java常用集合List Set Map 子类源码分析实现原理

集合相关

List跟Set的区别
两个接口都继承Collection,区别list有序且可以添加多个null元素,也可以添加重复元素;set不能添加重复元素,最多允许一个null,若要有序需实现comprable接口;

list 子类:ArrayList,LinkedList,Vector

ArrayList,源码比较简单,实际内部是Object[]数组,可以传入大小,默认是10,最大是Integer最大值,最大特点是增容,在add的时候判断容器大小是否需要扩容

/**
     * Increases the capacity to ensure that it can hold at least the
     * number of elements specified by the minimum capacity argument.
     *
     * @param minCapacity the desired minimum capacity
     */
    private void grow(int minCapacity) {
        // overflow-conscious code
        int oldCapacity = elementData.length;
        int newCapacity = oldCapacity + (oldCapacity >> 1);
        if (newCapacity - minCapacity < 0)
            newCapacity = minCapacity;
        if (newCapacity - MAX_ARRAY_SIZE > 0)
            newCapacity = hugeCapacity(minCapacity);
        // minCapacity is usually close to size, so this is a win:
        elementData = Arrays.copyOf(elementData, 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;
    }

还有一个特殊的部分是Iterator类

/**
     * An optimized version of AbstractList.Itr
     */
    private class Itr implements Iterator<E> {
        // The "limit" of this iterator. This is the size of the list at the time the
        // iterator was created. Adding & removing elements will invalidate the iteration
        // anyway (and cause next() to throw) so saving this value will guarantee that the
        // value of hasNext() remains stable and won't flap between true and false when elements
        // are added and removed from the list.
        protected int limit = ArrayList.this.size;

        int cursor;       // index of next element to return
        int lastRet = -1; // index of last element returned; -1 if no such
        int expectedModCount = modCount;

        public boolean hasNext() {
            return cursor < limit;
        }

        @SuppressWarnings("unchecked")
        public E next() {
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();
            int i = cursor;
            if (i >= limit)
                throw new NoSuchElementException();
            Object[] elementData = ArrayList.this.elementData;
            if (i >= elementData.length)
                throw new ConcurrentModificationException();
            cursor = i + 1;
            return (E) elementData[lastRet = i];
        }

        public void remove() {
            if (lastRet < 0)
                throw new IllegalStateException();
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();

            try {
                ArrayList.this.remove(lastRet);
                cursor = lastRet;
                lastRet = -1;
                expectedModCount = modCount;
                limit--;
            } catch (IndexOutOfBoundsException ex) {
                throw new ConcurrentModificationException();
            }
        }

        @Override
        @SuppressWarnings("unchecked")
        public void forEachRemaining(Consumer<? super E> consumer) {
            Objects.requireNonNull(consumer);
            final int size = ArrayList.this.size;
            int i = cursor;
            if (i >= size) {
                return;
            }
            final Object[] elementData = ArrayList.this.elementData;
            if (i >= elementData.length) {
                throw new ConcurrentModificationException();
            }
            while (i != size && modCount == expectedModCount) {
                consumer.accept((E) elementData[i++]);
            }
            // update once at end of iteration to reduce heap write traffic
            cursor = i;
            lastRet = i - 1;

            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();
        }
    }

    /**
     * An optimized version of AbstractList.ListItr
     */
    private class ListItr extends Itr implements ListIterator<E> {
        ListItr(int index) {
            super();
            cursor = index;
        }

        public boolean hasPrevious() {
            return cursor != 0;
        }

        public int nextIndex() {
            return cursor;
        }

        public int previousIndex() {
            return cursor - 1;
        }

        @SuppressWarnings("unchecked")
        public E previous() {
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();
            int i = cursor - 1;
            if (i < 0)
                throw new NoSuchElementException();
            Object[] elementData = ArrayList.this.elementData;
            if (i >= elementData.length)
                throw new ConcurrentModificationException();
            cursor = i;
            return (E) elementData[lastRet = i];
        }

        public void set(E e) {
            if (lastRet < 0)
                throw new IllegalStateException();
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();

            try {
                ArrayList.this.set(lastRet, e);
            } catch (IndexOutOfBoundsException ex) {
                throw new ConcurrentModificationException();
            }
        }

        public void add(E e) {
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();

            try {
                int i = cursor;
                ArrayList.this.add(i, e);
                cursor = i + 1;
                lastRet = -1;
                expectedModCount = modCount;
                limit++;
            } catch (IndexOutOfBoundsException ex) {
                throw new ConcurrentModificationException();
            }
        }
    }

Vector跟ArrayList同样继承AbstractList,方法都一样只是在跟数组操作的相关方法都加上了synchronized关键字,由此可知他是线程安全的ArrayList;

LinkedList,通过查看LinkedList源码我们很容易发现,他同样继承了AbstractList,但是多实现了Deque(双向队列),进一步查看顾名思义内部使用了双向列表的数据结构。

public class LinkedList<E>
    extends AbstractSequentialList<E>
    implements List<E>, Deque<E>, Cloneable, java.io.Serializable
{
    transient int size = 0;

    /**
     * Pointer to first node.
     * Invariant: (first == null && last == null) ||
     *            (first.prev == null && first.item != null)
     */
    transient Node<E> first;

    /**
     * Pointer to last node.
     * Invariant: (first == null && last == null) ||
     *            (last.next == null && last.item != null)
     */
    transient Node<E> last;

    /**
     * Constructs an empty list.
     */
    public LinkedList() {
    }

看node代码

private static class Node<E> {
        E item;
        Node<E> next;
        Node<E> prev;

        Node(Node<E> prev, E element, Node<E> next) {
            this.item = element;
            this.next = next;
            this.prev = prev;
        }
    }

当然既然是链表就不能向ArrayList的Iterator那样通过移动cursor了,下面是它的Iterator的实现,里面也是链表。

private class ListItr implements ListIterator<E> {
        private Node<E> lastReturned = null;
        private Node<E> next;
        private int nextIndex;
        private int expectedModCount = modCount;

