HashMap

通常我们知道 HashMap 的实现是 数组+链表.
这样的实现性能不够平滑, 因为无论hash算法再如何优化, 也很难让元素百分百均匀分布.
当 HashMap 中有大量的元素都存放到同一个容器中时, 这个容器下有一条长长的链表, 这个时候 HashMap 就相当于一个单链表, 假如单链表有 n 个元素, 遍历的时间复杂度就是 O(n), 完全失去了它的优势.
针对这种情况, JDK 8 中引入了 红黑树(查找时间复杂度为 O(log n)来优化这个问题.
思路就是当容器内的元素增加一定数量时, 将它转换为树, 同样, 当元素减少到一定数量时, 再次转换成链表.

1. 默认属性

• DEFAULT_INITIAL_CAPACITY = 1 << 4
  默认初始容器数量大小 16
• MAXIMUM_CAPACITY = 1 << 30
  最大容器数量 2^30
• DEFAULT_LOAD_FACTOR = 0.75f
  默认负载因子 0.75
• TREEIFY_THRESHOLD = 8
  树化临界值 8, 即当容器内元素增加到 8 个时, 容器由链表转换为树型结构
• UNTREEIFY_THRESHOLD = 6
  反树化临界值 6, 即当容器内元素减少到 6 个时, 容器由树型转换为链表结构
• MIN_TREEIFY_CAPACITY = 64
  最小树型化容器数量 64, 即当容器数量至少为该值时, 容器才能进行树型化

2. 特性

• 允许 key 和 value 为 null

• 不能保证顺序恒定不变

• 初始化的容器数量为大于等于该值的最小 2 幂指数

• 扩容为之前容器数量的 2 倍

• 当容器数量大于等于 64, 且容器中元素个数大于等于 8 时, 容器由链表转换为树型结构

• 当容器中元素个数小于 6 时, 容器由树型转换为链表结构

• 性能与容器数量 (capacity) 及负载因子 (load factor) 有关
  扩容前最大条目数 = 初始容器数量 * 负载因子
  所以初始容器数量可这样配置, 以减少 rehash 次数:
  初始容器数量 = 预计最大条目数 / 负载因子

• 很多 key 的 hashcode 值相同也会影响性能
  让 key 实现 Comparable 接口, HashMap 会使用它们的比较顺序来解决它们的碰撞问题
  如果还是相同使用 System.identityHashCode(key) 进行比较

• 树型优化提高了查找效率
  链表的时间复杂度是 O(n); 链表的时间复杂度是 O(log n)
  但是树型的删除操作的效率低于链表

• 非线程安全
  可以对封装的对象同步, 或者使用 Collections.synchronizedMap() 包装
  或者换用 HashTable 或 ConcurrentHashMap

• 从 HashMap 上获得的迭代器都采用 fast-fail 机制
  即除了 Iterator 的 remove 方法外, 其他在遍历时添加或删除元素, 都有可能抛出 ConcurrentModificationException, 但不能保证一定会抛错.

• HashMap 实现了 Serializable 接口, 但是字段使用 transient 修饰, 比如 table, entrySet 等.
  由于 hashCode 操作依赖于 jvm 所处的环境, 不同的环境下 hash 值可能不同. 如果直接将包含 hashCode 的数据持久化下来, 也无法通用.
  所以 HashMap 自己实现了 writeObject 和 readObject.

3. HashMap 源码

hashmap.javaview raw

/*
 * Copyright (c) 1997, 2013, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 */

package java.util;

import java.io.IOException;
import java.io.InvalidObjectException;
import java.io.Serializable;
import java.lang.reflect.ParameterizedType;
import java.lang.reflect.Type;
import java.util.function.BiConsumer;
import java.util.function.BiFunction;
import java.util.function.Consumer;
import java.util.function.Function;

