Class FibonacciHeap<T>
- java.lang.Object
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- org.jgrapht.util.FibonacciHeap<T>
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- Type Parameters:
T
- node data type
public class FibonacciHeap<T> extends java.lang.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) thedelete()
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.
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Field Summary
Fields Modifier and Type Field Description private FibonacciHeapNode<T>
minNode
Points to the minimum node in the heap.private int
nNodes
Number of nodes in the heap.private static double
ONEOVERLOGPHI
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Constructor Summary
Constructors Constructor Description FibonacciHeap()
Constructs a FibonacciHeap object that contains no elements.
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method Description protected void
cascadingCut(FibonacciHeapNode<T> y)
Performs a cascading cut operation.void
clear()
Removes all elements from this heap.protected void
consolidate()
Consolidate treesprotected 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.java.lang.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.
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Field Detail
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ONEOVERLOGPHI
private static final double ONEOVERLOGPHI
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minNode
private FibonacciHeapNode<T> minNode
Points to the minimum node in the heap.
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nNodes
private int nNodes
Number of nodes in the heap.
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Method Detail
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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
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clear
public void clear()
Removes all elements from this heap.
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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 ofk
- new key value for node x- Throws:
java.lang.IllegalArgumentException
- Thrown if k is larger than x.key value.
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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 -Infinity.Running time: O(log n) amortized
- Parameters:
x
- node to remove from heap
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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 heapkey
- key value associated with data object- Throws:
java.lang.IllegalArgumentException
- if the node already belongs to a heap
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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
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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
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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
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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 heaph2
- second heap- Returns:
- new heap containing h1 and h2
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toString
public java.lang.String toString()
Creates a String representation of this Fibonacci heap.- Overrides:
toString
in classjava.lang.Object
- Returns:
- String of this.
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cascadingCut
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
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consolidate
protected void consolidate()
Consolidate trees
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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 listy
- parent of x about to lose a child
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link
protected void link(FibonacciHeapNode<T> y, FibonacciHeapNode<T> x)
Make node y a child of node x.Running time: O(1) actual
- Parameters:
y
- node to become childx
- node to become parent
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