        ListItr(int index) {
            // assert isPositionIndex(index);
            next = (index == size) ? null : node(index);
            nextIndex = index;
        }

        public boolean hasNext() {
            return nextIndex < size;
        }

        public E next() {
            checkForComodification();
            if (!hasNext())
                throw new NoSuchElementException();

            lastReturned = next;
            next = next.next;
            nextIndex++;
            return lastReturned.item;
        }

        public boolean hasPrevious() {
            return nextIndex > 0;
        }

        public E previous() {
            checkForComodification();
            if (!hasPrevious())
                throw new NoSuchElementException();

            lastReturned = next = (next == null) ? last : next.prev;
            nextIndex--;
            return lastReturned.item;
        }

        public int nextIndex() {
            return nextIndex;
        }

        public int previousIndex() {
            return nextIndex - 1;
        }

        public void remove() {
            checkForComodification();
            if (lastReturned == null)
                throw new IllegalStateException();

            Node<E> lastNext = lastReturned.next;
            unlink(lastReturned);
            if (next == lastReturned)
                next = lastNext;
            else
                nextIndex--;
            lastReturned = null;
            expectedModCount++;
        }

        public void set(E e) {
            if (lastReturned == null)
                throw new IllegalStateException();
            checkForComodification();
            lastReturned.item = e;
        }

        public void add(E e) {
            checkForComodification();
            lastReturned = null;
            if (next == null)
                linkLast(e);
            else
                linkBefore(e, next);
            nextIndex++;
            expectedModCount++;
        }

        @Override
        public void forEachRemaining(Consumer<? super E> action) {
            Objects.requireNonNull(action);
            while (modCount == expectedModCount && nextIndex < size) {
                action.accept(next.item);
                lastReturned = next;
                next = next.next;
                nextIndex++;
            }
            checkForComodification();
        }

        final void checkForComodification() {
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();
        }
    }

到此,list分析完毕,ArrayList内部使用数组存储,LinkedList是双向链表,ArrayList查询效率高,LinkedList插入,删除效率高;

Set的实现子类HashSet、LinkedHashSet 以及 TreeSet
对比list的接口发现主要有以下的方法不同,从中可以发现主要是跟index的相关的也就是顺序相关的操作,由此得知set的基因就跟序列无关,即无序

// Positional Access Operations

    /**
     * Returns the element at the specified position in this list.
     *
     * @param index index of the element to return
     * @return the element at the specified position in this list
     * @throws IndexOutOfBoundsException if the index is out of range
     *         (<tt>index &lt; 0 || index &gt;= size()</tt>)
     */
    E get(int index);

    /**
     * Replaces the element at the specified position in this list with the
     * specified element (optional operation).
     *
     * @param index index of the element to replace
     * @param element element to be stored at the specified position
     * @return the element previously at the specified position
     * @throws UnsupportedOperationException if the <tt>set</tt> operation
     *         is not supported by this list
     * @throws ClassCastException if the class of the specified element
     *         prevents it from being added to this list
     * @throws NullPointerException if the specified element is null and
     *         this list does not permit null elements
     * @throws IllegalArgumentException if some property of the specified
     *         element prevents it from being added to this list
     * @throws IndexOutOfBoundsException if the index is out of range
     *         (<tt>index &lt; 0 || index &gt;= size()</tt>)
     */
    E set(int index, E element);

    /**
     * Inserts the specified element at the specified position in this list
     * (optional operation).  Shifts the element currently at that position
     * (if any) and any subsequent elements to the right (adds one to their
     * indices).
     *
     * @param index index at which the specified element is to be inserted
     * @param element element to be inserted
     * @throws UnsupportedOperationException if the <tt>add</tt> operation
     *         is not supported by this list
     * @throws ClassCastException if the class of the specified element
     *         prevents it from being added to this list
     * @throws NullPointerException if the specified element is null and
     *         this list does not permit null elements
     * @throws IllegalArgumentException if some property of the specified
     *         element prevents it from being added to this list
     * @throws IndexOutOfBoundsException if the index is out of range
     *         (<tt>index &lt; 0 || index &gt; size()</tt>)
     */
    void add(int index, E element);

    /**
     * Removes the element at the specified position in this list (optional
     * operation).  Shifts any subsequent elements to the left (subtracts one
     * from their indices).  Returns the element that was removed from the
     * list.
     *
     * @param index the index of the element to be removed
     * @return the element previously at the specified position
     * @throws UnsupportedOperationException if the <tt>remove</tt> operation
     *         is not supported by this list
     * @throws IndexOutOfBoundsException if the index is out of range
     *         (<tt>index &lt; 0 || index &gt;= size()</tt>)
     */
    E remove(int index);


    // Search Operations

    /**
     * Returns the index of the first occurrence of the specified element
     * in this list, or -1 if this list does not contain the element.
     * More formally, returns the lowest index <tt>i</tt> such that
     * <tt>(o==null&nbsp;?&nbsp;get(i)==null&nbsp;:&nbsp;o.equals(get(i)))</tt>,
     * or -1 if there is no such index.
     *
     * @param o element to search for
     * @return the index of the first occurrence of the specified element in
     *         this list, or -1 if this list does not contain the element
     * @throws ClassCastException if the type of the specified element
     *         is incompatible with this list
     *         (<a href="Collection.html#optional-restrictions">optional</a>)
     * @throws NullPointerException if the specified element is null and this
     *         list does not permit null elements
     *         (<a href="Collection.html#optional-restrictions">optional</a>)
     */
    int indexOf(Object o);

    /**
     * Returns the index of the last occurrence of the specified element
     * in this list, or -1 if this list does not contain the element.
     * More formally, returns the highest index <tt>i</tt> such that
     * <tt>(o==null&nbsp;?&nbsp;get(i)==null&nbsp;:&nbsp;o.equals(get(i)))</tt>,
     * or -1 if there is no such index.
     *
     * @param o element to search for
     * @return the index of the last occurrence of the specified element in
     *         this list, or -1 if this list does not contain the element
     * @throws ClassCastException if the type of the specified element
     *         is incompatible with this list
     *         (<a href="Collection.html#optional-restrictions">optional</a>)
     * @throws NullPointerException if the specified element is null and this
     *         list does not permit null elements
     *         (<a href="Collection.html#optional-restrictions">optional</a>)
     */
    int lastIndexOf(Object o);

HashSet继承AbstractSet,打开源码,一惊,竟然是基于HashMap实现的,源码完全没什么内容,等等,hashmap是键值对啊,看代码:

private transient HashMap<E,Object> map;