/**
 * Hash table based implementation of the {@code Map} interface.  This
 * implementation provides all of the optional map operations, and permits
 * {@code null} values and the {@code null} key.  (The {@code HashMap}
 * class is roughly equivalent to {@code Hashtable}, except that it is
 * unsynchronized and permits nulls.)  This class makes no guarantees as to
 * the order of the map; in particular, it does not guarantee that the order
 * will remain constant over time.
 *
 * 基于哈希表的 Map 接口的实现.
 * 此实现提供所有可选的映射操作，并允许key和value为null.
 * 除了非同步和允许null值, HashMap 类与 Hashtable 大致相同.
 * 此类不保证映射的顺序, 特别是它不保证该顺序恒久不变.
 *
 * <p>This implementation provides constant-time performance for the basic
 * operations ({@code get} and {@code put}), assuming the hash function
 * disperses the elements properly among the buckets.  Iteration over
 * collection views requires time proportional to the "capacity" of the
 * {@code HashMap} instance (the number of buckets) plus its size (the number
 * of key-value mappings).  Thus, it's very important not to set the initial
 * capacity too high (or the load factor too low) if iteration performance is
 * important.
 *
 * 此实现假设hash方法能把元素均匀的分布在各个容器之间, 以此保证基本操作(get和put)提供稳定的性能
 * 遍历整个集合所需的时间与HashMap实例的容量(容器的数量 capacity)及其大小(键值对数量)成正比
 * 因此, 如果遍历性能很重要, 则不要初始容量设置过高(或负载因子设置过低).
 *
 * <p>An instance of {@code HashMap} has two parameters that affect its
 * performance: <i>initial capacity</i> and <i>load factor</i>.  The
 * <i>capacity</i> is the number of buckets in the hash table, and the initial
 * capacity is simply the capacity at the time the hash table is created.  The
 * <i>load factor</i> is a measure of how full the hash table is allowed to
 * get before its capacity is automatically increased.  When the number of
 * entries in the hash table exceeds the product of the load factor and the
 * current capacity, the hash table is <i>rehashed</i> (that is, internal data
 * structures are rebuilt) so that the hash table has approximately twice the
 * number of buckets.
 *
 * HashMap的实例有2个参数影响它的性能: 初始容量和负载因子.
 * 容量是在哈希表中容器的数量, 而初始容量就是在哈希表创建时的容量.
 * 负载因子是哈希表在其容量自动增加之前可以达到多满的一个比例.
 * 当哈希表中元素数量超过负载因子和当前容量的乘积时, 哈希表会被rehash(即内部数据结构被重构), 从而哈希表将具有大约2倍的容器数量.
 *
 * <p>As a general rule, the default load factor (.75) offers a good
 * tradeoff between time and space costs.  Higher values decrease the
 * space overhead but increase the lookup cost (reflected in most of
 * the operations of the {@code HashMap} class, including
 * {@code get} and {@code put}).  The expected number of entries in
 * the map and its load factor should be taken into account when
 * setting its initial capacity, so as to minimize the number of
 * rehash operations.  If the initial capacity is greater than the
 * maximum number of entries divided by the load factor, no rehash
 * operations will ever occur.
 *
 * 一般来说, 默认负载因子(0.75)很好的权衡了时间和空间成本.
 * 负载因子过高虽然减少了空间开销, 但是增加了检索的开销(在HashMap的大多数操作都反映出这一点, 包括get和put)
 * 当设置哈希表的初始容量时, 应当考虑哈希表中所需的元素数量和它的负载因子, 以便减少rehash操作的次数.
 * 如果初始容量大于最大元素数量除以负载因子, 那么rehash将不会发生.
 *
 * <p>If many mappings are to be stored in a {@code HashMap}
 * instance, creating it with a sufficiently large capacity will allow
 * the mappings to be stored more efficiently than letting it perform
 * automatic rehashing as needed to grow the table.  Note that using
 * many keys with the same {@code hashCode()} is a sure way to slow
 * down performance of any hash table. To ameliorate impact, when keys
 * are {@link Comparable}, this class may use comparison order among
 * keys to help break ties.
 *
 * 如果很多键值对要存储, 那么创建一个足够大的容量的HashMap实例, 将比创建需要自动rehash来扩容的实例更高效.
 * 需要注意的是, 有很多相同hashCode值的key时, 将会降低哈希表的性能.
 * 为了改善这一点, 当key可比较时, HashMap会使用它们的比较顺序来打破这种关联.
 *
 * <p><strong>Note that this implementation is not synchronized.</strong>
 * If multiple threads access a hash map concurrently, and at least one of
 * the threads modifies the map structurally, it <i>must</i> be
 * synchronized externally.  (A structural modification is any operation
 * that adds or deletes one or more mappings; merely changing the value
 * associated with a key that an instance already contains is not a
 * structural modification.)  This is typically accomplished by
 * synchronizing on some object that naturally encapsulates the map.
 *
 * 需要注意的是, HashMap的实现是不同步的.
 * 如果多个线程同时访问哈希表, 而且其中至少有一个线程让哈希表做出结构性的改变, 那就必须保持外部同步.
 * (结构性的改变是指任何添加或删除一个或多个键值对;仅改变实例中已存在的一个key对应的value, 不是结构性改变)
 * 这一般通过对原本就封装在哈希表中的对象进行同步实现的.
 *
 * If no such object exists, the map should be "wrapped" using the
 * {@link Collections#synchronizedMap Collections.synchronizedMap}
 * method.  This is best done at creation time, to prevent accidental
 * unsynchronized access to the map:<pre>
 *   Map m = Collections.synchronizedMap(new HashMap(...));</pre>
 *
 * 如果没有这样的对象, 哈希表也可以通过Collections.synchronizedMap来包装.
 * 这最好在创建时完成这一操作, 以避免非同步访问.比如:
 *   Map m = Collections.synchronizedMap(new HashMap(...));
 *
 * <p>The iterators returned by all of this class's "collection view methods"
 * are <i>fail-fast</i>: if the map is structurally modified at any time after
 * the iterator is created, in any way except through the iterator's own
 * {@code remove} method, the iterator will throw a
 * {@link ConcurrentModificationException}.  Thus, in the face of concurrent
 * modification, the iterator fails quickly and cleanly, rather than risking
 * arbitrary, non-deterministic behavior at an undetermined time in the
 * future.
 *
 * 通过任何HashMap的集合视图方法得到的迭代器都采用fail-fast机制.
 * 如果在迭代器创建后, 除了迭代器本身的remove方法, 在任何时候, 任何方式, 哈希表被结构性的改变, 迭代器将抛出ConcurrentModificationException.
 * 因此, 在面对并发修改时, 迭代器将干净利落的抛错, 而不是在之后某个不确定的时间和不确定的操作下.
 *
 * <p>Note that the fail-fast behavior of an iterator cannot be guaranteed
 * as it is, generally speaking, impossible to make any hard guarantees in the
 * presence of unsynchronized concurrent modification.  Fail-fast iterators
 * throw {@code ConcurrentModificationException} on a best-effort basis.
 * Therefore, it would be wrong to write a program that depended on this
 * exception for its correctness: <i>the fail-fast behavior of iterators
 * should be used only to detect bugs.</i>
 *
 * 需要注意的是, 迭代器的fail-fast机制不能保证它的出现, 更通俗的说, 不能保证在不同步的并发修改时必定出现.
 * fail-fast机制的迭代器尽可能抛出ConcurrentModificationException异常.
 * 因此, 依靠这个异常来保证程序的正确性的写法是不对的.
 * fail-fast机制应该只能用来检测错误.
 *
 * <p>This class is a member of the
 * <a href="{@docRoot}/java/util/package-summary.html#CollectionsFramework">
 * Java Collections Framework</a>.
 *
 * @param <K> the type of keys maintained by this map
 * @param <V> the type of mapped values
 *
 * @author  Doug Lea
 * @author  Josh Bloch
 * @author  Arthur van Hoff
 * @author  Neal Gafter
 * @see     Object#hashCode()
 * @see     Collection
 * @see     Map
 * @see     TreeMap
 * @see     Hashtable
 * @since   1.2
 */
public class HashMap<K, V> extends AbstractMap<K, V>
        implements Map<K, V>, Cloneable, Serializable {

    private static final long serialVersionUID = 362498820763181265L;

