Class - java.util.PriorityQueue
Created by : Mr Dk.
2019 / 11 / 12 21:26
Nanjing, Jiangsu, China
Definition
public class PriorityQueue<E> extends AbstractQueue<E>
implements java.io.Serializable {
}
优先级队列的实现。基于 优先级 heap 来管理数据：优先级队列中的元素根据其自然顺序，或提供的 Comparator 排列。
- 不允许
null元素 - 不允许插入无法比较大小的元素
优先队列的大小不受限制，但是有一个内部的容量，用于管理实际用于存储元素的数组。所以容量根据队列自动增长。
迭代器无法保证遍历元素的顺序，如果需要按顺序遍历，考虑使用 Arrays.sort(pq.toArray())。
当前实现是非同步的，而 java.util.concurrent.PriorityBlockingQueue 是线程安全的。其中通过一个 ReentrantLock 来锁定优先队列的修改操作，从而保证线程安全。
时间复杂度：
- O(log(n)) -
offer()/poll()/remove()/add() - O(n) -
remove(Object)/contains(Object) - O(1) -
peek()/element()/size()
/**
* 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
*/
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.
*/
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
初始默认容量为 11，管理为二叉堆结构。
queue[0]是最小的元素queue[n]的子元素是queue[2n+1]和queue[2n+2]
如果 Comparator 为 null，就按照自然顺序排列。
Constructor
可以指定初始的容量和 Comparetor：
- 如果未指定初始容量，则使用
DEFAULT_INITIAL_CAPACITY，即 11 - 如果未指定
Comparator，则为 null，使用自然顺序排列
/**
* Creates a {@code PriorityQueue} with the specified initial capacity
* that orders its elements according to the specified comparator.
*
* @param initialCapacity the initial capacity for this priority queue
* @param comparator the comparator that will be used to order this
* priority queue. If {@code null}, the {@linkplain Comparable
* natural ordering} of the elements will be used.
* @throws IllegalArgumentException if {@code initialCapacity} is
* less than 1
*/
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;
}
从一个集合创建优先队列，分为三种情况：
- 排序后的 Set 集合
- 另一个优先队列
- 普通集合
/**
* 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.
*
* @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;
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);
}
}
如果是有序的 Set，那么直接按 Set 的顺序拷贝为优先队列，并初始化所有 metadata：
/**
* 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 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;
}
如果利用另一个优先队列构造，那么直接将对应的元素和 metadata 拷贝。如果不是优先队列，则需要将元素拷贝后，对元素进行 堆化：因为原顺序不是堆序。
/**
* 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);
}
private void initFromPriorityQueue(PriorityQueue<? extends E> c) {
if (c.getClass() == PriorityQueue.class) {
this.queue = c.toArray();
this.size = c.size();
} else {
initFromCollection(c);
}
}
/**
* Initializes queue array with elements from the given Collection.
*
* @param c the collection
*/
private void initFromCollection(Collection<? extends E> c) {
initElementsFromCollection(c);
heapify();
}
Add
插入元素（两个函数等价）
- 将元素放在数组的最后位置
- 从该位置开始，将元素从堆的根部向上移动，直到满足堆的条件
- 如果是第一个元素，则直接放在
queue[0] - 如果数组容量已经不够，那么将数组扩容
/**
* 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;
}
扩容的原则：
- 小于 64 个元素 - 新容量为 2n + 2
- 多于 64 个元素 - 扩容 50% (1.5 倍)
- 扩容要求的最小值超过
MAX_ARRAY_SIZE，就返回最大Integer，但扩容最小值不能溢出
/**
* Increases the capacity of the array.
*
* @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;
}
- 查找堆顶元素：直接查看
queue[0]即可 - 查找特定元素：需要在整个队列中搜索
- 是否包含特定元素：需要在整个队列中搜索
@SuppressWarnings("unchecked")
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;
}
/**
* Returns {@code true} if this queue contains the specified element.
* More formally, returns {@code true} if and only if this queue contains
* at least one element {@code e} such that {@code o.equals(e)}.