    // Dummy value to associate with an Object in the backing Map
private static final Object PRESENT = new Object();

 /**
     * Constructs a new, empty set; the backing <tt>HashMap</tt> instance has
     * default initial capacity (16) and load factor (0.75).
     */
    public HashSet() {
        map = new HashMap<>();
    }

    /**
     * Constructs a new set containing the elements in the specified
     * collection.  The <tt>HashMap</tt> is created with default load factor
     * (0.75) and an initial capacity sufficient to contain the elements in
     * the specified collection.
     *
     * @param c the collection whose elements are to be placed into this set
     * @throws NullPointerException if the specified collection is null
     */
    public HashSet(Collection<? extends E> c) {
        map = new HashMap<>(Math.max((int) (c.size()/.75f) + 1, 16));
        addAll(c);
    }

    /**
     * Constructs a new, empty set; the backing <tt>HashMap</tt> instance has
     * the specified initial capacity and the specified load factor.
     *
     * @param      initialCapacity   the initial capacity of the hash map
     * @param      loadFactor        the load factor of the hash map
     * @throws     IllegalArgumentException if the initial capacity is less
     *             than zero, or if the load factor is nonpositive
     */
    public HashSet(int initialCapacity, float loadFactor) {
        map = new HashMap<>(initialCapacity, 

 public boolean add(E e) {
        return map.put(e, PRESENT)==null;
    }

add操作实际就是放了一个空Object当value,这有点浪费内存吧,存疑,等分析HashMap再来分析这块;

LinkedHashSet继承HashSet方法上没有差异只是复写了构造方法,内部实现是LinkedHashMap

HashSet(int initialCapacity, float loadFactor, boolean dummy) {
        map = new LinkedHashMap<>(initialCapacity, loadFactor);
    }

TreeSet内部实现是TreeMap

接下来看一下Map
Map是一个接口里面Entry接口来存储键值对
Map的子类主要包含HashMap,TreeMap,HashTable,LinkedHashMap几个,下面分别从源码来分析一下几个子类;

HashMap,了解hashMap之前我们先带着几点疑问,1,HashSet是基于HashMap他们之前是什么关系?2,HashMap是怎么快速根据key拿到值的?3,HashMap内部的数据结构是什么样的?带着思考去做事情往往能获取更高的效率。

查询HashMap源码,首先寻找数据结构:发现了HashMapEntry<?,?>结构的数组,接着查看HashMapEntry的实现,HashMapEntry实现了 Map.Entry的接口,内部是个单向链表,一个单向列表的数组?轮廓已经有了,继续看

 /**
     * An empty table instance to share when the table is not inflated.
     */
    static final HashMapEntry<?,?>[] EMPTY_TABLE = {};

    /**
     * The table, resized as necessary. Length MUST Always be a power of two.
     */
    transient HashMapEntry<K,V>[] table = (HashMapEntry<K,V>[]) EMPTY_TABLE;
 /** @hide */  // Android added.
    static class HashMapEntry<K,V> implements Map.Entry<K,V> {
        final K key;
        V value;
        HashMapEntry<K,V> next;
        int hash;

        /**
         * Creates new entry.
         */
        HashMapEntry(int h, K k, V v, HashMapEntry<K,V> n) {
            value = v;
            next = n;
            key = k;
            hash = h;
        }

        public final K getKey() {
            return key;
        }

        public final V getValue() {
            return value;
        }

        public final V setValue(V newValue) {
            V oldValue = value;
            value = newValue;
            return oldValue;
        }

        public final boolean equals(Object o) {
            if (!(o instanceof Map.Entry))
                return false;
            Map.Entry e = (Map.Entry)o;
            Object k1 = getKey();
            Object k2 = e.getKey();
            if (k1 == k2 || (k1 != null && k1.equals(k2))) {
                Object v1 = getValue();
                Object v2 = e.getValue();
                if (v1 == v2 || (v1 != null && v1.equals(v2)))
                    return true;
            }
            return false;
        }

        public final int hashCode() {
            return Objects.hashCode(getKey()) ^ Objects.hashCode(getValue());
        }

        public final String toString() {
            return getKey() + "=" + getValue();
        }

        /**
         * This method is invoked whenever the value in an entry is
         * overwritten by an invocation of put(k,v) for a key k that's already
         * in the HashMap.
         */
        void recordAccess(HashMap<K,V> m) {
        }

        /**
         * This method is invoked whenever the entry is
         * removed from the table.
         */
        void recordRemoval(HashMap<K,V> m) {
        }
    }

瞅瞅构造方法,没有发现什么数据结构初始化相关。

 public HashMap(int initialCapacity, float loadFactor) {
        if (initialCapacity < 0)
            throw new IllegalArgumentException("Illegal initial capacity: " +
                                               initialCapacity);
        if (initialCapacity > MAXIMUM_CAPACITY) {
            initialCapacity = MAXIMUM_CAPACITY;
        } else if (initialCapacity < DEFAULT_INITIAL_CAPACITY) {
            initialCapacity = DEFAULT_INITIAL_CAPACITY;
        }

        if (loadFactor <= 0 || Float.isNaN(loadFactor))
            throw new IllegalArgumentException("Illegal load factor: " +
                                               loadFactor);
        // Android-Note: We always use the default load factor of 0.75f.