    /*
     * Implementation notes.
     *
     * This map usually acts as a binned (bucketed) hash table, but
     * when bins get too large, they are transformed into bins of
     * TreeNodes, each structured similarly to those in
     * java.util.TreeMap. Most methods try to use normal bins, but
     * relay to TreeNode methods when applicable (simply by checking
     * instanceof a node).  Bins of TreeNodes may be traversed and
     * used like any others, but additionally support faster lookup
     * when overpopulated. However, since the vast majority of bins in
     * normal use are not overpopulated, checking for existence of
     * tree bins may be delayed in the course of table methods.
     *
     * HashMap通常可以像哈希表一样使用, 但是当容器过大时, 它们会把容器转换成TreeNode类型, 每个的结构都类似于java.util.TreeMap.
     * 大多数方法先使用普通的容器类型, 但是当TreeNode的方法适用时将转变(简单的通过验证).
     * 容器内的TreeNode可以像其他节点一样遍历和使用, 但是当超载时将获得更快的检索速度.
     * 然而, 因为绝大多数容器在正常使用时不会超载, 所以检查是否是树型容器的检查可能在哈希表方法执行时中被推迟
     *
     * Tree bins (i.e., bins whose elements are all TreeNodes) are
     * ordered primarily by hashCode, but in the case of ties, if two
     * elements are of the same "class C implements Comparable<C>", 
     * type then their compareTo method is used for ordering. (We
     * conservatively check generic types via reflection to validate
     * this -- see method comparableClassFor).  The added complexity
     * of tree bins is worthwhile in providing worst-case O(log n)
     * operations when keys either have distinct hashes or are
     * orderable, Thus, performance degrades gracefully under
     * accidental or malicious usages in which hashCode() methods
     * return values that are poorly distributed, as well as those in
     * which many keys share a hashCode, so long as they are also
     * Comparable. (If neither of these apply, we may waste about a
     * factor of two in time and space compared to taking no
     * precautions. But the only known cases stem from poor user
     * programming practices that are already so slow that this makes
     * little difference.)
     *
     * 树型容器(即容器内的元素都是TreeNode)主要是按hashCode排序的, 但如果2个元素都是形如"class C implements Comparable<C>", 有这种关系的元素会使用它们的comapreTo方法来排序.
     * (我们通过反射来谨慎的检查这个类型, 见comparableClassFor)
     * 给树型容器增加复杂度是值得的, 这样无论key是使用hashCode还是排序, 在最坏的情况下也能提供O(log n)的操作复杂度.
     * 因此, 只要key可以比较, 那么就算在特殊或恶意的使用场景下, 如hashCode()返回的值不够分散, 甚至许多key有相同的hashCode, 性能的下降也比较平滑.
     * (如果这2种方式都不适用, 我们可能要花2倍的时间或空间, 在毫无措施的情况下比较.但是已知的这样的案例都源于糟糕的用户程序设计, 在已经很慢的基础上再慢点没啥区别了)
     *
     * Because TreeNodes are about twice the size of regular nodes, we
     * use them only when bins contain enough nodes to warrant use
     * (see TREEIFY_THRESHOLD). And when they become too small (due to
     * removal or resizing) they are converted back to plain bins.  In
     * usages with well-distributed user hashCodes, tree bins are
     * rarely used.  Ideally, under random hashCodes, the frequency of
     * nodes in bins follows a Poisson distribution
     * (http://en.wikipedia.org/wiki/Poisson_distribution) with a
     * parameter of about 0.5 on average for the default resizing
     * threshold of 0.75, although with a large variance because of
     * resizing granularity. Ignoring variance, the expected
     * occurrences of list size k are (exp(-0.5) * pow(0.5, k) /
     * factorial(k)). The first values are:
     *
     * 因为TreeNode的大小是普通节点的2倍, 所以我们只在容器中有足够多的节点时才被使用(见TREEIFY_THRESHOLD).
     * 当容器变的很小时(由于删除及调整大小), 树型容器也会转换成普通的容器.
     * 假如使用时能用hashCode均匀的分布元素, 树型容器很少被用到.
     * 理论上, 使用随机hashCode的节点在容器中的分布遵循泊松分布理论.
     * 抛开resize导致的粒度影响, 当负载因子是0.75时, 元素落在各个容器内的概率为 50%.
     * (exp(-0.5) * pow(0.5, k) / factorial(k))
     * 也就是 (e^-0.5 * 0.5^k) / k!
     * 通过公式计算出0~8个在同一个容器内出现的概率:
     *
     * 0:    0.60653066
     * 1:    0.30326533
     * 2:    0.07581633
     * 3:    0.01263606
     * 4:    0.00157952
     * 5:    0.00015795
     * 6:    0.00001316
     * 7:    0.00000094
     * 8:    0.00000006
     * more: less than 1 in ten million
     * 更多: 不到亿分之一
     *
     * The root of a tree bin is normally its first node.  However, 
     * sometimes (currently only upon Iterator.remove), the root might
     * be elsewhere, but can be recovered following parent links
     * (method TreeNode.root()).
     *
     * 树型容器的根节点一般是它的第一个加入的节点.
     * 然而, 某些时候(刚刚执行Iterator.remove时), 根节点可能是其他节点, 但是可以被重新分配(TreeNode.root()方法)
     *
     * All applicable internal methods accept a hash code as an
     * argument (as normally supplied from a public method), allowing
     * them to call each other without recomputing user hashCodes.
     * Most internal methods also accept a "tab" argument, that is
     * normally the current table, but may be a new or old one when
     * resizing or converting.
     *
     * 所有合适的内部方法接受一个hashCode作为参数(通常是由public方法提供的), 允许他们相互调用时不需要重新计算hashCode.
     * 大多数内部方法也接收一个"tab"参数, 这通常表示当前哈希表, 也能在调整大小或转换时代表表示新表或老表.
     *
     * When bin lists are treeified, split, or untreeified, we keep
     * them in the same relative access/traversal order (i.e., field
     * Node.next) to better preserve locality, and to slightly
     * simplify handling of splits and traversals that invoke
     * iterator.remove. When using comparators on insertion, to keep a
     * total ordering (or as close as is required here) across
     * rebalancings, we compare classes and identityHashCodes as
     * tie-breakers.
     *
     *
     * The use and transitions among plain vs tree modes is
     * complicated by the existence of subclass LinkedHashMap. See
     * below for hook methods defined to be invoked upon insertion, 
     * removal and access that allow LinkedHashMap internals to
     * otherwise remain independent of these mechanics. (This also
     * requires that a map instance be passed to some utility methods
     * that may create new nodes.)
     *
     * The concurrent-programming-like SSA-based coding style helps
     * avoid aliasing errors amid all of the twisty pointer operations.
     */

    /**
     * The default initial capacity - MUST be a power of two.
     *
     * 默认初始容量大小 - 必须是2的倍数
     */
    static final int DEFAULT_INITIAL_CAPACITY = 1 << 4; // aka 16

    /**
     * The maximum capacity, used if a higher value is implicitly specified
     * by either of the constructors with arguments.
     * MUST be a power of two <= 1<<30.
     *
     * 最大容量 - 必须是2^30的倍数
     */
    static final int MAXIMUM_CAPACITY = 1 << 30;

    /**
     * The load factor used when none specified in constructor.
     *
     * 默认负载因子
     */
    static final float DEFAULT_LOAD_FACTOR = 0.75f;

    /**
     * The bin count threshold for using a tree rather than list for a
     * bin.  Bins are converted to trees when adding an element to a
     * bin with at least this many nodes. The value must be greater
     * than 2 and should be at least 8 to mesh with assumptions in
     * tree removal about conversion back to plain bins upon
     * shrinkage.
     *
     * 树化临界值
     * bucket内元素个数的临界值, 用来决定bucket是树型结构还是list结构
     * 当bucket内内有如此多元素后再添加一个元素时, bucket将转换成树型结构
     */
    static final int TREEIFY_THRESHOLD = 8;

    /**
     * The bin count threshold for untreeifying a (split) bin during a
     * resize operation. Should be less than TREEIFY_THRESHOLD, and at
     * most 6 to mesh with shrinkage detection under removal.
     *
     * 在执行resize才做时, 反树化bucket的临界值
     */
    static final int UNTREEIFY_THRESHOLD = 6;

    /**
     * The smallest table capacity for which bins may be treeified.
     * (Otherwise the table is resized if too many nodes in a bin.)
     * Should be at least 4 * TREEIFY_THRESHOLD to avoid conflicts
     * between resizing and treeification thresholds.
     *
     * 最小树型化容器数量 64, 即当table大小(容器数量)至少为该值时, 容器才能进行树型化
     *
     */
    static final int MIN_TREEIFY_CAPACITY = 64;

    /**
     * Basic hash bin node, used for most entries.  (See below for
     * TreeNode subclass, and in LinkedHashMap for its Entry subclass.)
     *
     * 链表结构
     */
    static class Node<K, V> implements Map.Entry<K, V> {
        final int hash;
        final K key;
        V value;
        Node<K, V> next;

        Node(int hash, K key, V value, Node<K, V> next) {
            this.hash = hash;
            this.key = key;
            this.value = value;
            this.next = next;
        }

        public final K getKey()        { return key; }
        public final V getValue()      { return value; }
        public final String toString() { return key + "=" + value; }

        public final int hashCode() {
            return Objects.hashCode(key) ^ Objects.hashCode(value);
        }

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

        public final boolean equals(Object o) {
            if (o == this)
                return true;
            if (o instanceof Map.Entry) {
                Map.Entry<?, ?> e = (Map.Entry<?, ?>)o;
                if (Objects.equals(key, e.getKey()) &&
                        Objects.equals(value, e.getValue()))
                    return true;
            }
            return false;
        }
    }

    /* ---------------- Static utilities -------------- */

    /**
     * Computes key.hashCode() and spreads (XORs) higher bits of hash
     * to lower.  Because the table uses power-of-two masking, sets of
     * hashes that vary only in bits above the current mask will
     * always collide. (Among known examples are sets of Float keys
     * holding consecutive whole numbers in small tables.)  So we
     * apply a transform that spreads the impact of higher bits
     * downward. There is a tradeoff between speed, utility, and
     * quality of bit-spreading. Because many common sets of hashes
     * are already reasonably distributed (so don't benefit from
     * spreading), and because we use trees to handle large sets of
     * collisions in bins, we just XOR some shifted bits in the
     * cheapest possible way to reduce systematic lossage, as well as
     * to incorporate impact of the highest bits that would otherwise
     * never be used in index calculations because of table bounds.
     *
     * 计算 key.hashCode ^ hashCode的高16位.
     *
     */
    static final int hash(Object key) {
        int h;
        return (key == null) ? 0 : (h = key.hashCode()) ^ (h >>> 16);
    }

