PairingHeap (JHeaps)

java.lang.Object
- org.jheaps.tree.PairingHeap<K,V>

Type Parameters:

K - the type of keys maintained by this heap

V - the type of values maintained by this heap

All Implemented Interfaces:

Serializable, AddressableHeap<K,V>, MergeableAddressableHeap<K,V>
```
public class PairingHeap<K,V>
extends Object
implements MergeableAddressableHeap<K,V>, Serializable
```
Pairing heaps. The heap is sorted according to the natural ordering of its keys, or by a Comparator provided at heap creation time, depending on which constructor is used.
This implementation provides amortized O(log(n)) time cost for the insert, deleteMin, and decreaseKey operations. Operation 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 decreaseKey operation. The operation 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 equals if this heap is to correctly implement the AddressableHeap interface. (See Comparable or Comparator for a precise definition of consistent with equals.) This is so because the AddressableHeap interface is defined in terms of the equals operation, but a pairing heap performs all key comparisons using its compareTo (or 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 equals; it just fails to obey the general contract of the 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.
Author:

Dimitrios Michail

See Also:

CostlessMeldPairingHeap, FibonacciHeap, Serialized Form

Nested Class Summary
- Nested classes/interfaces inherited from interface org.jheaps.AddressableHeap
  AddressableHeap.Handle<K,V>

Constructor Summary

Constructors
Constructor and Description
`PairingHeap()` Constructs a new, empty heap, using the natural ordering of its keys.
`PairingHeap(Comparator<? super K> comparator)` Constructs a new, empty heap, ordered according to the given comparator.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`void`	`clear()` Clear all the elements of the heap.
`Comparator<? super K>`	`comparator()` Returns the comparator used to order the keys in this AddressableHeap, or `null` if this heap uses the natural ordering of its keys.
`AddressableHeap.Handle<K,V>`	`deleteMin()` Delete and return an element with the minimum key.
`AddressableHeap.Handle<K,V>`	`findMin()` Find an element with the minimum key.
`AddressableHeap.Handle<K,V>`	`insert(K key)` Insert a new element into the heap with a null value.
`AddressableHeap.Handle<K,V>`	`insert(K key, V value)` Insert a new element into the heap.
`boolean`	`isEmpty()` Returns `true` if this heap is empty.
`void`	`meld(MergeableAddressableHeap<K,V> other)` Meld a heap into the current heap.
`long`	`size()` Returns the number of elements in the heap.

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - PairingHeap
```
public PairingHeap()
```
    Constructs a new, empty heap, using the natural ordering of its keys. All keys inserted into the heap must implement the Comparable interface. Furthermore, all such keys must be mutually comparable: k1.compareTo(k2) must not throw a ClassCastException for any keys k1 and 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 insert(Object key) call will throw a ClassCastException.
  - PairingHeap
```
public PairingHeap(Comparator<? super K> comparator)
```
    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: comparator.compare(k1, k2) must not throw a ClassCastException for any keys k1 and k2 in the heap. If the user attempts to put a key into the heap that violates this constraint, the insert(Object key) call will throw a ClassCastException.
    
    Parameters:
    
    comparator - the comparator that will be used to order this heap. If null, the natural ordering of the keys will be used.
- Method Detail
  - insert
```
public AddressableHeap.Handle<K,V> insert(K key,
                                          V value)
```
    Insert a new element into the heap.
    
    Specified by:
    
    insert in interface AddressableHeap<K,V>
    
    Parameters:
    
    key - the element's key
    
    value - the element's value
    
    Returns:
    
    a handle for the newly added element
    
    Throws:
    
    IllegalStateException - if the heap has already been used in the right hand side of a meld
  - insert
```
public AddressableHeap.Handle<K,V> insert(K key)
```
    Insert a new element into the heap with a null value.
    
    Specified by:
    
    insert in interface AddressableHeap<K,V>
    
    Parameters:
    
    key - the element's key
    
    Returns:
    
    a handle for the newly added element
    
    Throws:
    
    IllegalStateException - if the heap has already been used in the right hand side of a meld
  - findMin
```
public AddressableHeap.Handle<K,V> findMin()
```
    Find an element with the minimum key.
    
    Specified by:
    
    findMin in interface AddressableHeap<K,V>
    
    Returns:
    
    a handle to an element with minimum key
  - deleteMin
```
public AddressableHeap.Handle<K,V> deleteMin()
```
    Delete and return an element with the minimum key. If multiple such elements exists, only one of them will be deleted. After the element is deleted the handle is invalidated and only method AddressableHeap.Handle.getKey() and AddressableHeap.Handle.getValue() can be used.
    
    Specified by:
    
    deleteMin in interface AddressableHeap<K,V>
    
    Returns:
    
    a handle to the deleted element with minimum key
  - isEmpty
```
public boolean isEmpty()
```
    Returns true if this heap is empty.
    
    Specified by:
    
    isEmpty in interface AddressableHeap<K,V>
    
    Returns:
    
    true if this heap is empty, false otherwise
  - size
```
public long size()
```
    Returns the number of elements in the heap.
    
    Specified by:
    
    size in interface AddressableHeap<K,V>
    
    Returns:
    
    the number of elements in the heap
  - comparator
```
public Comparator<? super K> comparator()
```
    Returns the comparator used to order the keys in this AddressableHeap, or null if this heap uses the natural ordering of its keys.
    
    Specified by:
    
    comparator in interface AddressableHeap<K,V>
    
    Returns:
    
    the comparator used to order the keys in this heap, or null if this addressable heap uses the natural ordering of its keys
  - clear
```
public void clear()
```
    Clear all the elements of the heap. After calling this method all handles should be considered invalidated and the behavior of methods AddressableHeap.Handle.decreaseKey(Object) and AddressableHeap.Handle.delete() is undefined.
    
    Specified by:
    
    clear in interface AddressableHeap<K,V>
  - meld
```
public void meld(MergeableAddressableHeap<K,V> other)
```
    Meld a heap into the current heap. After the operation the other heap will be empty and will not permit further insertions.
    
    Specified by:
    
    meld in interface MergeableAddressableHeap<K,V>
    
    Parameters:
    
    other - a merge-able heap

Class PairingHeap<K,V>

Nested Class Summary

Nested classes/interfaces inherited from interface org.jheaps.AddressableHeap

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

PairingHeap

PairingHeap

Method Detail

insert

insert

findMin

deleteMin

isEmpty

size

comparator

clear

meld