        // This might appear wrong but it's just awkward design. We always call
        // inflateTable() when table == EMPTY_TABLE. That method will take "threshold"
        // to mean "capacity" and then replace it with the real threshold (i.e, multiplied with
        // the load factor).
        threshold = initialCapacity;
        init();
    }

看put方法, inflateTable(threshold);threshold这个值在构造方法里见过,果然这里就是初始化table的地方,一部一部分析,感觉有意思了

 public V put(K key, V value) {
        if (table == EMPTY_TABLE) {
            inflateTable(threshold);
        }
        if (key == null)
            return putForNullKey(value);
        int hash = sun.misc.Hashing.singleWordWangJenkinsHash(key);
        int i = indexFor(hash, table.length);
        for (HashMapEntry<K,V> e = table[i]; e != null; e = e.next) {
            Object k;
            if (e.hash == hash && ((k = e.key) == key || key.equals(k))) {
                V oldValue = e.value;
                e.value = value;
                e.recordAccess(this);
                return oldValue;
            }
        }

        modCount++;
        addEntry(hash, key, value, i);
        return null;
    }

  
    private void inflateTable(int toSize) {
        // Find a power of 2 >= toSize
        int capacity = roundUpToPowerOf2(toSize);

        // Android-changed: Replace usage of Math.min() here because this method is
        // called from the <clinit> of runtime, at which point the native libraries
        // needed by Float.* might not be loaded.
        float thresholdFloat = capacity * loadFactor;
        if (thresholdFloat > MAXIMUM_CAPACITY + 1) {
            thresholdFloat = MAXIMUM_CAPACITY + 1;
        }

        threshold = (int) thresholdFloat;
        table = new HashMapEntry[capacity];
    }
    private static int roundUpToPowerOf2(int number) {
        // assert number >= 0 : "number must be non-negative";
        int rounded = number >= MAXIMUM_CAPACITY
                ? MAXIMUM_CAPACITY
                : (rounded = Integer.highestOneBit(number)) != 0
                    ? (Integer.bitCount(number) > 1) ? rounded << 1 : rounded
                    : 1;

        return rounded;
    }

static int indexFor(int h, int length) {
        // assert Integer.bitCount(length) == 1 : "length must be a non-zero power of 2";
        return h & (length-1);
    }

初始化时候传过来的容量这时候被更改了 int capacity = roundUpToPowerOf2(toSize);实际把toSize变为2的乘幂,table = new HashMapEntry[capacity];table初始成了2的乘幂的数组,回到put方法,if (key == null) return putForNullKey(value);发现key可以为空;int hash = sun.misc.Hashing.singleWordWangJenkinsHash(key);这句关键了HashMap,hash来了,这里通过key生成一个hash值,int i = indexFor(hash, table.length);
length 为2的乘幂,length-1说就是111111·····h & 11111,就会消掉不同的值,通过这个方法可以得到key在table里面的一个索引,这里就有一个疑问了,那不同的hash值& (length-1)后是会相同的,这应该就是传说中的hash碰撞吧,这也就明白了为什么数组中放的是链表了,如果出现了hash碰撞,值就可以像列表中添加了,但是列表越来越长,又怎么来保证get(key)的效率呢?先记录一下问题,慢慢解开谜团;

接下来通过循环看索引下的链表中是否存在此hash的entry如果存在,更新entry值,否则add entry

void addEntry(int hash, K key, V value, int bucketIndex) {
        if ((size >= threshold) && (null != table[bucketIndex])) {
            resize(2 * table.length);
            hash = (null != key) ? sun.misc.Hashing.singleWordWangJenkinsHash(key) : 0;
            bucketIndex = indexFor(hash, table.length);
        }

        createEntry(hash, key, value, bucketIndex);
    }

void resize(int newCapacity) {
        HashMapEntry[] oldTable = table;
        int oldCapacity = oldTable.length;
        if (oldCapacity == MAXIMUM_CAPACITY) {
            threshold = Integer.MAX_VALUE;
            return;
        }

        HashMapEntry[] newTable = new HashMapEntry[newCapacity];
        transfer(newTable);
        table = newTable;
        threshold = (int)Math.min(newCapacity * loadFactor, MAXIMUM_CAPACITY + 1);
    }
void transfer(HashMapEntry[] newTable) {
        int newCapacity = newTable.length;
        for (HashMapEntry<K,V> e : table) {
            while(null != e) {
                HashMapEntry<K,V> next = e.next;
                int i = indexFor(e.hash, newCapacity);
                e.next = newTable[i];
                newTable[i] = e;
                e = next;
            }
        }
    }

resize(2 * table.length)扩容,扩容就可以减小hash碰撞,从而提高效率,问题又来了,扩容后h & (length-1)就会变了,key的hash还能正确找到位置吗?进入
resize方法transfer(newTable);解决我的疑问遍历老的table,将所有的HashMapEntry元素重新indexFor放入新的table这样就没问题了;至此我们解决了上述3的问题和2的问题indexFor拿到index可以高效的拿到HashMapEntry,通过扩容来减少hash碰撞;关于上述问题1肯定跟Iterator相关

public Set<K> keySet() {
        Set<K> ks = keySet;
        return (ks != null ? ks : (keySet = new KeySet()));
    }

    private final class KeySet extends AbstractSet<K> {
        public Iterator<K> iterator() {
            return newKeyIterator();
        }
        public int size() {
            return size;
        }
        public boolean contains(Object o) {
            return containsKey(o);
        }
        public boolean remove(Object o) {
            return HashMap.this.removeEntryForKey(o) != null;
        }
        public void clear() {
            HashMap.this.clear();
        }
        public final Spliterator<K> spliterator() {
            return new KeySpliterator<>(HashMap.this, 0, -1, 0, 0);
        }
        public final void forEach(Consumer<? super K> action) {
            HashMapEntry<K,V>[] tab;
            if (action == null)
                throw new NullPointerException();
            if (size > 0 && (tab = table) != null) {
                int mc = modCount;
                for (int i = 0; i < tab.length; ++i) {
                    for (HashMapEntry<K,V> e = tab[i]; e != null; e = e.next) {
                        action.accept(e.key);
                        // Android-modified - this was outside of the loop, inconsistent with other
                        // collections
                        if (modCount != mc) {
                            throw new ConcurrentModificationException();
                        }
                    }
                }

            }
        }
    }


private abstract class HashIterator<E> implements Iterator<E> {
        HashMapEntry<K,V> next;        // next entry to return
        int expectedModCount;   // For fast-fail
        int index;              // current slot
        HashMapEntry<K,V> current;     // current entry