    /**
     * Returns x's Class if it is of the form "class C implements
     * Comparable<C>", else null.
     */
    static Class<?> comparableClassFor(Object x) {
        if (x instanceof Comparable) {
            Class<?> c; Type[] ts, as; ParameterizedType p;
            if ((c = x.getClass()) == String.class) // bypass checks
                return c;
            if ((ts = c.getGenericInterfaces()) != null) {
                for (Type t : ts) {
                    if ((t instanceof ParameterizedType) &&
                            ((p = (ParameterizedType) t).getRawType() ==
                                    Comparable.class) &&
                            (as = p.getActualTypeArguments()) != null &&
                            as.length == 1 && as[0] == c) // type arg is c
                        return c;
                }
            }
        }
        return null;
    }

    /**
     * Returns k.compareTo(x) if x matches kc (k's screened comparable
     * class), else 0.
     */
    @SuppressWarnings({"rawtypes", "unchecked"}) // for cast to Comparable
    static int compareComparables(Class<?> kc, Object k, Object x) {
        return (x == null || x.getClass() != kc ? 0 :
                ((Comparable)k).compareTo(x));
    }

    /**
     * Returns a power of two size for the given target capacity.
     *
     * table的大小为之前的2倍.并并总是2的倍数
     * 思路是把低位全部转换为1
     */
    static final int tableSizeFor(int cap) {
        int n = cap - 1;
        n |= n >>> 1;
        n |= n >>> 2;
        n |= n >>> 4;
        n |= n >>> 8;
        n |= n >>> 16;
        return (n < 0) ? 1 : (n >= MAXIMUM_CAPACITY) ? MAXIMUM_CAPACITY : n + 1;
    }

    /* ---------------- Fields -------------- */

    /**
     * The table, initialized on first use, and resized as
     * necessary. When allocated, length is always a power of two.
     * (We also tolerate length zero in some operations to allow
     * bootstrapping mechanics that are currently not needed.)
     */
    transient Node<K, V>[] table;

    /**
     * Holds cached entrySet(). Note that AbstractMap fields are used
     * for keySet() and values().
     */
    transient Set<Map.Entry<K, V>> entrySet;

    /**
     * The number of key-value mappings contained in this map.
     */
    transient int size;

    /**
     * The number of times this HashMap has been structurally modified
     * Structural modifications are those that change the number of mappings in
     * the HashMap or otherwise modify its internal structure (e.g., 
     * rehash).  This field is used to make iterators on Collection-views of
     * the HashMap fail-fast.  (See ConcurrentModificationException).
     *
     * 用于记录修改的次数
     * 如果modCount匹配不上, 就会抛ConcurrentModificationException.
     * fail-fast机制就是基于它实现的.
     */
    transient int modCount;

    /**
     * The next size value at which to resize (capacity * load factor).
     *
     * @serial
     */
    // (The javadoc description is true upon serialization.
    // Additionally, if the table array has not been allocated, this
    // field holds the initial array capacity, or zero signifying
    // DEFAULT_INITIAL_CAPACITY.)
    int threshold;

    /**
     * The load factor for the hash table.
     *
     * @serial
     */
    final float loadFactor;

    /* ---------------- Public operations -------------- */

    /**
     * Constructs an empty {@code HashMap} with the specified initial
     * capacity and load factor.
     *
     * @param  initialCapacity the initial capacity
     * @param  loadFactor      the load factor
     * @throws IllegalArgumentException if the initial capacity is negative
     *         or the load factor is nonpositive
     */
    public HashMap(int initialCapacity, float loadFactor) {
        if (initialCapacity < 0)
            throw new IllegalArgumentException("Illegal initial capacity: " +
                    initialCapacity);
        if (initialCapacity > MAXIMUM_CAPACITY)
            initialCapacity = MAXIMUM_CAPACITY;
        if (loadFactor <= 0 || Float.isNaN(loadFactor))
            throw new IllegalArgumentException("Illegal load factor: " +
                    loadFactor);
        this.loadFactor = loadFactor;
        this.threshold = tableSizeFor(initialCapacity);
    }

    /**
     * Constructs an empty {@code HashMap} with the specified initial
     * capacity and the default load factor (0.75).
     *
     * @param  initialCapacity the initial capacity.
     * @throws IllegalArgumentException if the initial capacity is negative.
     */
    public HashMap(int initialCapacity) {
        this(initialCapacity, DEFAULT_LOAD_FACTOR);
    }

    /**
     * Constructs an empty {@code HashMap} with the default initial capacity
     * (16) and the default load factor (0.75).
     */
    public HashMap() {
        this.loadFactor = DEFAULT_LOAD_FACTOR; // all other fields defaulted
    }

    /**
     * Constructs a new {@code HashMap} with the same mappings as the
     * specified {@code Map}.  The {@code HashMap} is created with
     * default load factor (0.75) and an initial capacity sufficient to
     * hold the mappings in the specified {@code Map}.
     *
     * @param   m the map whose mappings are to be placed in this map
     * @throws  NullPointerException if the specified map is null
     */
    public HashMap(Map<? extends K, ? extends V> m) {
        this.loadFactor = DEFAULT_LOAD_FACTOR;
        putMapEntries(m, false);
    }

    /**
     * Implements Map.putAll and Map constructor
     *
     * @param m the map
     * @param evict false when initially constructing this map, else
     * true (relayed to method afterNodeInsertion).
     */
    final void putMapEntries(Map<? extends K, ? extends V> m, boolean evict) {
        int s = m.size();
        if (s > 0) {
            if (table == null) { // pre-size
                float ft = ((float)s / loadFactor) + 1.0F;
                int t = ((ft < (float)MAXIMUM_CAPACITY) ?
                        (int)ft : MAXIMUM_CAPACITY);
                if (t > threshold)
                    threshold = tableSizeFor(t);
            }
            else if (s > threshold)
                resize();
            for (Map.Entry<? extends K, ? extends V> e : m.entrySet()) {
                K key = e.getKey();
                V value = e.getValue();
                putVal(hash(key), key, value, false, evict);
            }
        }
    }

    /**
     * Returns the number of key-value mappings in this map.
     *
     * @return the number of key-value mappings in this map
     */
    public int size() {
        return size;
    }

    /**
     * Returns {@code true} if this map contains no key-value mappings.
     *
     * @return {@code true} if this map contains no key-value mappings
     */
    public boolean isEmpty() {
        return size == 0;
    }

    /**
     * Returns the value to which the specified key is mapped, 
     * or {@code null} if this map contains no mapping for the key.
     *
     * <p>More formally, if this map contains a mapping from a key
     * {@code k} to a value {@code v} such that {@code (key==null ? k==null :
     * key.equals(k))}, then this method returns {@code v}; otherwise
     * it returns {@code null}.  (There can be at most one such mapping.)
     *
     * <p>A return value of {@code null} does not <i>necessarily</i>
     * indicate that the map contains no mapping for the key; it's also
     * possible that the map explicitly maps the key to {@code null}.
     * The {@link #containsKey containsKey} operation may be used to
     * distinguish these two cases.
     *
     * @see #put(Object, Object)
     */
    public V get(Object key) {
        Node<K, V> e;
        return (e = getNode(hash(key), key)) == null ? null : e.value;
    }

