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Heap
s support create, insert, minimum, extract-min,
union, decrease-key, and delete operations. There are three primary
implementations, each with different expected run-times:
Procedure | BinaryHeap (worst-case) |
BinomialHeap (worst-case) |
FibonacciHeap (amortized) |
---|---|---|---|
MAKE-HEAP | Theta(1) | Theta(1) | Theta(1) |
INSERT | Theta(lg n) | O(lg n) | Theta(1) |
MINIMUM | Theta(1) | O(lg n) | Theta(1) |
EXTRACT-MIN | Theta(lg n) | Theta(lg n) | O(lg n) |
UNION | Theta(n) | O(lg n) | Theta(1) |
DECREASE-KEY | Theta(lg n) | Theta(lg n) | Theta(1) |
UPDATE-KEY | Theta(lg n) | Theta(lg n) | Theta(lg n) |
DELETE | Theta(lg n) | Theta(lg n) | O(lg n) |
All implementations of Heap
should have a no-argument
constructor which implements the
MAKE-HEAP operation in
the above-stated time bound. In addition, certain implementations
may also have constructors which take a Map
or
Heap
and construct a heap in less time than it would
take to call insert()
on each item on an initially-empty
Heap
.
Note that the
UPDATE-KEY operation is
typically implemented as a delete followed by an insert, which
often has worse performance than a
DECREASE-KEY operation.
However, some algorithms need to increase keys as well as decrease
them; there's nothing you can do about that.
BinaryHeap
,
BinomialHeap
,
FibonacciHeap
Method Summary | |
void |
clear()
Removes all entries from this Heap . |
Comparator |
comparator()
Returns the comparator associated with this Heap ,
or null if it uses its elements' natural ordering. |
void |
decreaseKey(Map.Entry me,
Object newkey)
Replace the key in the specified map entry with the specified smaller key. |
void |
delete(Map.Entry me)
Remove the specified map entry from the mapping. |
Collection |
entries()
Returns a collection view of all the Map.Entry s
in this Heap . |
boolean |
equals(Object o)
Compares the specified object with this heap for equality. |
Map.Entry |
extractMinimum()
Remove and return a map entry with minimal key. |
int |
hashCode()
Returns the hash code for this heap. |
Map.Entry |
insert(Object key,
Object value)
Inserts a node with the specified key and value into the Heap . |
boolean |
isEmpty()
Returns true if this Heap has no more
entries. |
Map.Entry |
minimum()
Returns a mapping entry with minimal key. |
int |
size()
Returns the number of entries in this Heap . |
String |
toString()
Returns a string representation of this Heap . |
void |
union(Heap h)
Merges all of the mappings from the specified Heap
into this Heap . |
void |
updateKey(Map.Entry me,
Object newkey)
Replace the key in the specified map entry with the specified key, which may be either larger or smaller than its current key. |
Method Detail |
public Map.Entry insert(Object key, Object value)
Heap
. Returns the generated Map.Entry
which may be stored and eventually passed back to
decreaseKey()
or delete
to remove
this node.
public Map.Entry minimum()
NoSuchElementException
- if the heap has no entries.public Map.Entry extractMinimum()
NoSuchElementException
- if the heap has no entries.public void union(Heap h)
Heap
into this Heap
. Note that duplicates are
permitted. After calling union()
, the Heap
passed in as an argument will be empty.
Note that usually efficient implementations of this method require
that the Heap
argument be from the same implementation
as this
. (That is, they must both be binomial heaps, or
both fibonacci heaps, etc.)
public void decreaseKey(Map.Entry me, Object newkey)
public void updateKey(Map.Entry me, Object newkey)
public void delete(Map.Entry me)
public boolean isEmpty()
true
if this Heap
has no more
entries.
public void clear()
Heap
.
public int size()
Heap
.
public Collection entries()
Map.Entry
s
in this Heap
.
public int hashCode()
Collection
returned by entries()
.
hashCode
in class Object
public boolean equals(Object o)
true
iff the given object is also a
Heap
and the Collection
s returned
by their entries()
methods are equal using
the equals()
method of Collection
.
equals
in class Object
public String toString()
Heap
.
toString
in class Object
public Comparator comparator()
Heap
,
or null
if it uses its elements' natural ordering.
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