        HashIterator() {
            expectedModCount = modCount;
            if (size > 0) { // advance to first entry
                HashMapEntry[] t = table;
                while (index < t.length && (next = t[index++]) == null)
                    ;
            }
        }

        public final boolean hasNext() {
            return next != null;
        }

        final Entry<K,V> nextEntry() {
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();
            HashMapEntry<K,V> e = next;
            if (e == null)
                throw new NoSuchElementException();

            if ((next = e.next) == null) {
                HashMapEntry[] t = table;
                while (index < t.length && (next = t[index++]) == null)
                    ;
            }
            current = e;
            return e;
        }

        public void remove() {
            if (current == null)
                throw new IllegalStateException();
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();
            Object k = current.key;
            current = null;
            HashMap.this.removeEntryForKey(k);
            expectedModCount = modCount;
        }
    }

    private final class ValueIterator extends HashIterator<V> {
        public V next() {
            return nextEntry().getValue();
        }
    }

    private final class KeyIterator extends HashIterator<K> {
        public K next() {
            return nextEntry().getKey();
        }
    }

说一下这段有意思的代码:先取当前链表中的节点,直到为空if ((next = e.next) == null) ,接着 while (index < t.length && (next = t[index++]) == null),将next指向table的下一个元素,不得不感慨这样的代码看着太过清爽;;;;;

if ((next = e.next) == null) {
                HashMapEntry[] t = table;
                while (index < t.length && (next = t[index++]) == null)
                    ;
            }

到此hashMap分析完成,解决了自己的疑问;

LinkedHashSet继承了HashMap,不同之处LinkedHashMapEntry记录了插入顺序


 private transient LinkedHashMapEntry<K,V> header;
 /**
     * LinkedHashMap entry.
     */
    private static class LinkedHashMapEntry<K,V> extends HashMapEntry<K,V> {
        // These fields comprise the doubly linked list used for iteration.
        LinkedHashMapEntry<K,V> before, after;

        LinkedHashMapEntry(int hash, K key, V value, HashMapEntry<K,V> next) {
            super(hash, key, value, next);
        }

        /**
         * Removes this entry from the linked list.
         */
        private void remove() {
            before.after = after;
            after.before = before;
        }

        /**
         * Inserts this entry before the specified existing entry in the list.
         */
        private void addBefore(LinkedHashMapEntry<K,V> existingEntry) {
            after  = existingEntry;
            before = existingEntry.before;
            before.after = this;
            after.before = this;
        }

        /**
         * This method is invoked by the superclass whenever the value
         * of a pre-existing entry is read by Map.get or modified by Map.set.
         * If the enclosing Map is access-ordered, it moves the entry
         * to the end of the list; otherwise, it does nothing.
         */
        void recordAccess(HashMap<K,V> m) {
            LinkedHashMap<K,V> lm = (LinkedHashMap<K,V>)m;
            if (lm.accessOrder) {
                lm.modCount++;
                remove();
                addBefore(lm.header);
            }
        }

        void recordRemoval(HashMap<K,V> m) {
            remove();
        }
    }

    private abstract class LinkedHashIterator<T> implements Iterator<T> {
        LinkedHashMapEntry<K,V> nextEntry    = header.after;
        LinkedHashMapEntry<K,V> lastReturned = null;

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

        public boolean hasNext() {
            return nextEntry != header;
        }

        public void remove() {
            if (lastReturned == null)
                throw new IllegalStateException();
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();

            LinkedHashMap.this.remove(lastReturned.key);
            lastReturned = null;
            expectedModCount = modCount;
        }

        Entry<K,V> nextEntry() {
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();
            if (nextEntry == header)
                throw new NoSuchElementException();

            LinkedHashMapEntry<K,V> e = lastReturned = nextEntry;
            nextEntry = e.after;
            return e;
        }
    }

HashTable,因为已经完成的看了HashMap,所以再看跟他相关的类的时候,我就先看他们的不同点,首先他并没有跟前面两个map一样继承AbstractMap而是继承了Dictionary(Dictionary是干嘛的?),然后看到了一大堆synchronized修饰的方法,可知HashTable操作都是线程安全的;接着又发现一张陌生的面孔
public synchronized Enumeration<K> keys() {
return this.<K>getEnumeration(KEYS);
}
看样子跟iterator有点相似啊?是不是呢?等会看再接下来
if (value == null) {
throw new NullPointerException();
}
哎,值为空的话会报空指针,这是个坑,HashTable的值不能等于空,以后使用的时候要判断,那key呢?相关联想,
int hash = hash(key);
private static int hash(Object k) {
return k.hashCode();
}
哎,这个跟之前的hash算法不同,key不能等于null的疑问也能揭晓,
int index = (hash & 0x7FFFFFFF) % tab.length;通过构造方法我们也能看到初始化的initialCapacity也并不是2的乘幂了,通过上述 int index = (hash & 0x7FFFFFFF) % tab.length;HashTable是对数组长度取模,也是为了数组的均匀分布,减少碰撞,但是这个计算效率比h&length-1,那就差很多了,但是为什么HashTable不采取效率更高的方式呢?

public Hashtable(int initialCapacity, float loadFactor) {
        if (initialCapacity < 0)
            throw new IllegalArgumentException("Illegal Capacity: "+
                                               initialCapacity);
        if (loadFactor <= 0 || Float.isNaN(loadFactor))
            throw new IllegalArgumentException("Illegal Load: "+loadFactor);

        if (initialCapacity==0)
            initialCapacity = 1;
        this.loadFactor = loadFactor;
        table = new HashtableEntry[initialCapacity];
        threshold = (initialCapacity <= MAX_ARRAY_SIZE + 1) ? initialCapacity : MAX_ARRAY_SIZE + 1;
    }

回头看Enumeration,比Iterator少了remove的方法,从他的实现类也可以看出他同时实现了Iterator接口,这就有点矛盾了,在remove方法中
public void remove() {
if (!iterator)
throw new UnsupportedOperationException();
可以看到boolean iterator;是来控制Enumeration还是Iterator的

public interface Enumeration<E> {
    /**
     * Tests if this enumeration contains more elements.
     *
     * @return  <code>true</code> if and only if this enumeration object
     *           contains at least one more element to provide;
     *          <code>false</code> otherwise.
     */
    boolean hasMoreElements();

    /**
     * Returns the next element of this enumeration if this enumeration
     * object has at least one more element to provide.
     *
     * @return     the next element of this enumeration.
     * @exception  NoSuchElementException  if no more elements exist.
     */
    E nextElement();
}

private class Enumerator<T> implements Enumeration<T>, Iterator<T> {
        HashtableEntry[] table = Hashtable.this.table;
        int index = table.length;
        HashtableEntry<K,V> entry = null;
        HashtableEntry<K,V> lastReturned = null;
        int type;