    /**
     * Implements Map.get and related methods
     *
     * @param hash hash for key
     * @param key the key
     * @return the node, or null if none
     *
     */
    final Node<K, V> getNode(int hash, Object key) {
        Node<K, V>[] tab; Node<K, V> first, e; int n; K k;
        if ((tab = table) != null && (n = tab.length) > 0 &&
                // (n - 1) & hash 计算下标, 获得对应bucket的第一个元素
                (first = tab[(n - 1) & hash]) != null) {
            // 先判断第一个元素是否是需要的那个
            if (first.hash == hash && // always check first node
                    ((k = first.key) == key || (key != null && key.equals(k))))
                return first;
            // 如果不是, 判断第一个元素的类型, 用对应的方法遍历
            if ((e = first.next) != null) {
                if (first instanceof TreeNode)
                    return ((TreeNode<K, V>)first).getTreeNode(hash, key);
                do {
                    if (e.hash == hash &&
                            ((k = e.key) == key || (key != null && key.equals(k))))
                        return e;
                } while ((e = e.next) != null);
            }
        }
        return null;
    }

    /**
     * Returns {@code true} if this map contains a mapping for the
     * specified key.
     *
     * @param   key   The key whose presence in this map is to be tested
     * @return {@code true} if this map contains a mapping for the specified
     * key.
     */
    public boolean containsKey(Object key) {
        return getNode(hash(key), key) != null;
    }

    /**
     * Associates the specified value with the specified key in this map.
     * If the map previously contained a mapping for the key, the old
     * value is replaced.
     *
     * @param key key with which the specified value is to be associated
     * @param value value to be associated with the specified key
     * @return the previous value associated with {@code key}, or
     *         {@code null} if there was no mapping for {@code key}.
     *         (A {@code null} return can also indicate that the map
     *         previously associated {@code null} with {@code key}.)
     */
    public V put(K key, V value) {
        return putVal(hash(key), key, value, false, true);
    }

    /**
     * Implements Map.put and related methods
     *
     * @param hash hash for key
     * @param key the key
     * @param value the value to put
     * @param onlyIfAbsent if true, don't change existing value 如果为true, 则不改变原有值
     * @param evict if false, the table is in creation mode. 如果是false, 则table使用创建模式
     * @return previous value, or null if none
     */
    final V putVal(int hash, K key, V value, boolean onlyIfAbsent, 
                   boolean evict) {
        Node<K, V>[] tab; Node<K, V> p; int n, i;
        // 空table, 则先做resize
        // n = table.length
        if ((tab = table) == null || (n = tab.length) == 0)
            n = (tab = resize()).length;
        // hash 取模, 计算出该键值对放在哪个 bucket
        // p 为 table 中第一个元素
        if ((p = tab[i = (n - 1) & hash]) == null)
            tab[i] = newNode(hash, key, value, null);
        else {
            Node<K, V> e; K k;
            // 判断 p.key 和 key 相同
            // 如果是, e = table 中第一个元素
            if (p.hash == hash &&
                    ((k = p.key) == key || (key != null && key.equals(k))))
                e = p;
            // 树结构操作
            else if (p instanceof TreeNode)
                e = ((TreeNode<K, V>)p).putTreeVal(this, tab, hash, key, value);
            else {
                // 遍历链表
                for (int binCount = 0; ; ++binCount) {
                    // 在尾部插入该元素
                    if ((e = p.next) == null) {
                        p.next = newNode(hash, key, value, null);
                        // 插入之后看看是否需要树化
                        if (binCount >= TREEIFY_THRESHOLD - 1) // -1 for 1st
                            treeifyBin(tab, hash);
                        break;
                    }
                    // 如果发现 key 相同, 则取回该元素
                    if (e.hash == hash &&
                            ((k = e.key) == key || (key != null && key.equals(k))))
                        break;
                    p = e;
                }
            }
            // 修改value
            if (e != null) { // existing mapping for key
                V oldValue = e.value;
                if (!onlyIfAbsent || oldValue == null)
                    e.value = value;
                afterNodeAccess(e);
                return oldValue;
            }
        }
        ++modCount;
        // 判断是否需要resize
        if (++size > threshold)
            resize();
        afterNodeInsertion(evict);
        return null;
    }

    /**
     * Initializes or doubles table size.  If null, allocates in
     * accord with initial capacity target held in field threshold.
     * Otherwise, because we are using power-of-two expansion, the
     * elements from each bin must either stay at same index, or move
     * with a power of two offset in the new table.
     *
     * 初始化或table扩容2倍
     * 如果是给table扩容, 由于我们是扩大2的倍数, 所以元素那么留在原地, 要么偏移2的倍数的下标
     *
     * @return the table
     */
    final Node<K, V>[] resize() {
        Node<K, V>[] oldTab = table;
        int oldCap = (oldTab == null) ? 0 : oldTab.length;
        int oldThr = threshold;
        int newCap, newThr = 0;
        if (oldCap > 0) {
            if (oldCap >= MAXIMUM_CAPACITY) {
                threshold = Integer.MAX_VALUE;
                return oldTab;
            }
            else if ((newCap = oldCap << 1) < MAXIMUM_CAPACITY &&
                    oldCap >= DEFAULT_INITIAL_CAPACITY)
                newThr = oldThr << 1; // double threshold
        }
        else if (oldThr > 0) // initial capacity was placed in threshold
            newCap = oldThr;
        else {               // zero initial threshold signifies using defaults
            newCap = DEFAULT_INITIAL_CAPACITY;
            newThr = (int)(DEFAULT_LOAD_FACTOR * DEFAULT_INITIAL_CAPACITY);
        }
        if (newThr == 0) {
            float ft = (float)newCap * loadFactor;
            newThr = (newCap < MAXIMUM_CAPACITY && ft < (float)MAXIMUM_CAPACITY ?
                    (int)ft : Integer.MAX_VALUE);
        }
        threshold = newThr;
        @SuppressWarnings({"rawtypes", "unchecked"})
        Node<K, V>[] newTab = (Node<K, V>[])new Node[newCap];
        table = newTab;
        if (oldTab != null) {
            for (int j = 0; j < oldCap; ++j) {
                Node<K, V> e;
                if ((e = oldTab[j]) != null) {
                    oldTab[j] = null;
                    if (e.next == null)
                        newTab[e.hash & (newCap - 1)] = e;
                    else if (e instanceof TreeNode)
                        // 树型节点分割
                        ((TreeNode<K, V>)e).split(this, newTab, j, oldCap);
                    else { // preserve order
                        Node<K, V> loHead = null, loTail = null;
                        Node<K, V> hiHead = null, hiTail = null;
                        Node<K, V> next;
                        do {
                            next = e.next;
                            if ((e.hash & oldCap) == 0) {
                                if (loTail == null)
                                    loHead = e;
                                else
                                    loTail.next = e;
                                loTail = e;
                            }
                            else {
                                if (hiTail == null)
                                    hiHead = e;
                                else
                                    hiTail.next = e;
                                hiTail = e;
                            }
                        } while ((e = next) != null);
                        if (loTail != null) {
                            loTail.next = null;
                            newTab[j] = loHead;
                        }
                        if (hiTail != null) {
                            hiTail.next = null;
                            newTab[j + oldCap] = hiHead;
                        }
                    }
                }
            }
        }
        return newTab;
    }

