首先我们要明白,堆实际上是一颗完全二叉树,借助完全二叉树父子节点关系的性质,我们就可以很方便的在数组中实现这一结构,而堆也分为两种,一种是大根堆,顾名思义也就是父节点value大于子节点value,小根堆则相反

动态数组

借助这个类实现堆结构,直接用ArrayList也可以


public class Array<E> {

private E[] data;
private int size;

// 构造函数,传入数组的容量capacity构造Array
public Array(int capacity){
data = (E[])new Object[capacity];
size = 0;
}

// 无参数的构造函数,默认数组的容量capacity=10
public Array(){
this(10);
}

// 获取数组的容量
public int getCapacity(){
return data.length;
}

// 获取数组中的元素个数
public int getSize(){
return size;
}

// 返回数组是否为空
public boolean isEmpty(){
return size == 0;
}

// 在index索引的位置插入一个新元素e
public void add(int index, E e){
if(index < 0 || index > size)
throw new IllegalArgumentException("Add failed. Require index >= 0 and index <= size.");
if(size == data.length)
resize(2 * data.length); //2倍扩容
for(int i = size - 1; i >= index ; i --){
data[i + 1] = data[i];
}
data[index] = e;
size ++;
}

// 向所有元素后添加一个新元素
public void addLast(E e){
add(size, e);
}

// 在所有元素前添加一个新元素
public void addFirst(E e){
add(0, e);
}

// 获取index索引位置的元素
public E get(int index){
if(index < 0 || index >= size)
throw new IllegalArgumentException("Get failed. Index is illegal.");
return data[index];
}

// 修改index索引位置的元素为e
public void set(int index, E e){
if(index < 0 || index >= size)
throw new IllegalArgumentException("Set failed. Index is illegal.");
data[index] = e;
}

// 查找数组中是否有元素e
public boolean contains(E e){
for(int i = 0 ; i < size ; i ++){
if(data[i].equals(e))
return true;
}
return false;
}

// 查找数组中元素e所在的索引,如果不存在元素e,则返回-1
public int find(E e){
for(int i = 0 ; i < size ; i ++){
if(data[i].equals(e))
return i;
}
return -1;
}

// 从数组中删除index位置的元素, 返回删除的元素
public E remove(int index){
if(index < 0 || index >= size)
throw new IllegalArgumentException("Remove failed. Index is illegal.");

E ret = data[index];
for(int i = index + 1 ; i < size ; i ++)
data[i - 1] = data[i];
size --;
data[size] = null; // loitering objects != memory leak
//数据不到1/4的时候缩减
if(size == data.length / 4 && data.length / 2 != 0)
resize(data.length / 2);
return ret;
}

// 从数组中删除第一个元素, 返回删除的元素
public E removeFirst(){
return remove(0);
}

// 从数组中删除最后一个元素, 返回删除的元素
public E removeLast(){
return remove(size - 1);
}

// 从数组中删除元素e
public void removeElement(E e){
int index = find(e);
if(index != -1)
remove(index);
}

//交换
public void swap(int a,int b){
if (a<0||a>=size || b<0||b>=size) {
throw new IllegalArgumentException("index illegal");
}
E temp=data[a];
data[a]=data[b];
data[b]=temp;
}

@Override
public String toString(){

StringBuilder res = new StringBuilder();
res.append(String.format("Array: size = %d , capacity = %d\n", size, data.length));
res.append('[');
for(int i = 0 ; i < size ; i ++){
res.append(data[i]);
if(i != size - 1)
res.append(", ");
}
res.append(']');
return res.toString();
}

// 将数组空间的容量变成newCapacity大小
private void resize(int newCapacity){
E[] newData = (E[])new Object[newCapacity];
for(int i = 0 ; i < size ; i ++)
newData[i] = data[i];
data = newData;
}
}

大根堆

public class MaxHeap<E extends Comparable<E>>{
private Array<E> data;

public MaxHeap(int capacity){
data=new Array<>(capacity);
}

public MaxHeap(){
data=new Array<>();
}

public int size(){
return data.getSize();
}

public boolean isEmpty(){
return data.isEmpty();
}

//父节点
private int parent(int index){
if (index==0) {
throw new IllegalArgumentException("index 0 don't have parent");
}
return (index-1)/2;
}