        /**
         * Indicates whether this Enumerator is serving as an Iterator
         * or an Enumeration.  (true -> Iterator).
         */
        boolean iterator;

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

        Enumerator(int type, boolean iterator) {
            this.type = type;
            this.iterator = iterator;
        }

        public boolean hasMoreElements() {
            HashtableEntry<K,V> e = entry;
            int i = index;
            HashtableEntry[] t = table;
            /* Use locals for faster loop iteration */
            while (e == null && i > 0) {
                e = t[--i];
            }
            entry = e;
            index = i;
            return e != null;
        }

        public T nextElement() {
            HashtableEntry<K,V> et = entry;
            int i = index;
            HashtableEntry[] t = table;
            /* Use locals for faster loop iteration */
            while (et == null && i > 0) {
                et = t[--i];
            }
            entry = et;
            index = i;
            if (et != null) {
                HashtableEntry<K,V> e = lastReturned = entry;
                entry = e.next;
                return type == KEYS ? (T)e.key : (type == VALUES ? (T)e.value : (T)e);
            }
            throw new NoSuchElementException("Hashtable Enumerator");
        }

        // Iterator methods
        public boolean hasNext() {
            return hasMoreElements();
        }

        public T next() {
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();
            return nextElement();
        }

        public void remove() {
            if (!iterator)
                throw new UnsupportedOperationException();
            if (lastReturned == null)
                throw new IllegalStateException("Hashtable Enumerator");
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();

            synchronized(Hashtable.this) {
                HashtableEntry[] tab = Hashtable.this.table;
                int index = (lastReturned.hash & 0x7FFFFFFF) % tab.length;

                for (HashtableEntry<K,V> e = tab[index], prev = null; e != null;
                     prev = e, e = e.next) {
                    if (e == lastReturned) {
                        modCount++;
                        expectedModCount++;
                        if (prev == null)
                            tab[index] = e.next;
                        else
                            prev.next = e.next;
                        count--;
                        lastReturned = null;
                        return;
                    }
                }
                throw new ConcurrentModificationException();
            }
        }
    }

Dictionary没看出有什么特殊的功能多了两个方法,说白了是返回不能删除的Iterator

abstract public Enumeration<K> keys();

    /**
     * Returns an enumeration of the values in this dictionary. The general
     * contract for the <tt>elements</tt> method is that an
     * <tt>Enumeration</tt> is returned that will generate all the elements
     * contained in entries in this dictionary.
     *
     * @return  an enumeration of the values in this dictionary.
     * @see     java.util.Dictionary#keys()
     * @see     java.util.Enumeration
     */
    abstract public Enumeration<V> elements();

TreeMap,同样带着思考,HashMap跟TreeMap选择的时候,无需排序选择HashMap需要就选择TreeMap,所以TreeMap是怎么实现排序的?

查看源码先找不同点,跟HashMap一样继承AbstractMap类,但是多实现了NavigableMap接口,可通行的Map是个什么鬼?迎面向我们走来的是
private final Comparator<? super K> comparator;
跟心想的一样,排序吗怎少得了Comparator,当然陌生苗孔SortedMap出现,
数据结构这不想其他entry[]了,而是出现了
private transient TreeMapEntry<K,V> root = null;
根节点,???非hash怎么保证效率,往下看,好吧,这货跟上面的不是一回事,没有什么一样的,那就只能细细读了
从SortedMap开始吧,他只是一个接口继承Map,多了一些head,tail,frist,last的字眼,NavigableMap多了一些比较的名词在上面,可知这些都跟排序有着极大的关系;

public interface SortedMap<K,V> extends Map<K,V> {
  Comparator<? super K> comparator();
  SortedMap<K,V> headMap(K toKey);
  SortedMap<K,V> tailMap(K fromKey);
  ···
}

public interface NavigableMap<K,V> extends SortedMap<K,V> {
    ···
     K floorKey(K key);
     Map.Entry<K,V> ceilingEntry(K key);
    ····
}

查看结构TreeMapEntry,left ,right ,parent代表它是一颗树,color = BLACK,红黑二叉树,treeMap内部使用了红黑树来实现有序排列

private static final boolean RED   = false;
private static final boolean BLACK = true;
static final class TreeMapEntry<K,V> implements Map.Entry<K,V> {
        K key;
        V value;
        TreeMapEntry<K,V> left = null;
        TreeMapEntry<K,V> right = null;
        TreeMapEntry<K,V> parent;
        boolean color = BLACK;

构造方法没什么特别,添加构造器了,添加map集合了这些,应该从查找,添加,删除操作,揭开它的神秘面纱;
从getEntry可以看出key不能等于null
if (key == null)
throw new NullPointerException();
如果Comparator不等于空的,就从根节点,通过比较逐步找到节点,否则key就要实现Comparable接口,然后也是通过比较找到;看到这里又有疑问如果可以没有实现Comparable接口,是不是在put的时候有什么特殊的处理?如果有多个key比较相同呢?可能还得往下看

public TreeMap(Comparator<? super K> comparator) {
        this.comparator = comparator;
    }
···
final TreeMapEntry<K,V> getEntry(Object key) {
        // Offload comparator-based version for sake of performance
        if (comparator != null)
            return getEntryUsingComparator(key);
        if (key == null)
            throw new NullPointerException();
        @SuppressWarnings("unchecked")
            Comparable<? super K> k = (Comparable<? super K>) key;
        TreeMapEntry<K,V> p = root;
        while (p != null) {
            int cmp = k.compareTo(p.key);
            if (cmp < 0)
                p = p.left;
            else if (cmp > 0)
                p = p.right;
            else
                return p;
        }
        return null;
    }
//构造器不空
final TreeMapEntry<K,V> getEntryUsingComparator(Object key) {
        @SuppressWarnings("unchecked")
            K k = (K) key;
        Comparator<? super K> cpr = comparator;
        if (cpr != null) {
            TreeMapEntry<K,V> p = root;
            while (p != null) {
                int cmp = cpr.compare(k, p.key);
                if (cmp < 0)
                    p = p.left;
                else if (cmp > 0)
                    p = p.right;
                else
                    return p;
            }
        }
        return null;
    }