    /**
     * Replaces all linked nodes in bin at index for given hash unless
     * table is too small, in which case resizes instead.
     */
    final void treeifyBin(Node<K, V>[] tab, int hash) {
        int n, index; Node<K, V> e;
        // table 太小, 使用 resize
        if (tab == null || (n = tab.length) < MIN_TREEIFY_CAPACITY)
            resize();
        else if ((e = tab[index = (n - 1) & hash]) != null) {
            TreeNode<K, V> hd = null, tl = null;
            // 遍历转换成 TreeNode 类型
            do {
                TreeNode<K, V> p = replacementTreeNode(e, null);
                if (tl == null)
                    hd = p;
                else {
                    p.prev = tl;
                    tl.next = p;
                }
                tl = p;
            } while ((e = e.next) != null);
            // 转换结构
            if ((tab[index] = hd) != null)
                hd.treeify(tab);
        }
    }

    /**
     * Copies all of the mappings from the specified map to this map.
     * These mappings will replace any mappings that this map had for
     * any of the keys currently in the specified map.
     *
     * @param m mappings to be stored in this map
     * @throws NullPointerException if the specified map is null
     */
    public void putAll(Map<? extends K, ? extends V> m) {
        putMapEntries(m, true);
    }

    /**
     * Removes the mapping for the specified key from this map if present.
     *
     * @param  key key whose mapping is to be removed from the map
     * @return the previous value associated with {@code key}, or
     *         {@code null} if there was no mapping for {@code key}.
     *         (A {@code null} return can also indicate that the map
     *         previously associated {@code null} with {@code key}.)
     */
    public V remove(Object key) {
        Node<K, V> e;
        return (e = removeNode(hash(key), key, null, false, true)) == null ?
                null : e.value;
    }

    /**
     * Implements Map.remove and related methods
     *
     * @param hash hash for key
     * @param key the key
     * @param value the value to match if matchValue, else ignored
     * @param matchValue if true only remove if value is equal
     * @param movable if false do not move other nodes while removing
     * @return the node, or null if none
     */
    final Node<K, V> removeNode(int hash, Object key, Object value, 
                               boolean matchValue, boolean movable) {
        Node<K, V>[] tab; Node<K, V> p; int n, index;
        if ((tab = table) != null && (n = tab.length) > 0 &&
                (p = tab[index = (n - 1) & hash]) != null) {
            Node<K, V> node = null, e; K k; V v;
            if (p.hash == hash &&
                    ((k = p.key) == key || (key != null && key.equals(k))))
                node = p;
            else if ((e = p.next) != null) {
                if (p instanceof TreeNode)
                    node = ((TreeNode<K, V>)p).getTreeNode(hash, key);
                else {
                    do {
                        if (e.hash == hash &&
                                ((k = e.key) == key ||
                                        (key != null && key.equals(k)))) {
                            node = e;
                            break;
                        }
                        p = e;
                    } while ((e = e.next) != null);
                }
            }
            if (node != null && (!matchValue || (v = node.value) == value ||
                    (value != null && value.equals(v)))) {
                if (node instanceof TreeNode)
                    ((TreeNode<K, V>)node).removeTreeNode(this, tab, movable);
                else if (node == p)
                    tab[index] = node.next;
                else
                    p.next = node.next;
                ++modCount;
                --size;
                afterNodeRemoval(node);
                return node;
            }
        }
        return null;
    }

    /**
     * Removes all of the mappings from this map.
     * The map will be empty after this call returns.
     */
    public void clear() {
        Node<K, V>[] tab;
        modCount++;
        if ((tab = table) != null && size > 0) {
            size = 0;
            for (int i = 0; i < tab.length; ++i)
                tab[i] = null;
        }
    }

    /**
     * Returns {@code true} if this map maps one or more keys to the
     * specified value.
     *
     * @param value value whose presence in this map is to be tested
     * @return {@code true} if this map maps one or more keys to the
     *         specified value
     */
    public boolean containsValue(Object value) {
        Node<K, V>[] tab; V v;
        if ((tab = table) != null && size > 0) {
            for (Node<K, V> e : tab) {
                for (; e != null; e = e.next) {
                    if ((v = e.value) == value ||
                            (value != null && value.equals(v)))
                        return true;
                }
            }
        }
        return false;
    }

    /**
     * Returns a {@link Set} view of the keys contained in this map.
     * The set is backed by the map, so changes to the map are
     * reflected in the set, and vice-versa.  If the map is modified
     * while an iteration over the set is in progress (except through
     * the iterator's own {@code remove} operation), the results of
     * the iteration are undefined.  The set supports element removal, 
     * which removes the corresponding mapping from the map, via the
     * {@code Iterator.remove}, {@code Set.remove}, 
     * {@code removeAll}, {@code retainAll}, and {@code clear}
     * operations.  It does not support the {@code add} or {@code addAll}
     * operations.
     *
     * @return a set view of the keys contained in this map
     */
    public Set<K> keySet() {
        Set<K> ks = keySet;
        if (ks == null) {
            ks = new KeySet();
            keySet = ks;
        }
        return ks;
    }

    final class KeySet extends AbstractSet<K> {
        public final int size()                 { return size; }
        public final void clear()               { HashMap.this.clear(); }
        public final Iterator<K> iterator()     { return new KeyIterator(); }
        public final boolean contains(Object o) { return containsKey(o); }
        public final boolean remove(Object key) {
            return removeNode(hash(key), key, null, false, true) != null;
        }
        public final Spliterator<K> spliterator() {
            return new KeySpliterator<>(HashMap.this, 0, -1, 0, 0);
        }
        public final void forEach(Consumer<? super K> action) {
            Node<K, V>[] tab;
            if (action == null)
                throw new NullPointerException();
            if (size > 0 && (tab = table) != null) {
                int mc = modCount;
                for (Node<K, V> e : tab) {
                    for (; e != null; e = e.next)
                        action.accept(e.key);
                }
                if (modCount != mc)
                    throw new ConcurrentModificationException();
            }
        }
    }

    /**
     * Returns a {@link Collection} view of the values contained in this map.
     * The collection is backed by the map, so changes to the map are
     * reflected in the collection, and vice-versa.  If the map is
     * modified while an iteration over the collection is in progress
     * (except through the iterator's own {@code remove} operation), 
     * the results of the iteration are undefined.  The collection
     * supports element removal, which removes the corresponding
     * mapping from the map, via the {@code Iterator.remove}, 
     * {@code Collection.remove}, {@code removeAll}, 
     * {@code retainAll} and {@code clear} operations.  It does not
     * support the {@code add} or {@code addAll} operations.
     *
     * @return a view of the values contained in this map
     */
    public Collection<V> values() {
        Collection<V> vs = values;
        if (vs == null) {
            vs = new Values();
            values = vs;
        }
        return vs;
    }

    final class Values extends AbstractCollection<V> {
        public final int size()                 { return size; }
        public final void clear()               { HashMap.this.clear(); }
        public final Iterator<V> iterator()     { return new ValueIterator(); }
        public final boolean contains(Object o) { return containsValue(o); }
        public final Spliterator<V> spliterator() {
            return new ValueSpliterator<>(HashMap.this, 0, -1, 0, 0);
        }
        public final void forEach(Consumer<? super V> action) {
            Node<K, V>[] tab;
            if (action == null)
                throw new NullPointerException();
            if (size > 0 && (tab = table) != null) {
                int mc = modCount;
                for (Node<K, V> e : tab) {
                    for (; e != null; e = e.next)
                        action.accept(e.value);
                }
                if (modCount != mc)
                    throw new ConcurrentModificationException();
            }
        }
    }