//左孩子
private int leftChild(int index){
return index*2+1;
}

//右孩子
private int rightChild(int index){
return index*2+2;
}

public void add(E e){
data.addLast(e);
siftUp(data.getSize()-1);
}

//上浮
private void siftUp(int cur){
while(cur>0 && data.get(parent(cur)).compareTo(data.get(cur)) < 0){
data.swap(cur,parent(cur));
cur=parent(cur);
}
}

public E findMax(){
if (data.getSize()==0) {
throw new IllegalArgumentException("heap is empty !!!");
}
return data.get(0);
}

public E popMax(){
if (data.getSize()==0) {
throw new IllegalArgumentException("heap is empty !!!");
}
E res=findMax();
data.swap(0,data.getSize()-1);
data.removeLast();
siftDown(0);
return res;
}

private void siftDown(int cur){
while(leftChild(cur)<data.getSize()){ //有左孩子
int large=leftChild(cur);
//如果也有右孩子,就比较下两个节点的值取最大值
if (large+1<data.getSize() && data.get(large).compareTo(data.get(large+1))<0) {
large=large+1;
}
//比左右孩子都大就直接结束了
if (data.get(large).compareTo(data.get(cur))<=0){
return;
}
data.swap(large,cur);
cur=large;
}
}
}

其实上面的实现还是有一些缺陷的,只能按照给定的键的默认排序规则进行比较,不方便实现自定义的比较规则,需要进行封装才可以,关于这一点其实可以借鉴Java中的PriorityQueue

测试

import java.util.*;
public class HeapTest{
public static void main(String[] args) {
int[] nums=generateRandomArray(50000000,500);
MaxHeap heap=new MaxHeap();
for (int i=0;i<nums.length;i++) {
heap.add(nums[i]);
}
for (int i=0;i<nums.length;i++) {
nums[i]=(int)heap.popMax();
}
for (int i=1;i<nums.length;i++) {
if (nums[i-1]<nums[i]) {
System.out.println("fuxk!!!");
return;
}
}
System.out.println("sucess!!!!!");
}

// for test
public static int[] generateRandomArray(int maxSize, int maxValue) {
int[] arr = new int[(int) ((maxSize + 1) * Math.random())];
for (int i = 0; i < arr.length; i++) {
arr[i] = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());
}
return arr;
}
}

PriorityQueue

package java.util;

import java.util.function.Consumer;
import sun.misc.SharedSecrets;

/**
* An unbounded priority {@linkplain Queue queue} based on a priority heap.
* The elements of the priority queue are ordered according to their
* {@linkplain Comparable natural ordering}, or by a {@link Comparator}
* provided at queue construction time, depending on which constructor is
* used. A priority queue does not permit {@code null} elements.
* A priority queue relying on natural ordering also does not permit
* insertion of non-comparable objects (doing so may result in
* {@code ClassCastException}).
*
* <p>The <em>head</em> of this queue is the <em>least</em> element
* with respect to the specified ordering. If multiple elements are
* tied for least value, the head is one of those elements -- ties are
* broken arbitrarily. The queue retrieval operations {@code poll},
* {@code remove}, {@code peek}, and {@code element} access the
* element at the head of the queue.
*
* <p>A priority queue is unbounded, but has an internal
* <i>capacity</i> governing the size of an array used to store the
* elements on the queue. It is always at least as large as the queue
* size. As elements are added to a priority queue, its capacity
* grows automatically. The details of the growth policy are not
* specified.
*
* <p>This class and its iterator implement all of the
* <em>optional</em> methods of the {@link Collection} and {@link
* Iterator} interfaces. The Iterator provided in method {@link
* #iterator()} is <em>not</em> guaranteed to traverse the elements of
* the priority queue in any particular order. If you need ordered
* traversal, consider using {@code Arrays.sort(pq.toArray())}.
*
* <p><strong>Note that this implementation is not synchronized.</strong>
* Multiple threads should not access a {@code PriorityQueue}
* instance concurrently if any of the threads modifies the queue.
* Instead, use the thread-safe {@link
* java.util.concurrent.PriorityBlockingQueue} class.
*
* <p>Implementation note: this implementation provides
* O(log(n)) time for the enqueuing and dequeuing methods
* ({@code offer}, {@code poll}, {@code remove()} and {@code add});
* linear time for the {@code remove(Object)} and {@code contains(Object)}
* methods; and constant time for the retrieval methods
* ({@code peek}, {@code element}, and {@code size}).
*
* <p>This class is a member of the
* <a href="{@docRoot}/../technotes/guides/collections/index.html">
* Java Collections Framework</a>.
*
* @since 1.5
* @author Josh Bloch, Doug Lea
* @param <E> the type of elements held in this collection
*/
public class PriorityQueue<E> extends AbstractQueue<E>
implements java.io.Serializable {