*
* @param o object to be checked for containment in this queue
* @return {@code true} if this queue contains the specified element
*/
public boolean contains(Object o) {
return indexOf(o) != -1;
}
Remove
删除特定的元素，同样也需要先遍历整个队列，找到对应元素所在的位置（下标），然后调用对应的堆操作将该元素移除。
/**
* 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;
}
出队操作：
- 将队头 (即堆顶) 的元素删除，
size减小了 1 - 将
queue[0]元素用数组的最后一个元素代替 - 向下调整堆
@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;
}
删除任意指定数组下标的元素，将数组中的最后一个元素放到被删除的位置
- 试图向下调整堆（向下调整的概率较大，因为原最后一个元素位于堆底），并返回
null - 如果不能再向下调整堆，则向上调整堆
- 如果也无法向上调整堆，则说明该位置刚好适合该元素，返回
null - 否则返回该元素本身
- 如果也无法向上调整堆，则说明该位置刚好适合该元素，返回
这个操作用于防止迭代器调用 remove() 后漏掉遍历的元素：
- 如果返回
null，说明最后一个元素被放到了做删除操作的地方，没有上浮或下沉；该元素会被漏掉，迭代器的指针需要回退一下 - 如果返回不为
null，说明最后一个元素移到做删除操作的地方后已经上浮；该元素会被漏掉，而且靠迭代器指针回退一格已经无法遍历到它
/**
* Removes the ith element from queue.
*
* 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.
*/
@SuppressWarnings("unchecked")
private E removeAt(int i) {
// assert i >= 0 && i < size;
modCount++;
int s = --size;
if (s == i) // removed last element
queue[i] = null;
else {
E moved = (E) queue[s];
queue[s] = null;
siftDown(i, moved);
if (queue[i] == moved) {
siftUp(i, moved);
if (queue[i] != moved)
return moved;
}
}
return null;
}
在这种情况下，可以看看迭代器的实现。迭代器中维护一个 forgetMeNot 队列，用于记录所有从未被访问的位置上浮到已被访问的位置后的元素。
- 如果被提上来的最后一个元素 下沉，或在原删除位置 不上浮也不下沉；这种情况下，只有原删除位置的元素会被忽略一次，只需要让
cursor--，重新迭代原删除位置，就能保证所有元素都被迭代 - 如果被提上来的元素上浮，被置换到原删除位置的元素肯定已经被访问过；这种情况下，浮上去的那个元素显然被忽略了，而且退指针也没用，就将其加入
forgetMeNot队列中
在常规遍历结束后，还需要遍历 forgetMeNot 队列，才算完成一次完整的迭代。
/**
* Returns an iterator over the elements in this queue. The iterator
* does not return the elements in any particular order.
*
* @return an iterator over the elements in this queue
*/
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;
/**
* A queue of elements that were moved from the unvisited portion of
* the heap into the visited portion as a result of "unlucky" element
* removals during the iteration. (Unlucky element removals are those
* that require a siftup instead of a siftdown.) We must visit all of
* the elements in this list to complete the iteration. We do this
* after we've completed the "normal" iteration.
*
* We expect that most iterations, even those involving removals,
* will not need to store elements in this field.
*/
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;
}
}
在逻辑上将 x 元素插入到 k 位置 (实际上暂时不用)。因为要保证其堆的合法性而将 x 上浮到堆的某个位置，直到大于等于它的 parent，或成为 root。
/**
* 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.
*
* 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;
}
将 x 插入到 k 位置，为维护堆合法性，将其向堆下移动，直到其小于等于其 children，或成为叶子结点。half 为第一个非叶子结点，如果 k 已经是叶子结点，则不用做操作了。
/**
* 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.
*
* @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);
else
siftDownComparable(k, x);
}
@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;
}
从第一个非叶子结点开始建立堆序，将每一个非叶子结点做一次下沉操作。
/**
* 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]);
}
Summary
根据代码中的比较逻辑，Java 维护的堆是一个小顶堆，堆顶是最小元素。如果想要颠覆这一比较方法，那就自己实现 Comparator 颠倒过来吧。顺带复习了一下堆 - 发现自己已经快忘了 😥