    /**
     * Returns a {@link Set} view of the mappings contained in this map.
     * The set is backed by the map, so changes to the map are
     * reflected in the set, and vice-versa.  If the map is modified
     * while an iteration over the set is in progress (except through
     * the iterator's own {@code remove} operation, or through the
     * {@code setValue} operation on a map entry returned by the
     * iterator) the results of the iteration are undefined.  The set
     * supports element removal, which removes the corresponding
     * mapping from the map, via the {@code Iterator.remove}, 
     * {@code Set.remove}, {@code removeAll}, {@code retainAll} and
     * {@code clear} operations.  It does not support the
     * {@code add} or {@code addAll} operations.
     *
     * @return a set view of the mappings contained in this map
     */
    public Set<Map.Entry<K, V>> entrySet() {
        Set<Map.Entry<K, V>> es;
        return (es = entrySet) == null ? (entrySet = new EntrySet()) : es;
    }

    final class EntrySet extends AbstractSet<Map.Entry<K, V>> {
        public final int size()                 { return size; }
        public final void clear()               { HashMap.this.clear(); }
        public final Iterator<Map.Entry<K, V>> iterator() {
            return new EntryIterator();
        }
        public final boolean contains(Object o) {
            if (!(o instanceof Map.Entry))
                return false;
            Map.Entry<?, ?> e = (Map.Entry<?, ?>) o;
            Object key = e.getKey();
            Node<K, V> candidate = getNode(hash(key), key);
            return candidate != null && candidate.equals(e);
        }
        public final boolean remove(Object o) {
            if (o instanceof Map.Entry) {
                Map.Entry<?, ?> e = (Map.Entry<?, ?>) o;
                Object key = e.getKey();
                Object value = e.getValue();
                return removeNode(hash(key), key, value, true, true) != null;
            }
            return false;
        }
        public final Spliterator<Map.Entry<K, V>> spliterator() {
            return new EntrySpliterator<>(HashMap.this, 0, -1, 0, 0);
        }
        public final void forEach(Consumer<? super Map.Entry<K, V>> action) {
            Node<K, V>[] tab;
            if (action == null)
                throw new NullPointerException();
            if (size > 0 && (tab = table) != null) {
                int mc = modCount;
                for (Node<K, V> e : tab) {
                    for (; e != null; e = e.next)
                        action.accept(e);
                }
                if (modCount != mc)
                    throw new ConcurrentModificationException();
            }
        }
    }

    // Overrides of JDK8 Map extension methods

    @Override
    public V getOrDefault(Object key, V defaultValue) {
        Node<K, V> e;
        return (e = getNode(hash(key), key)) == null ? defaultValue : e.value;
    }

    @Override
    public V putIfAbsent(K key, V value) {
        return putVal(hash(key), key, value, true, true);
    }

    @Override
    public boolean remove(Object key, Object value) {
        return removeNode(hash(key), key, value, true, true) != null;
    }

    @Override
    public boolean replace(K key, V oldValue, V newValue) {
        Node<K, V> e; V v;
        if ((e = getNode(hash(key), key)) != null &&
                ((v = e.value) == oldValue || (v != null && v.equals(oldValue)))) {
            e.value = newValue;
            afterNodeAccess(e);
            return true;
        }
        return false;
    }

    @Override
    public V replace(K key, V value) {
        Node<K, V> e;
        if ((e = getNode(hash(key), key)) != null) {
            V oldValue = e.value;
            e.value = value;
            afterNodeAccess(e);
            return oldValue;
        }
        return null;
    }

    /**
     * {@inheritDoc}
     *
     * <p>This method will, on a best-effort basis, throw a
     * {@link ConcurrentModificationException} if it is detected that the
     * mapping function modifies this map during computation.
     *
     * @throws ConcurrentModificationException if it is detected that the
     * mapping function modified this map
     */
    @Override
    public V computeIfAbsent(K key, 
                             Function<? super K, ? extends V> mappingFunction) {
        if (mappingFunction == null)
            throw new NullPointerException();
        int hash = hash(key);
        Node<K, V>[] tab; Node<K, V> first; int n, i;
        int binCount = 0;
        TreeNode<K, V> t = null;
        Node<K, V> old = null;
        if (size > threshold || (tab = table) == null ||
                (n = tab.length) == 0)
            n = (tab = resize()).length;
        if ((first = tab[i = (n - 1) & hash]) != null) {
            if (first instanceof TreeNode)
                old = (t = (TreeNode<K, V>)first).getTreeNode(hash, key);
            else {
                Node<K, V> e = first; K k;
                do {
                    if (e.hash == hash &&
                            ((k = e.key) == key || (key != null && key.equals(k)))) {
                        old = e;
                        break;
                    }
                    ++binCount;
                } while ((e = e.next) != null);
            }
            V oldValue;
            if (old != null && (oldValue = old.value) != null) {
                afterNodeAccess(old);
                return oldValue;
            }
        }
        int mc = modCount;
        V v = mappingFunction.apply(key);
        if (mc != modCount) { throw new ConcurrentModificationException(); }
        if (v == null) {
            return null;
        } else if (old != null) {
            old.value = v;
            afterNodeAccess(old);
            return v;
        }
        else if (t != null)
            t.putTreeVal(this, tab, hash, key, v);
        else {
            tab[i] = newNode(hash, key, v, first);
            if (binCount >= TREEIFY_THRESHOLD - 1)
                treeifyBin(tab, hash);
        }
        modCount = mc + 1;
        ++size;
        afterNodeInsertion(true);
        return v;
    }

    /**
     * {@inheritDoc}
     *
     * <p>This method will, on a best-effort basis, throw a
     * {@link ConcurrentModificationException} if it is detected that the
     * remapping function modifies this map during computation.
     *
     * @throws ConcurrentModificationException if it is detected that the
     * remapping function modified this map
     */
    @Override
    public V computeIfPresent(K key, 
                              BiFunction<? super K, ? super V, ? extends V> remappingFunction) {
        if (remappingFunction == null)
            throw new NullPointerException();
        Node<K, V> e; V oldValue;
        int hash = hash(key);
        if ((e = getNode(hash, key)) != null &&
                (oldValue = e.value) != null) {
            int mc = modCount;
            V v = remappingFunction.apply(key, oldValue);
            if (mc != modCount) { throw new ConcurrentModificationException(); }
            if (v != null) {
                e.value = v;
                afterNodeAccess(e);
                return v;
            }
            else
                removeNode(hash, key, null, false, true);
        }
        return null;
    }

    /**
     * {@inheritDoc}
     *
     * <p>This method will, on a best-effort basis, throw a
     * {@link ConcurrentModificationException} if it is detected that the
     * remapping function modifies this map during computation.
     *
     * @throws ConcurrentModificationException if it is detected that the
     * remapping function modified this map
     */
    @Override
    public V compute(K key, 
                     BiFunction<? super K, ? super V, ? extends V> remappingFunction) {
        if (remappingFunction == null)
            throw new NullPointerException();
        int hash = hash(key);
        Node<K, V>[] tab; Node<K, V> first; int n, i;
        int binCount = 0;
        TreeNode<K, V> t = null;
        Node<K, V> old = null;
        if (size > threshold || (tab = table) == null ||
                (n = tab.length) == 0)
            n = (tab = resize()).length;
        if ((first = tab[i = (n - 1) & hash]) != null) {
            if (first instanceof TreeNode)
                old = (t = (TreeNode<K, V>)first).getTreeNode(hash, key);
            else {
                Node<K, V> e = first; K k;
                do {
                    if (e.hash == hash &&
                            ((k = e.key) == key || (key != null && key.equals(k)))) {
                        old = e;
                        break;
                    }
                    ++binCount;
                } while ((e = e.next) != null);
            }
        }
        V oldValue = (old == null) ? null : old.value;
        int mc = modCount;
        V v = remappingFunction.apply(key, oldValue);
        if (mc != modCount) { throw new ConcurrentModificationException(); }
        if (old != null) {
            if (v != null) {
                old.value = v;
                afterNodeAccess(old);
            }
            else
                removeNode(hash, key, null, false, true);
        }
        else if (v != null) {
            if (t != null)
                t.putTreeVal(this, tab, hash, key, v);
            else {
                tab[i] = newNode(hash, key, v, first);
                if (binCount >= TREEIFY_THRESHOLD - 1)
                    treeifyBin(tab, hash);
            }
            modCount = mc + 1;
            ++size;
            afterNodeInsertion(true);
        }
        return v;
    }