private static final long serialVersionUID = -7720805057305804111L;

private static final int DEFAULT_INITIAL_CAPACITY = 11;

/**
* Priority queue represented as a balanced binary heap: the two
* children of queue[n] are queue[2*n+1] and queue[2*(n+1)]. The
* priority queue is ordered by comparator, or by the elements'
* natural ordering, if comparator is null: For each node n in the
* heap and each descendant d of n, n <= d. The element with the
* lowest value is in queue[0], assuming the queue is nonempty.
*/
transient Object[] queue; // non-private to simplify nested class access

/**
* The number of elements in the priority queue.
*/
private int size = 0;

/**
* The comparator, or null if priority queue uses elements'
* natural ordering.
* 如果没有传入比较器的话,按照元素的自然排序进行比较
*/
private final Comparator<? super E> comparator;

/**
* The number of times this priority queue has been
* <i>structurally modified</i>. See AbstractList for gory details.
*/
transient int modCount = 0; // non-private to simplify nested class access

/**
* Creates a {@code PriorityQueue} with the default initial
* capacity (11) that orders its elements according to their
* {@linkplain Comparable natural ordering}.
*/
public PriorityQueue() {
this(DEFAULT_INITIAL_CAPACITY, null);
}

public PriorityQueue(int initialCapacity) {
this(initialCapacity, null);
}

//传入自定义的比较规则
public PriorityQueue(Comparator<? super E> comparator) {
this(DEFAULT_INITIAL_CAPACITY, comparator);
}

public PriorityQueue(int initialCapacity,
Comparator<? super E> comparator) {
// Note: This restriction of at least one is not actually needed,
// but continues for 1.5 compatibility
if (initialCapacity < 1)
throw new IllegalArgumentException();
this.queue = new Object[initialCapacity];
this.comparator = comparator;
}

/**
* Creates a {@code PriorityQueue} containing the elements in the
* specified collection. If the specified collection is an instance of
* a {@link SortedSet} or is another {@code PriorityQueue}, this
* priority queue will be ordered according to the same ordering.
* Otherwise, this priority queue will be ordered according to the
* {@linkplain Comparable natural ordering} of its elements.
* 传入一个集合类型,如果是SortSet(有序)类型的集合或者也是PriorityQueue就会按照相同的规则去比较。
* 否则就会按照元素的自然排序规则去比较。
*
* @param c the collection whose elements are to be placed
* into this priority queue
* @throws ClassCastException if elements of the specified collection
* cannot be compared to one another according to the priority
* queue's ordering
* @throws NullPointerException if the specified collection or any
* of its elements are null
*/
@SuppressWarnings("unchecked")
public PriorityQueue(Collection<? extends E> c) {
if (c instanceof SortedSet<?>) {
SortedSet<? extends E> ss = (SortedSet<? extends E>) c;
//拿到SortSet集合中元素的比较器,用于后序的操作
this.comparator = (Comparator<? super E>) ss.comparator();
initElementsFromCollection(ss);
}
else if (c instanceof PriorityQueue<?>) {
PriorityQueue<? extends E> pq = (PriorityQueue<? extends E>) c;
this.comparator = (Comparator<? super E>) pq.comparator();
initFromPriorityQueue(pq);
}
else {
this.comparator = null;
initFromCollection(c);
}
}

