org.jgrapht.util

## Class FibonacciHeap<T>

• Type Parameters:
T - node data type

public class FibonacciHeap<T>
extends Object
This class implements a Fibonacci heap data structure. Much of the code in this class is based on the algorithms in the "Introduction to Algorithms" by Cormen, Leiserson, and Rivest in Chapter 21. The amortized running time of most of these methods is $O(1)$, making it a very fast data structure. Several have an actual running time of $O(1)$. removeMin() and delete() have $O(log n)$ amortized running times because they do the heap consolidation. If you attempt to store nodes in this heap with key values of -Infinity (Double.NEGATIVE_INFINITY) the delete() operation may fail to remove the correct element.

Note that this implementation is not synchronized. If multiple threads access a set concurrently, and at least one of the threads modifies the set, it must be synchronized externally. This is typically accomplished by synchronizing on some object that naturally encapsulates the set.

This class was originally developed by Nathan Fiedler for the GraphMaker project. It was imported to JGraphT with permission, courtesy of Nathan Fiedler.

Author:
Nathan Fiedler
• ### Constructor Summary

Constructors
Constructor and Description
FibonacciHeap()
Constructs a FibonacciHeap object that contains no elements.
• ### Method Summary

All Methods
Modifier and Type Method and Description
protected void cascadingCut(FibonacciHeapNode<T> y)
void clear()
Removes all elements from this heap.
protected void consolidate()
Consolidate trees
protected void cut(FibonacciHeapNode<T> x, FibonacciHeapNode<T> y)
The reverse of the link operation: removes $x$ from the child list of $y$.
void decreaseKey(FibonacciHeapNode<T> x, double k)
Decreases the key value for a heap node, given the new value to take on.
void delete(FibonacciHeapNode<T> x)
Deletes a node from the heap given the reference to the node.
void insert(FibonacciHeapNode<T> node, double key)
Inserts a new data element into the heap.
boolean isEmpty()
Tests if the Fibonacci heap is empty or not.
protected void link(FibonacciHeapNode<T> y, FibonacciHeapNode<T> x)
Make node $y$ a child of node $x$.
FibonacciHeapNode<T> min()
Returns the smallest element in the heap.
FibonacciHeapNode<T> removeMin()
Removes the smallest element from the heap.
int size()
Returns the size of the heap which is measured in the number of elements contained in the heap.
String toString()
Creates a String representation of this Fibonacci heap.
static <T> FibonacciHeap<T> union(FibonacciHeap<T> h1, FibonacciHeap<T> h2)
Joins two Fibonacci heaps into a new one.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
• ### Constructor Detail

• #### FibonacciHeap

public FibonacciHeap()
Constructs a FibonacciHeap object that contains no elements.
• ### Method Detail

• #### isEmpty

public boolean isEmpty()
Tests if the Fibonacci heap is empty or not. Returns true if the heap is empty, false otherwise.

Running time: $O(1)$ actual

Returns:
true if the heap is empty, false otherwise
• #### clear

public void clear()
Removes all elements from this heap.
• #### decreaseKey

public void decreaseKey(FibonacciHeapNode<T> x,
double k)
Decreases the key value for a heap node, given the new value to take on. The structure of the heap may be changed and will not be consolidated.

Running time: $O(1)$ amortized

Parameters:
x - node to decrease the key of
k - new key value for node x
Throws:
IllegalArgumentException - Thrown if $k$ is larger than x.key value.
• #### delete

public void delete(FibonacciHeapNode<T> x)
Deletes a node from the heap given the reference to the node. The trees in the heap will be consolidated, if necessary. This operation may fail to remove the correct element if there are nodes with key value $-\infty$.

Running time: $O(\log n)$ amortized

Parameters:
x - node to remove from heap
• #### insert

public void insert(FibonacciHeapNode<T> node,
double key)
Inserts a new data element into the heap. No heap consolidation is performed at this time, the new node is simply inserted into the root list of this heap.

Running time: $O(1)$ actual

Parameters:
node - new node to insert into heap
key - key value associated with data object
Throws:
IllegalArgumentException - if the node already belongs to a heap
• #### min

public FibonacciHeapNode<T> min()
Returns the smallest element in the heap. This smallest element is the one with the minimum key value.

Running time: $O(1)$ actual

Returns:
heap node with the smallest key
• #### removeMin

public FibonacciHeapNode<T> removeMin()
Removes the smallest element from the heap. This will cause the trees in the heap to be consolidated, if necessary.

Running time: $O(\log n)$ amortized

Returns:
node with the smallest key
• #### size

public int size()
Returns the size of the heap which is measured in the number of elements contained in the heap.

Running time: $O(1)$ actual

Returns:
number of elements in the heap
• #### union

public static <T> FibonacciHeap<T> union(FibonacciHeap<T> h1,
FibonacciHeap<T> h2)
Joins two Fibonacci heaps into a new one. No heap consolidation is performed at this time. The two root lists are simply joined together.

Running time: $O(1)$ actual

Type Parameters:
T - type of data stored in the heap
Parameters:
h1 - first heap
h2 - second heap
Returns:
new heap containing h1 and h2
• #### toString

public String toString()
Creates a String representation of this Fibonacci heap.
Overrides:
toString in class Object
Returns:
String of this.

protected void cascadingCut(FibonacciHeapNode<T> y)
Performs a cascading cut operation. This cuts y from its parent and then does the same for its parent, and so on up the tree.

Running time: $O(\log n)$; $O(1)$ excluding the recursion

Parameters:
y - node to perform cascading cut on
• #### consolidate

protected void consolidate()
Consolidate trees
• #### cut

protected void cut(FibonacciHeapNode<T> x,
FibonacciHeapNode<T> y)
The reverse of the link operation: removes $x$ from the child list of $y$. This method assumes that min is non-null.

Running time: $O(1)$

Parameters:
x - child of $y$ to be removed from $y$'s child list
y - parent of $x$ about to lose a child
protected void link(FibonacciHeapNode<T> y,
FibonacciHeapNode<T> x)
Make node $y$ a child of node $x$.
Running time: $O(1)$ actual
y - node to become child
x - node to become parent