堆和优先队列

堆

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

赞赏

感谢鼓励