/**
* Creates a {@code PriorityQueue} containing the elements in the
* specified priority queue. This priority queue will be
* ordered according to the same ordering as the given priority
* queue.
*
* @param c the priority queue whose elements are to be placed
* into this priority queue
* @throws ClassCastException if elements of {@code c} cannot be
* compared to one another according to {@code c}'s
* ordering
* @throws NullPointerException if the specified priority queue or any
* of its elements are null
*/
@SuppressWarnings("unchecked")
public PriorityQueue(PriorityQueue<? extends E> c) {
this.comparator = (Comparator<? super E>) c.comparator();
initFromPriorityQueue(c);
}

/**
* Creates a {@code PriorityQueue} containing the elements in the
* specified sorted set. This priority queue will be ordered
* according to the same ordering as the given sorted set.
*
* @param c the sorted set whose elements are to be placed
* into this priority queue
* @throws ClassCastException if elements of the specified sorted
* set cannot be compared to one another according to the
* sorted set's ordering
* @throws NullPointerException if the specified sorted set or any
* of its elements are null
*/
@SuppressWarnings("unchecked")
public PriorityQueue(SortedSet<? extends E> c) {
this.comparator = (Comparator<? super E>) c.comparator();
initElementsFromCollection(c);
}

private void initFromPriorityQueue(PriorityQueue<? extends E> c) {
if (c.getClass() == PriorityQueue.class) {
this.queue = c.toArray();
this.size = c.size();
} else {
initFromCollection(c);
}
}

//从SortSet有序集合中的元素直接复制到当前的queue中
private void initElementsFromCollection(Collection<? extends E> c) {
Object[] a = c.toArray();
// If c.toArray incorrectly doesn't return Object[], copy it.
if (a.getClass() != Object[].class)
a = Arrays.copyOf(a, a.length, Object[].class);
int len = a.length;
if (len == 1 || this.comparator != null)
for (int i = 0; i < len; i++)
if (a[i] == null)
throw new NullPointerException();
this.queue = a;
this.size = a.length;
}

/**
* Initializes queue array with elements from the given Collection.
* 从无序集合中构建queue
* @param c the collection
*/
private void initFromCollection(Collection<? extends E> c) {
initElementsFromCollection(c);
//复制完成之后进行调整
heapify();
}

/**
* The maximum size of array to allocate.
* Some VMs reserve some header words in an array.
* Attempts to allocate larger arrays may result in
* OutOfMemoryError: Requested array size exceeds VM limit
*/
private static final int MAX_ARRAY_SIZE = Integer.MAX_VALUE - 8;

/**
* Increases the capacity of the array.
* queue 数组扩容
* @param minCapacity the desired minimum capacity
*/
private void grow(int minCapacity) {
int oldCapacity = queue.length;
// Double size if small; else grow by 50%
int newCapacity = oldCapacity + ((oldCapacity < 64) ?
(oldCapacity + 2) :
(oldCapacity >> 1));
// overflow-conscious code
if (newCapacity - MAX_ARRAY_SIZE > 0)
newCapacity = hugeCapacity(minCapacity);
queue = Arrays.copyOf(queue, newCapacity);
}

private static int hugeCapacity(int minCapacity) {
if (minCapacity < 0) // overflow
throw new OutOfMemoryError();
return (minCapacity > MAX_ARRAY_SIZE) ?
Integer.MAX_VALUE :
MAX_ARRAY_SIZE;
}

/**
* Inserts the specified element into this priority queue.
*
* @return {@code true} (as specified by {@link Collection#add})
* @throws ClassCastException if the specified element cannot be
* compared with elements currently in this priority queue
* according to the priority queue's ordering
* @throws NullPointerException if the specified element is null
*/
public boolean add(E e) {
return offer(e);
}

/**
* Inserts the specified element into this priority queue.
*
* @return {@code true} (as specified by {@link Queue#offer})
* @throws ClassCastException if the specified element cannot be
* compared with elements currently in this priority queue
* according to the priority queue's ordering
* @throws NullPointerException if the specified element is null
*/
public boolean offer(E e) {
if (e == null)
throw new NullPointerException();
modCount++;
int i = size;
if (i >= queue.length)
grow(i + 1);
size = i + 1;
if (i == 0)
queue[0] = e;
else
siftUp(i, e);
return true;
}

public E peek() {
return (size == 0) ? null : (E) queue[0];
}

private int indexOf(Object o) {
if (o != null) {
for (int i = 0; i < size; i++)
if (o.equals(queue[i]))
return i;
}
return -1;
}

