org.jheaps.array.BinaryArrayWeakHeap 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.array;
import java.io.Serializable;
import java.util.BitSet;
import java.util.Comparator;
import java.util.NoSuchElementException;
import org.jheaps.Constants;
import org.jheaps.annotations.ConstantTime;
import org.jheaps.annotations.LinearTime;
import org.jheaps.annotations.LogarithmicTime;
/**
* An array based binary weak heap. 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.
*
*
* The implementation uses an array in order to store the elements and
* automatically maintains the size of the array much like a
* {@link java.util.Vector} does, providing amortized O(log(n)) time cost for
* the {@code insert} and {@code deleteMin} operations. Operation
* {@code findMin}, is a worst-case O(1) operation. The bounds are worst-case if
* the user initializes the heap with a capacity larger or equal to the total
* number of elements that are going to be inserted into the heap.
*
*
* Constructing such a heap from an array of elements can be performed using the
* method {@link #heapify(Object[])} or {@link #heapify(Object[], Comparator)}
* in linear time.
*
*
* Note that the ordering maintained by a binary 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 Heap} interface. (See {@code Comparable} or {@code Comparator} for a
* precise definition of consistent with equals.) This is so because
* the {@code Heap} interface is defined in terms of the {@code equals}
* operation, but a binary 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 binary 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 Heap} 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
*
* @author Dimitrios Michail
*/
public class BinaryArrayWeakHeap extends AbstractArrayWeakHeap implements Serializable {
private static final long serialVersionUID = 7721391024028836146L;
/**
* Default initial capacity of the binary heap.
*/
public static final int DEFAULT_HEAP_CAPACITY = 16;
/**
* Reverse bits
*/
protected BitSet reverse;
/**
* 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}.
*
*
* The initial capacity of the heap is
* {@link BinaryArrayWeakHeap#DEFAULT_HEAP_CAPACITY} and adjusts
* automatically based on the sequence of insertions and deletions.
*/
public BinaryArrayWeakHeap() {
super(null, DEFAULT_HEAP_CAPACITY);
}
/**
* Constructs a new, empty heap, with a provided initial capacity 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}.
*
*
* The initial capacity of the heap is provided by the user and is adjusted
* automatically based on the sequence of insertions and deletions. The
* capacity will never become smaller than the initial requested capacity.
*
* @param capacity
* the initial heap capacity
*/
public BinaryArrayWeakHeap(int capacity) {
super(null, capacity);
}
/**
* 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}.
*
*
* The initial capacity of the heap is
* {@link BinaryArrayWeakHeap#DEFAULT_HEAP_CAPACITY} and adjusts
* automatically based on the sequence of insertions and deletions.
*
* @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.
*/
public BinaryArrayWeakHeap(Comparator comparator) {
super(comparator, DEFAULT_HEAP_CAPACITY);
}
/**
* Constructs a new, empty heap, with a provided initial capacity 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}.
*
*
* The initial capacity of the heap is provided by the user and is adjusted
* automatically based on the sequence of insertions and deletions. The
* capacity will never become smaller than the initial requested capacity.
*
* @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.
* @param capacity
* the initial heap capacity
*/
public BinaryArrayWeakHeap(Comparator comparator, int capacity) {
super(comparator, capacity);
}
/**
* Create a heap from an array of elements. The elements of the array are
* not destroyed. The method has linear time complexity.
*
* @param
* the type of keys maintained by the heap
* @param array
* an array of elements
* @return a heap
* @throws IllegalArgumentException
* in case the array is null
*/
@LinearTime
public static BinaryArrayWeakHeap heapify(K[] array) {
if (array == null) {
throw new IllegalArgumentException("Array cannot be null");
}
if (array.length == 0) {
return new BinaryArrayWeakHeap();
}
BinaryArrayWeakHeap h = new BinaryArrayWeakHeap(array.length);
System.arraycopy(array, 0, h.array, 0, array.length);
h.size = array.length;
for (int j = h.size - 1; j > 0; j--) {
h.join(h.dancestor(j), j);
}
return h;
}
/**
* Create a heap from an array of elements. The elements of the array are
* not destroyed. The method has linear time complexity.
