other;
/**
* Constructs a new, empty heap, using the natural ordering of its keys. All
* keys inserted into the heap must implement the {@link Comparable}
* interface. Furthermore, all such keys must be mutually
* comparable: {@code k1.compareTo(k2)} must not throw a
* {@code ClassCastException} for any keys {@code k1} and {@code k2} in the
* heap. If the user attempts to put a key into the heap that violates this
* constraint (for example, the user attempts to put a string key into a
* heap whose keys are integers), the {@code insert(Object key)} call will
* throw a {@code ClassCastException}.
*/
@ConstantTime
public PairingHeap() {
this(null);
}
/**
* Constructs a new, empty heap, ordered according to the given comparator.
* All keys inserted into the heap must be mutually comparable by
* the given comparator: {@code comparator.compare(k1,
* k2)} must not throw a {@code ClassCastException} for any keys {@code k1}
* and {@code k2} in the heap. If the user attempts to put a key into the
* heap that violates this constraint, the {@code insert(Object key)} call
* will throw a {@code ClassCastException}.
*
* @param comparator
* the comparator that will be used to order this heap. If
* {@code null}, the {@linkplain Comparable natural ordering} of
* the keys will be used.
*/
@ConstantTime
public PairingHeap(Comparator comparator) {
this.root = null;
this.comparator = comparator;
this.size = 0;
this.other = this;
}
/**
* {@inheritDoc}
*
* @throws IllegalStateException
* if the heap has already been used in the right hand side of a
* meld
*/
@Override
@LogarithmicTime(amortized = true)
public AddressableHeap.Handle insert(K key, V value) {
if (other != this) {
throw new IllegalStateException("A heap cannot be used after a meld");
}
if (key == null) {
throw new NullPointerException("Null keys not permitted");
}
Node n = new Node(this, key, value);
if (comparator == null) {
root = link(root, n);
} else {
root = linkWithComparator(root, n);
}
size++;
return n;
}
/**
* {@inheritDoc}
*
* @throws IllegalStateException
* if the heap has already been used in the right hand side of a
* meld
*/
@Override
@LogarithmicTime(amortized = true)
public AddressableHeap.Handle insert(K key) {
return insert(key, null);
}
/**
* {@inheritDoc}
*/
@Override
@ConstantTime(amortized = false)
public AddressableHeap.Handle findMin() {
if (size == 0) {
throw new NoSuchElementException();
}
return root;
}
/**
* {@inheritDoc}
*/
@Override
@LogarithmicTime(amortized = true)
public AddressableHeap.Handle deleteMin() {
if (size == 0) {
throw new NoSuchElementException();
}
// assert root.o_s == null && root.y_s == null;
Handle oldRoot = root;
// cut all children, combine them and overwrite old root
root = combine(cutChildren(root));
// decrease size
size--;
return oldRoot;
}
/**
* {@inheritDoc}
*/
@Override
@ConstantTime
public boolean isEmpty() {
return size == 0;
}
/**
* {@inheritDoc}
*/
@Override
@ConstantTime
public long size() {
return size;
}
/**
* {@inheritDoc}
*/
@Override
public Comparator comparator() {
return comparator;
}
/**
* {@inheritDoc}
*/
@Override
@ConstantTime(amortized = false)
public void clear() {
root = null;
size = 0;
}
/**
* {@inheritDoc}
*/
@Override
@LogarithmicTime(amortized = true)
public void meld(MergeableAddressableHeap other) {
PairingHeap h = (PairingHeap) other;
// check same comparator
if (comparator != null) {
if (h.comparator == null || !h.comparator.equals(comparator)) {
throw new IllegalArgumentException("Cannot meld heaps using different comparators!");
}
} else if (h.comparator != null) {
throw new IllegalArgumentException("Cannot meld heaps using different comparators!");
}
if (h.other != h) {
throw new IllegalStateException("A heap cannot be used after a meld.");
}
// perform the meld
size += h.size;
if (comparator == null) {
root = link(root, h.root);
} else {
root = linkWithComparator(root, h.root);
}
// clear other
h.size = 0;
h.root = null;
// take ownership
h.other = this;
}
// --------------------------------------------------------------------
static class Node implements AddressableHeap.Handle, Serializable {
private final static long serialVersionUID = 1;
/*
* We maintain explicitly the belonging heap, instead of using an inner
* class due to possible cascading melding.
*/
PairingHeap heap;
K key;
V value;
Node o_c; // older child
Node y_s; // younger sibling
Node o_s; // older sibling or parent
Node(PairingHeap heap, K key, V value) {
this.heap = heap;
this.key = key;
this.value = value;
this.o_c = null;
this.y_s = null;
this.o_s = null;
}
/**
* {@inheritDoc}
*/
@Override
public K getKey() {
return key;
}
/**
* {@inheritDoc}
*/
@Override
public V getValue() {
return value;
}
/**
* {@inheritDoc}
*/
@Override
public void setValue(V value) {
this.value = value;
}
/**
* {@inheritDoc}
*/
@Override
@LogarithmicTime(amortized = true)
public void decreaseKey(K newKey) {
getOwner().decreaseKey(this, newKey);
}
/**
* {@inheritDoc}
*/
@Override
@LogarithmicTime(amortized = true)
public void delete() {
getOwner().delete(this);
}
/*
* Get the owner heap of the handle. This is union-find with
* path-compression between heaps.