/**
* Removes a single instance of the specified element from this queue,
* if it is present. More formally, removes an element {@code e} such
* that {@code o.equals(e)}, if this queue contains one or more such
* elements. Returns {@code true} if and only if this queue contained
* the specified element (or equivalently, if this queue changed as a
* result of the call).
*
* @param o element to be removed from this queue, if present
* @return {@code true} if this queue changed as a result of the call
*/
public boolean remove(Object o) {
int i = indexOf(o);
if (i == -1)
return false;
else {
removeAt(i);
return true;
}
}

/**
* Version of remove using reference equality, not equals.
* Needed by iterator.remove.
*
* @param o element to be removed from this queue, if present
* @return {@code true} if removed
*/
boolean removeEq(Object o) {
for (int i = 0; i < size; i++) {
if (o == queue[i]) {
removeAt(i);
return true;
}
}
return false;
}


public boolean contains(Object o) {
return indexOf(o) != -1;
}


public Object[] toArray() {
return Arrays.copyOf(queue, size);
}

public <T> T[] toArray(T[] a) {
final int size = this.size;
if (a.length < size)
// Make a new array of a's runtime type, but my contents:
return (T[]) Arrays.copyOf(queue, size, a.getClass());
System.arraycopy(queue, 0, a, 0, size);
if (a.length > size)
a[size] = null;
return a;
}

public Iterator<E> iterator() {
return new Itr();
}

private final class Itr implements Iterator<E> {
/**
* Index (into queue array) of element to be returned by
* subsequent call to next.
*/
private int cursor = 0;

/**
* Index of element returned by most recent call to next,
* unless that element came from the forgetMeNot list.
* Set to -1 if element is deleted by a call to remove.
*/
private int lastRet = -1;


private ArrayDeque<E> forgetMeNot = null;

/**
* Element returned by the most recent call to next iff that
* element was drawn from the forgetMeNot list.
*/
private E lastRetElt = null;

/**
* The modCount value that the iterator believes that the backing
* Queue should have. If this expectation is violated, the iterator
* has detected concurrent modification.
*/
private int expectedModCount = modCount;

public boolean hasNext() {
return cursor < size ||
(forgetMeNot != null && !forgetMeNot.isEmpty());
}

@SuppressWarnings("unchecked")
public E next() {
if (expectedModCount != modCount)
throw new ConcurrentModificationException();
if (cursor < size)
return (E) queue[lastRet = cursor++];
if (forgetMeNot != null) {
lastRet = -1;
lastRetElt = forgetMeNot.poll();
if (lastRetElt != null)
return lastRetElt;
}
throw new NoSuchElementException();
}

public void remove() {
if (expectedModCount != modCount)
throw new ConcurrentModificationException();
if (lastRet != -1) {
E moved = PriorityQueue.this.removeAt(lastRet);
lastRet = -1;
if (moved == null)
cursor--;
else {
if (forgetMeNot == null)
forgetMeNot = new ArrayDeque<>();
forgetMeNot.add(moved);
}
} else if (lastRetElt != null) {
PriorityQueue.this.removeEq(lastRetElt);
lastRetElt = null;
} else {
throw new IllegalStateException();
}
expectedModCount = modCount;
}
}

public int size() {
return size;
}

public void clear() {
modCount++;
for (int i = 0; i < size; i++)
queue[i] = null;
size = 0;
}

@SuppressWarnings("unchecked")
public E poll() {
if (size == 0)
return null;
int s = --size;
modCount++;
E result = (E) queue[0];
E x = (E) queue[s];
queue[s] = null;
if (s != 0)
siftDown(0, x);
return result;
}

/**
* Removes the ith element from queue.
* 删除某个位置的元素
* Normally this method leaves the elements at up to i-1,
* inclusive, untouched. Under these circumstances, it returns
* null. Occasionally, in order to maintain the heap invariant,
* it must swap a later element of the list with one earlier than
* i. Under these circumstances, this method returns the element
* that was previously at the end of the list and is now at some
* position before i. This fact is used by iterator.remove so as to
* avoid missing traversing elements.
*/
private E removeAt(int i) {
// assert i >= 0 && i < size;
modCount++;
int s = --size;
if (s == i) // removed last element 移除最后一个元素
queue[i] = null;
else {
E moved = (E) queue[s]; //保存队列尾部的元素
queue[s] = null; //置为null
siftDown(i, moved); //moved直接插入到i位置,相当于直接删除了i位置的元素
if (queue[i] == moved) {
siftUp(i, moved);
if (queue[i] != moved)
return moved;
}
}
return null;
}