*
* @param
* the type of keys maintained by the heap
* @param array
* an array of elements
* @param comparator
* the comparator to use
* @return a heap
* @throws IllegalArgumentException
* in case the array is null
*/
@LinearTime
public static BinaryArrayWeakHeap heapify(K[] array, Comparator comparator) {
if (array == null) {
throw new IllegalArgumentException("Array cannot be null");
}
if (array.length == 0) {
return new BinaryArrayWeakHeap(comparator);
}
BinaryArrayWeakHeap h = new BinaryArrayWeakHeap(comparator, array.length);
System.arraycopy(array, 0, h.array, 0, array.length);
h.size = array.length;
for (int j = h.size - 1; j > 0; j--) {
h.joinWithComparator(h.dancestor(j), j);
}
return h;
}
/**
* {@inheritDoc}
*/
@Override
@ConstantTime
public K findMin() {
if (Constants.NOT_BENCHMARK && size == 0) {
throw new NoSuchElementException();
}
return array[0];
}
/**
* {@inheritDoc}
*/
@Override
@LogarithmicTime(amortized = true)
public void insert(K key) {
if (Constants.NOT_BENCHMARK) {
if (key == null) {
throw new NullPointerException("Null keys not permitted");
}
// make sure there is space
if (size == array.length) {
if (size == 0) {
ensureCapacity(1);
} else {
ensureCapacity(2 * array.length);
}
}
}
array[size] = key;
reverse.clear(size);
if (size % 2 == 0) {
reverse.clear(size / 2);
}
if (comparator == null) {
fixup(size);
} else {
fixupWithComparator(size);
}
++size;
}
/**
* {@inheritDoc}
*/
@Override
@LogarithmicTime(amortized = true)
public K deleteMin() {
if (Constants.NOT_BENCHMARK && size == 0) {
throw new NoSuchElementException();
}
K result = array[0];
size--;
array[0] = array[size];
array[size] = null;
if (size > 1) {
if (comparator == null) {
fixdown(0);
} else {
fixdownWithComparator(0);
}
}
if (Constants.NOT_BENCHMARK) {
if (2 * minCapacity <= array.length && 4 * size < array.length) {
ensureCapacity(array.length / 2);
}
}
return result;
}
@Override
@SuppressWarnings("unchecked")
protected void initCapacity(int capacity) {
this.array = (K[]) new Object[capacity];
this.reverse = new BitSet(capacity);
}
/**
* Ensure that the array representation has the necessary capacity.
*
* @param capacity
* the requested capacity
*/
@Override
@SuppressWarnings("unchecked")
protected void ensureCapacity(int capacity) {
checkCapacity(capacity);
K[] newArray = (K[]) new Object[capacity];
System.arraycopy(array, 0, newArray, 0, size);
array = newArray;
BitSet newBitSet = new BitSet(capacity);
newBitSet.or(reverse);
reverse = newBitSet;
}
/**
* Return the distinguished ancestor of an element.
*
* @param j
* the element
* @return the distinguished ancestor of the element
*/
protected int dancestor(int j) {
while ((j % 2 == 1) == reverse.get(j / 2)) {
j = j / 2;
}
return j / 2;
}
/**
* Join two weak heaps into one.
*
* @param i
* root of the first weak heap
* @param j
* root of the second weak heap
* @return true if already a weak heap, false if a flip was needed
*/
@SuppressWarnings("unchecked")
protected boolean join(int i, int j) {
if (((Comparable) array[j]).compareTo(array[i]) < 0) {
K tmp = array[i];
array[i] = array[j];
array[j] = tmp;
reverse.flip(j);
return false;
}
return true;
}
/**
* Join two weak heaps into one.
*
* @param i
* root of the first weak heap
* @param j
* root of the second weak heap
* @return true if already a weak heap, false if a flip was needed
*/
protected boolean joinWithComparator(int i, int j) {
if (comparator.compare(array[j], array[i]) < 0) {
K tmp = array[i];
array[i] = array[j];
array[j] = tmp;
reverse.flip(j);
return false;
}
return true;
}
@Override
protected void fixup(int j) {
int i;
while (j > 0) {
i = dancestor(j);
if (join(i, j)) {
break;
}
j = i;
}
}
@Override
protected void fixupWithComparator(int j) {
int i;
while (j > 0) {
i = dancestor(j);
if (joinWithComparator(i, j)) {
break;
}
j = i;
}
}
@Override
protected void fixdown(int j) {
int k = 2 * j + (reverse.get(j) ? 0 : 1);
int c;
while ((c = 2 * k + (reverse.get(k) ? 1 : 0)) < size) {
k = c;
}
while (k != j) {
join(j, k);
k = k / 2;
}
}
@Override
protected void fixdownWithComparator(int j) {
int k = 2 * j + (reverse.get(j) ? 0 : 1);
int c;
while ((c = 2 * k + (reverse.get(k) ? 1 : 0)) < size) {
k = c;
}
while (k != j) {
joinWithComparator(j, k);
k = k / 2;
}
}
}