接下来查看put方法,当根节点为null,比较器不为null的时候key可以为null,否则key不等于null,解决上述key不实现comparable的疑问 (!(key instanceof Comparable)是会报异常的;

else if (!(key instanceof Comparable)) {
throw new ClassCastException(
"Cannot cast" + key.getClass().getName() + " to Comparable.");
}
如果找到相同节点只会更新value, t.setValue(value);所以不会有重复节点,key比较相同的,可能会被替换,慎用;
下面的插入很简单就是比较大于右边,小于左边,直至插入合适的位置;那么疑问来了,有可能根节点一侧的数据特别特别多,另外一侧没有数据,偏树,这样查询效率就会低了;接着看,肯定有让树平衡的算法,下面有个方法fixAfterInsertion,插入后修理,那应该就是他了,看了一下他的算法,然后用笔在纸上花了一下,就明白了他的算法,之前看了红黑二叉树的算法,不是特别的理解,看了这个一下就通了;下面在系统的说明一下:

public V put(K key, V value) {
        TreeMapEntry<K,V> t = root;
        if (t == null) {
           
            if (comparator != null) {
                if (key == null) {
                    comparator.compare(key, key);
                }
            } else {
                if (key == null) {
                    throw new NullPointerException("key == null");
                } else if (!(key instanceof Comparable)) {
                    throw new ClassCastException(
                            "Cannot cast" + key.getClass().getName() + " to Comparable.");
                }
            }

            root = new TreeMapEntry<>(key, value, null);
            size = 1;
            modCount++;
            return null;
        }
        int cmp;
        TreeMapEntry<K,V> parent;
        // split comparator and comparable paths
        Comparator<? super K> cpr = comparator;
        if (cpr != null) {
            do {
                parent = t;
                cmp = cpr.compare(key, t.key);
                if (cmp < 0)
                    t = t.left;
                else if (cmp > 0)
                    t = t.right;
                else
                    return t.setValue(value);
            } while (t != null);
        }
        else {
            if (key == null)
                throw new NullPointerException();
            @SuppressWarnings("unchecked")
                Comparable<? super K> k = (Comparable<? super K>) key;
            do {
                parent = t;
                cmp = k.compareTo(t.key);
                if (cmp < 0)
                    t = t.left;
                else if (cmp > 0)
                    t = t.right;
                else
                    return t.setValue(value);
            } while (t != null);
        }
        TreeMapEntry<K,V> e = new TreeMapEntry<>(key, value, parent);
        if (cmp < 0)
            parent.left = e;
        else
            parent.right = e;
        fixAfterInsertion(e);
        size++;
        modCount++;
        return null;
    }


 /** From CLR */
    private void fixAfterInsertion(TreeMapEntry<K,V> x) {
        x.color = RED;

        while (x != null && x != root && x.parent.color == RED) {
            if (parentOf(x) == leftOf(parentOf(parentOf(x)))) {
                TreeMapEntry<K,V> y = rightOf(parentOf(parentOf(x)));
                if (colorOf(y) == RED) {
                    setColor(parentOf(x), BLACK);
                    setColor(y, BLACK);
                    setColor(parentOf(parentOf(x)), RED);
                    x = parentOf(parentOf(x));
                } else {
                    if (x == rightOf(parentOf(x))) {
                        x = parentOf(x);
                        rotateLeft(x);
                    }
                    setColor(parentOf(x), BLACK);
                    setColor(parentOf(parentOf(x)), RED);
                    rotateRight(parentOf(parentOf(x)));
                }
            } else {
                TreeMapEntry<K,V> y = leftOf(parentOf(parentOf(x)));
                if (colorOf(y) == RED) {
                    setColor(parentOf(x), BLACK);
                    setColor(y, BLACK);
                    setColor(parentOf(parentOf(x)), RED);
                    x = parentOf(parentOf(x));
                } else {
                    if (x == leftOf(parentOf(x))) {
                        x = parentOf(x);
                        rotateRight(x);
                    }
                    setColor(parentOf(x), BLACK);
                    setColor(parentOf(parentOf(x)), RED);
                    rotateLeft(parentOf(parentOf(x)));
                }
            }
        }
        root.color = BLACK;
    }

之前就通过各种途径了解过红黑二叉树,因为没有看实际的例子所以有些抽象,集合TreeMap一下就通了,以此记录一下:
首先什么是红黑二叉树,有什么特点?
1.根节点是黑色
2.叶子节点是黑色
3.每个节点只能是黑色或者红色的一种
4.不可能出现两个连续的红色节点
5.从任何一个节点出发,包含黑色节点的个数是一样的
顺序是left<parent<right,注意上述并没有说不可能存在两个相同的黑色节点,实际业火发生这种情况。
回到代码
put方法显示根据一系列比较算法将对应的节点插入对应的父亲下,接着进入fixAfterInsertion方法(这个就是红黑树保持平衡的关键所在),首先将最后插入的节点颜色设置为红, while (x != null && x != root && x.parent.color == RED) 说明根节点或者父节点为黑色的话,树不需要平衡,大家动手画画还是画画吧比较清晰


来源于网络

接着判断父节点在爷爷节点的左侧还是右侧,如果是在左侧判断叔叔节点是不是红色,如果是红色把父亲和叔叔的颜色设置成黑色,爷爷改成红色,然后把当前节点移到爷爷节点继续遍历;如果叔叔节点是黑色,判断当前节点如果在右侧,然后做一个左旋转,将父设置成黑色,爷爷设成红色对爷爷右旋。左旋右旋看图片可能比较好,自己照着画一下,就更清晰了


左旋

右旋
/** From CLR */
    private void rotateLeft(TreeMapEntry<K,V> p) {
        if (p != null) {
            TreeMapEntry<K,V> r = p.right;
            p.right = r.left;
            if (r.left != null)
                r.left.parent = p;
            r.parent = p.parent;
            if (p.parent == null)
                root = r;
            else if (p.parent.left == p)
                p.parent.left = r;
            else
                p.parent.right = r;
            r.left = p;
            p.parent = r;
        }
    }