/**
* Inserts item x at position k, maintaining heap invariant by
* promoting x up the tree until it is greater than or equal to
* its parent, or is the root.
* 将x插入k位置,并进行上浮调整
* To simplify and speed up coercions and comparisons. the
* Comparable and Comparator versions are separated into different
* methods that are otherwise identical. (Similarly for siftDown.)
*
* @param k the position to fill
* @param x the item to insert
*/
private void siftUp(int k, E x) {
if (comparator != null)
siftUpUsingComparator(k, x);
else
siftUpComparable(k, x);
}

@SuppressWarnings("unchecked")
private void siftUpComparable(int k, E x) {
Comparable<? super E> key = (Comparable<? super E>) x;
while (k > 0) {
int parent = (k - 1) >>> 1;
Object e = queue[parent];
if (key.compareTo((E) e) >= 0)
break;
queue[k] = e;
k = parent;
}
queue[k] = key;
}

@SuppressWarnings("unchecked")
private void siftUpUsingComparator(int k, E x) {
while (k > 0) {
int parent = (k - 1) >>> 1;
Object e = queue[parent];
if (comparator.compare(x, (E) e) >= 0)
break;
queue[k] = e;
k = parent;
}
queue[k] = x;
}

/**
* Inserts item x at position k, maintaining heap invariant by
* demoting x down the tree repeatedly until it is less than or
* equal to its children or is a leaf.
* 插入元素x到到位置k,并进行下沉调整
*
* @param k the position to fill
* @param x the item to insert
*/
private void siftDown(int k, E x) {
if (comparator != null)
siftDownUsingComparator(k, x); //带比较器的
else
siftDownComparable(k, x); //不带比较器,用x的compator
}

@SuppressWarnings("unchecked")
private void siftDownComparable(int k, E x) {
Comparable<? super E> key = (Comparable<? super E>)x;
int half = size >>> 1; // loop while a non-leaf
while (k < half) {
int child = (k << 1) + 1; // assume left child is least
Object c = queue[child];
int right = child + 1;
if (right < size &&
((Comparable<? super E>) c).compareTo((E) queue[right]) > 0)
c = queue[child = right];
if (key.compareTo((E) c) <= 0)
break;
queue[k] = c;
k = child;
}
queue[k] = key;
}

@SuppressWarnings("unchecked")
private void siftDownUsingComparator(int k, E x) {
int half = size >>> 1;
while (k < half) {
int child = (k << 1) + 1;
Object c = queue[child];
int right = child + 1;
if (right < size &&
comparator.compare((E) c, (E) queue[right]) > 0)
c = queue[child = right];
if (comparator.compare(x, (E) c) <= 0)
break;
queue[k] = c;
k = child;
}
queue[k] = x;
}

/**
* Establishes the heap invariant (described above) in the entire tree,
* assuming nothing about the order of the elements prior to the call.
*/
@SuppressWarnings("unchecked")
private void heapify() {
for (int i = (size >>> 1) - 1; i >= 0; i--)
siftDown(i, (E) queue[i]);
}

public Comparator<? super E> comparator() {
return comparator;
}

/**
* Saves this queue to a stream (that is, serializes it).
*
* @serialData The length of the array backing the instance is
* emitted (int), followed by all of its elements
* (each an {@code Object}) in the proper order.
* @param s the stream
*/
private void writeObject(java.io.ObjectOutputStream s)
throws java.io.IOException {
// Write out element count, and any hidden stuff
s.defaultWriteObject();

// Write out array length, for compatibility with 1.5 version
s.writeInt(Math.max(2, size + 1));

// Write out all elements in the "proper order".
for (int i = 0; i < size; i++)
s.writeObject(queue[i]);
}

