org.jheaps.array.BinaryArrayHeap Maven / Gradle / Ivy
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/*
* (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.util.Comparator;
import org.jheaps.annotations.LinearTime;
/**
* An array based binary 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 BinaryArrayHeap extends AbstractArrayHeap {
private static final long serialVersionUID = 1L;
/**
* Default initial capacity of the binary heap.
*/
public static final int DEFAULT_HEAP_CAPACITY = 16;
/**
* 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 #DEFAULT_HEAP_CAPACITY} and
* adjusts automatically based on the sequence of insertions and deletions.
*/
public BinaryArrayHeap() {
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 BinaryArrayHeap(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 BinaryArrayHeap#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 BinaryArrayHeap(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 BinaryArrayHeap(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 binary heap
* @throws IllegalArgumentException
* in case the array is null
*/
@LinearTime
public static BinaryArrayHeap heapify(K[] array) {
if (array == null) {
throw new IllegalArgumentException("Array cannot be null");
}
if (array.length == 0) {
return new BinaryArrayHeap();
}
BinaryArrayHeap h = new BinaryArrayHeap(array.length);
System.arraycopy(array, 0, h.array, 1, array.length);
h.size = array.length;
for (int i = array.length / 2; i > 0; i--) {
h.fixdown(i);
}
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 binary heap
* @throws IllegalArgumentException
* in case the array is null
*/
@LinearTime
public static BinaryArrayHeap heapify(K[] array, Comparator comparator) {
if (array == null) {
throw new IllegalArgumentException("Array cannot be null");
}
if (array.length == 0) {
return new BinaryArrayHeap(comparator);
}
BinaryArrayHeap h = new BinaryArrayHeap(comparator, array.length);
System.arraycopy(array, 0, h.array, 1, array.length);
h.size = array.length;
for (int i = array.length / 2; i > 0; i--) {
h.fixdownWithComparator(i);
}
return h;
}
/**
* 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 + 1];
System.arraycopy(array, 1, newArray, 1, size);
array = newArray;
}
@Override
@SuppressWarnings("unchecked")
protected void fixup(int k) {
K key = array[k];
while (k > 1 && ((Comparable) array[k >> 1]).compareTo(key) > 0) {
array[k] = array[k >> 1];
k >>= 1;
}
array[k] = key;
}
@Override
protected void fixupWithComparator(int k) {
K key = array[k];
while (k > 1 && comparator.compare(array[k >> 1], key) > 0) {
array[k] = array[k >> 1];
k >>= 1;
}
array[k] = key;
}
@Override
@SuppressWarnings("unchecked")
protected void fixdown(int k) {
K key = array[k];
while (2 * k <= size) {
int j = 2 * k;
if (j < size && ((Comparable) array[j]).compareTo(array[j + 1]) > 0) {
j++;
}
if (((Comparable) key).compareTo(array[j]) <= 0) {
break;
}
array[k] = array[j];
k = j;
}
array[k] = key;
}
@Override
protected void fixdownWithComparator(int k) {
K key = array[k];
while (2 * k <= size) {
int j = 2 * k;
if (j < size && comparator.compare(array[j], array[j + 1]) > 0) {
j++;
}
if (comparator.compare(key, array[j]) <= 0) {
break;
}
array[k] = array[j];
k = j;
}
array[k] = key;
}
}