*/
PairingHeap getOwner() {
if (heap.other != heap) {
// find root
PairingHeap root = heap;
while (root != root.other) {
root = root.other;
}
// path-compression
PairingHeap cur = heap;
while (cur.other != root) {
PairingHeap next = cur.other;
cur.other = root;
cur = next;
}
heap = root;
}
return heap;
}
}
/**
* Decrease the key of a node.
*
* @param n
* the node
* @param newKey
* the new key
*/
@SuppressWarnings("unchecked")
private void decreaseKey(Node n, K newKey) {
int c;
if (comparator == null) {
c = ((Comparable) newKey).compareTo(n.key);
} else {
c = comparator.compare(newKey, n.key);
}
if (c > 0) {
throw new IllegalArgumentException("Keys can only be decreased!");
}
n.key = newKey;
if (c == 0 || root == n) {
return;
}
if (n.o_s == null) {
throw new IllegalArgumentException("Invalid handle!");
}
// unlink from parent
if (n.y_s != null) {
n.y_s.o_s = n.o_s;
}
if (n.o_s.o_c == n) { // I am the oldest :(
n.o_s.o_c = n.y_s;
} else { // I have an older sibling!
n.o_s.y_s = n.y_s;
}
n.y_s = null;
n.o_s = null;
// merge with root
if (comparator == null) {
root = link(root, n);
} else {
root = linkWithComparator(root, n);
}
}
/*
* Delete a node
*/
private void delete(Node n) {
if (root == n) {
deleteMin();
n.o_c = null;
n.y_s = null;
n.o_s = null;
return;
}
if (n.o_s == null) {
throw new IllegalArgumentException("Invalid handle!");
}
// unlink from parent
if (n.y_s != null) {
n.y_s.o_s = n.o_s;
}
if (n.o_s.o_c == n) { // I am the oldest :(
n.o_s.o_c = n.y_s;
} else { // I have an older sibling!
n.o_s.y_s = n.y_s;
}
n.y_s = null;
n.o_s = null;
// perform delete-min at tree rooted at this
Node t = combine(cutChildren(n));
// and merge with other cut tree
if (comparator == null) {
root = link(root, t);
} else {
root = linkWithComparator(root, t);
}
size--;
}
/*
* Two pass pair and compute root.
*/
private Node combine(Node l) {
if (l == null) {
return null;
}
assert l.o_s == null;
// left-right pass
Node pairs = null;
Node it = l, p_it;
if (comparator == null) { // no comparator
while (it != null) {
p_it = it;
it = it.y_s;
if (it == null) {
// append last node to pair list
p_it.y_s = pairs;
p_it.o_s = null;
pairs = p_it;
} else {
Node n_it = it.y_s;
// disconnect both
p_it.y_s = null;
p_it.o_s = null;
it.y_s = null;
it.o_s = null;
// link trees
p_it = link(p_it, it);
// append to pair list
p_it.y_s = pairs;
pairs = p_it;
// advance
it = n_it;
}
}
} else {
while (it != null) {
p_it = it;
it = it.y_s;
if (it == null) {
// append last node to pair list
p_it.y_s = pairs;
p_it.o_s = null;
pairs = p_it;
} else {
Node n_it = it.y_s;
// disconnect both
p_it.y_s = null;
p_it.o_s = null;
it.y_s = null;
it.o_s = null;
// link trees
p_it = linkWithComparator(p_it, it);
// append to pair list
p_it.y_s = pairs;
pairs = p_it;
// advance
it = n_it;
}
}
}
// second pass (reverse order - due to add first)
it = pairs;
Node f = null;
if (comparator == null) {
while (it != null) {
Node nextIt = it.y_s;
it.y_s = null;
f = link(f, it);
it = nextIt;
}
} else {
while (it != null) {
Node nextIt = it.y_s;
it.y_s = null;
f = linkWithComparator(f, it);
it = nextIt;
}
}
return f;
}
/**
* Cut the children of a node and return the list.
*
* @param n
* the node
* @return the first node in the children list
*/
private Node cutChildren(Node n) {
Node child = n.o_c;
n.o_c = null;
if (child != null) {
child.o_s = null;
}
return child;
}
@SuppressWarnings("unchecked")
private Node link(Node f, Node s) {
if (s == null) {
return f;
} else if (f == null) {
return s;
} else if (((Comparable) f.key).compareTo(s.key) <= 0) {
s.y_s = f.o_c;
s.o_s = f;
if (f.o_c != null) {
f.o_c.o_s = s;
}
f.o_c = s;
return f;
} else {
return link(s, f);
}
}
private Node linkWithComparator(Node f, Node s) {
if (s == null) {
return f;
} else if (f == null) {
return s;
} else if (comparator.compare(f.key, s.key) <= 0) {
s.y_s = f.o_c;
s.o_s = f;
if (f.o_c != null) {
f.o_c.o_s = s;
}
f.o_c = s;
return f;
} else {
return linkWithComparator(s, f);
}
}
}