/**
* Reconstitutes the {@code PriorityQueue} instance from a stream
* (that is, deserializes it).
*
* @param s the stream
*/
private void readObject(java.io.ObjectInputStream s)
throws java.io.IOException, ClassNotFoundException {
// Read in size, and any hidden stuff
s.defaultReadObject();

// Read in (and discard) array length
s.readInt();

SharedSecrets.getJavaOISAccess().checkArray(s, Object[].class, size);
queue = new Object[size];

// Read in all elements.
for (int i = 0; i < size; i++)
queue[i] = s.readObject();

// Elements are guaranteed to be in "proper order", but the
// spec has never explained what that might be.
heapify();
}

/**
* Creates a <em><a href="Spliterator.html#binding">late-binding</a></em>
* and <em>fail-fast</em> {@link Spliterator} over the elements in this
* queue.
*
* <p>The {@code Spliterator} reports {@link Spliterator#SIZED},
* {@link Spliterator#SUBSIZED}, and {@link Spliterator#NONNULL}.
* Overriding implementations should document the reporting of additional
* characteristic values.
*
* @return a {@code Spliterator} over the elements in this queue
* @since 1.8
*/
public final Spliterator<E> spliterator() {
return new PriorityQueueSpliterator<E>(this, 0, -1, 0);
}

static final class PriorityQueueSpliterator<E> implements Spliterator<E> {
/*
* This is very similar to ArrayList Spliterator, except for
* extra null checks.
*/
private final PriorityQueue<E> pq;
private int index; // current index, modified on advance/split
private int fence; // -1 until first use
private int expectedModCount; // initialized when fence set

/** Creates new spliterator covering the given range */
PriorityQueueSpliterator(PriorityQueue<E> pq, int origin, int fence,
int expectedModCount) {
this.pq = pq;
this.index = origin;
this.fence = fence;
this.expectedModCount = expectedModCount;
}

private int getFence() { // initialize fence to size on first use
int hi;
if ((hi = fence) < 0) {
expectedModCount = pq.modCount;
hi = fence = pq.size;
}
return hi;
}

public PriorityQueueSpliterator<E> trySplit() {
int hi = getFence(), lo = index, mid = (lo + hi) >>> 1;
return (lo >= mid) ? null :
new PriorityQueueSpliterator<E>(pq, lo, index = mid,
expectedModCount);
}

@SuppressWarnings("unchecked")
public void forEachRemaining(Consumer<? super E> action) {
int i, hi, mc; // hoist accesses and checks from loop
PriorityQueue<E> q; Object[] a;
if (action == null)
throw new NullPointerException();
if ((q = pq) != null && (a = q.queue) != null) {
if ((hi = fence) < 0) {
mc = q.modCount;
hi = q.size;
}
else
mc = expectedModCount;
if ((i = index) >= 0 && (index = hi) <= a.length) {
for (E e;; ++i) {
if (i < hi) {
if ((e = (E) a[i]) == null) // must be CME
break;
action.accept(e);
}
else if (q.modCount != mc)
break;
else
return;
}
}
}
throw new ConcurrentModificationException();
}

public boolean tryAdvance(Consumer<? super E> action) {
if (action == null)
throw new NullPointerException();
int hi = getFence(), lo = index;
if (lo >= 0 && lo < hi) {
index = lo + 1;
@SuppressWarnings("unchecked") E e = (E)pq.queue[lo];
if (e == null)
throw new ConcurrentModificationException();
action.accept(e);
if (pq.modCount != expectedModCount)
throw new ConcurrentModificationException();
return true;
}
return false;
}

public long estimateSize() {
return (long) (getFence() - index);
}

public int characteristics() {
return Spliterator.SIZED | Spliterator.SUBSIZED | Spliterator.NONNULL;
}
}
}

扩展

d叉堆:多叉堆,上面我们实现的都是二叉堆,但是其实我们还可以将其扩展为多叉堆,一个节点有多个子节点

索引堆:我们上面实现的二叉堆只能看见堆顶的元素,看不到堆中的元素,有时候我们可能需要操作堆中间的元素,索引堆顾名思义就是有索引可以对应每个元素,借此就可以操作堆中间的元素

二项堆斐波拉契堆 ….. 这些结构其实都是扩展的,简单了解即可

源码地址

Github