    /** From CLR */
    private void rotateRight(TreeMapEntry<K,V> p) {
        if (p != null) {
            TreeMapEntry<K,V> l = p.left;
            p.left = l.right;
            if (l.right != null) l.right.parent = p;
            l.parent = p.parent;
            if (p.parent == null)
                root = l;
            else if (p.parent.right == p)
                p.parent.right = l;
            else p.parent.left = l;
            l.right = p;
            p.parent = l;
        }
    }

"删除常规二叉查找树中删除节点的方法是一样的"。分3种情况:
① 被删除节点没有儿子,即为叶节点。那么,直接将该节点删除就OK了。
② 被删除节点只有一个儿子。那么,直接删除该节点,并用该节点的唯一子节点顶替它的位置。
③ 被删除节点有两个儿子。那么,先找出它的后继节点;然后把“它的后继节点的内容”复制给“该节点的内容”;之后,删除“它的后继节点”。在这里,后继节点相当于替身,在将后继节点的内容复制给"被删除节点"之后,再将后继节点删除。这样就巧妙的将问题转换为"删除后继节点"的情况了,下面就考虑后继节点。 在"被删除节点"有两个非空子节点的情况下,它的后继节点不可能是双子非空。既然"的后继节点"不可能双子都非空,就意味着"该节点的后继节点"要么没有儿子,要么只有一个儿子。若没有儿子,则按"情况① "进行处理;若只有一个儿子,则按"情况② "进行处理。
处理完后这个树可能就不符合二叉树的要求,需要做一下修整修整算法

 /** From CLR */
    private void fixAfterDeletion(TreeMapEntry<K,V> x) {
        while (x != root && colorOf(x) == BLACK) {
            if (x == leftOf(parentOf(x))) {
                TreeMapEntry<K,V> sib = rightOf(parentOf(x));

                if (colorOf(sib) == RED) {
                    setColor(sib, BLACK);
                    setColor(parentOf(x), RED);
                    rotateLeft(parentOf(x));
                    sib = rightOf(parentOf(x));
                }

                if (colorOf(leftOf(sib))  == BLACK &&
                    colorOf(rightOf(sib)) == BLACK) {
                    setColor(sib, RED);
                    x = parentOf(x);
                } else {
                    if (colorOf(rightOf(sib)) == BLACK) {
                        setColor(leftOf(sib), BLACK);
                        setColor(sib, RED);
                        rotateRight(sib);
                        sib = rightOf(parentOf(x));
                    }
                    setColor(sib, colorOf(parentOf(x)));
                    setColor(parentOf(x), BLACK);
                    setColor(rightOf(sib), BLACK);
                    rotateLeft(parentOf(x));
                    x = root;
                }
            } else { // symmetric
                TreeMapEntry<K,V> sib = leftOf(parentOf(x));

                if (colorOf(sib) == RED) {
                    setColor(sib, BLACK);
                    setColor(parentOf(x), RED);
                    rotateRight(parentOf(x));
                    sib = leftOf(parentOf(x));
                }

                if (colorOf(rightOf(sib)) == BLACK &&
                    colorOf(leftOf(sib)) == BLACK) {
                    setColor(sib, RED);
                    x = parentOf(x);
                } else {
                    if (colorOf(leftOf(sib)) == BLACK) {
                        setColor(rightOf(sib), BLACK);
                        setColor(sib, RED);
                        rotateLeft(sib);
                        sib = leftOf(parentOf(x));
                    }
                    setColor(sib, colorOf(parentOf(x)));
                    setColor(parentOf(x), BLACK);
                    setColor(leftOf(sib), BLACK);
                    rotateRight(parentOf(x));
                    x = root;
                }
            }
        }

        setColor(x, BLACK);
    }

看着代码都能看懂,但是这样的操作是怎么保持平衡的,画一画,就会清晰
从网上截一些图,主要是跟兄弟节点,和侄子节点有关系

待删除节点D的兄弟节点S为红色,D没了这个树肯定就无法保持平衡。



调整做法是将父亲节点和兄弟节点的颜色互换,也就是p变成红色,S变成黑色,然后将P树进行左旋型操作,结果如下图,D删掉,同样不平衡,还需要继续向下操作,等会说明



D是右节点的情况,跟上面一样只是操作的方向相反


情况2:兄弟节点为黑色,且远侄子节点为红色。
D为左孩子对的情况,这时D的远侄子节点为S的右孩子


没有上色的节点表示黑色红色均可,注意如果SL为黑色,则SL必为NULL节点。

这个时候,如果我们删除D,这样经过D的子节点(NULL节点)的路径的黑色节点个数就会减1,但是我们看到S的孩子中有红色的节点,如果我们能把这棵红色的节点移动到左侧,并把它改成黑色,那么就满足要求了,这也是为什么P的颜色无关,因为调整过程只在P整棵子树的内部进行。

调整过程为,将P和S的颜色对调,然后对P树进行类似AVL树RR型的操作,最后把SR节点变成黑色,并删除D即可。



另外一边也一样



情况3:兄弟节点S为黑色,远侄子节点为黑色,近侄子节点为红色
D为左孩子的情况,此时近侄子节点为S的左孩子



做法是,将SL右旋,并将S和SL的颜色互换



相反情况


情况4:父亲节p为红色,兄弟节点和兄弟节点的两个孩子(只能是NULL节点)都为黑色的情况。



如果删除D,那经过P到D的子节点NULL的路径上黑色就少了一个,这个时候我们可以把P变成黑色,这样删除D后经过D子节点(NULL节点)路径上的黑色节点就和原来一样了。但是这样会导致经过S的子节点(NULL节点)的路径上的黑色节点数增加一个,所以这个时候可以再将S节点变成红色,这样路径上的黑色节点数就和原来一样啦!

所以做法是,将父亲节点P改成黑色,将兄弟节点S改成红色,然后删除D即可。如下图:



情况5:父亲节点p,兄弟节点s和兄弟节点的两个孩子(只能为NULL节点)都为黑色的情况



方法是将兄弟节点S的颜色改成红色,这样删除D后P的左右两支的黑节点数就相等了,但是经过P的路径上的黑色节点数会少1,这个时候,我们再以P为起始点,继续根据情况进行平衡操作(这句话的意思就是把P当成D(只是不要再删除P了),再看是那种情况,再进行对应的调整,这样一直向上,直到新的起始点为根节点)。结果如下图:
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