    /**
     * {@inheritDoc}
     *
     * <p>This method will, on a best-effort basis, throw a
     * {@link ConcurrentModificationException} if it is detected that the
     * remapping function modifies this map during computation.
     *
     * @throws ConcurrentModificationException if it is detected that the
     * remapping function modified this map
     */
    @Override
    public V merge(K key, V value, 
                   BiFunction<? super V, ? super V, ? extends V> remappingFunction) {
        if (value == null)
            throw new NullPointerException();
        if (remappingFunction == null)
            throw new NullPointerException();
        int hash = hash(key);
        Node<K, V>[] tab; Node<K, V> first; int n, i;
        int binCount = 0;
        TreeNode<K, V> t = null;
        Node<K, V> old = null;
        if (size > threshold || (tab = table) == null ||
                (n = tab.length) == 0)
            n = (tab = resize()).length;
        if ((first = tab[i = (n - 1) & hash]) != null) {
            if (first instanceof TreeNode)
                old = (t = (TreeNode<K, V>)first).getTreeNode(hash, key);
            else {
                Node<K, V> e = first; K k;
                do {
                    if (e.hash == hash &&
                            ((k = e.key) == key || (key != null && key.equals(k)))) {
                        old = e;
                        break;
                    }
                    ++binCount;
                } while ((e = e.next) != null);
            }
        }
        if (old != null) {
            V v;
            if (old.value != null) {
                int mc = modCount;
                v = remappingFunction.apply(old.value, value);
                if (mc != modCount) {
                    throw new ConcurrentModificationException();
                }
            } else {
                v = value;
            }
            if (v != null) {
                old.value = v;
                afterNodeAccess(old);
            }
            else
                removeNode(hash, key, null, false, true);
            return v;
        }
        if (value != null) {
            if (t != null)
                t.putTreeVal(this, tab, hash, key, value);
            else {
                tab[i] = newNode(hash, key, value, first);
                if (binCount >= TREEIFY_THRESHOLD - 1)
                    treeifyBin(tab, hash);
            }
            ++modCount;
            ++size;
            afterNodeInsertion(true);
        }
        return value;
    }

    @Override
    public void forEach(BiConsumer<? super K, ? super V> action) {
        Node<K, V>[] tab;
        if (action == null)
            throw new NullPointerException();
        if (size > 0 && (tab = table) != null) {
            int mc = modCount;
            for (Node<K, V> e : tab) {
                for (; e != null; e = e.next)
                    action.accept(e.key, e.value);
            }
            if (modCount != mc)
                throw new ConcurrentModificationException();
        }
    }

    @Override
    public void replaceAll(BiFunction<? super K, ? super V, ? extends V> function) {
        Node<K, V>[] tab;
        if (function == null)
            throw new NullPointerException();
        if (size > 0 && (tab = table) != null) {
            int mc = modCount;
            for (Node<K, V> e : tab) {
                for (; e != null; e = e.next) {
                    e.value = function.apply(e.key, e.value);
                }
            }
            if (modCount != mc)
                throw new ConcurrentModificationException();
        }
    }

    /* ------------------------------------------------------------ */
    // Cloning and serialization

    /**
     * Returns a shallow copy of this {@code HashMap} instance: the keys and
     * values themselves are not cloned.
     *
     * @return a shallow copy of this map
     */
    @SuppressWarnings("unchecked")
    @Override
    public Object clone() {
        HashMap<K, V> result;
        try {
            result = (HashMap<K, V>)super.clone();
        } catch (CloneNotSupportedException e) {
            // this shouldn't happen, since we are Cloneable
            throw new InternalError(e);
        }
        result.reinitialize();
        result.putMapEntries(this, false);
        return result;
    }

    // These methods are also used when serializing HashSets
    final float loadFactor() { return loadFactor; }
    final int capacity() {
        return (table != null) ? table.length :
                (threshold > 0) ? threshold :
                        DEFAULT_INITIAL_CAPACITY;
    }

    /**
     * Save the state of the {@code HashMap} instance to a stream (i.e., 
     * serialize it).
     *
     * @serialData The <i>capacity</i> of the HashMap (the length of the
     *             bucket array) is emitted (int), followed by the
     *             <i>size</i> (an int, the number of key-value
     *             mappings), followed by the key (Object) and value (Object)
     *             for each key-value mapping.  The key-value mappings are
     *             emitted in no particular order.
     */
    private void writeObject(java.io.ObjectOutputStream s)
            throws IOException {
        int buckets = capacity();
        // Write out the threshold, loadfactor, and any hidden stuff
        s.defaultWriteObject();
        s.writeInt(buckets);
        s.writeInt(size);
        internalWriteEntries(s);
    }

    /**
     * Reconstitute the {@code HashMap} instance from a stream (i.e., 
     * deserialize it).
     */
    private void readObject(java.io.ObjectInputStream s)
            throws IOException, ClassNotFoundException {
        // Read in the threshold (ignored), loadfactor, and any hidden stuff
        s.defaultReadObject();
        reinitialize();
        if (loadFactor <= 0 || Float.isNaN(loadFactor))
            throw new InvalidObjectException("Illegal load factor: " +
                    loadFactor);
        s.readInt();                // Read and ignore number of buckets
        int mappings = s.readInt(); // Read number of mappings (size)
        if (mappings < 0)
            throw new InvalidObjectException("Illegal mappings count: " +
                    mappings);
        else if (mappings > 0) { // (if zero, use defaults)
            // Size the table using given load factor only if within
            // range of 0.25...4.0
            float lf = Math.min(Math.max(0.25f, loadFactor), 4.0f);
            float fc = (float)mappings / lf + 1.0f;
            int cap = ((fc < DEFAULT_INITIAL_CAPACITY) ?
                    DEFAULT_INITIAL_CAPACITY :
                    (fc >= MAXIMUM_CAPACITY) ?
                            MAXIMUM_CAPACITY :
                            tableSizeFor((int)fc));
            float ft = (float)cap * lf;
            threshold = ((cap < MAXIMUM_CAPACITY && ft < MAXIMUM_CAPACITY) ?
                    (int)ft : Integer.MAX_VALUE);
            @SuppressWarnings({"rawtypes", "unchecked"})
            Node<K, V>[] tab = (Node<K, V>[])new Node[cap];
            table = tab;

            // Read the keys and values, and put the mappings in the HashMap
            for (int i = 0; i < mappings; i++) {
                @SuppressWarnings("unchecked")
                K key = (K) s.readObject();
                @SuppressWarnings("unchecked")
                V value = (V) s.readObject();
                putVal(hash(key), key, value, false, false);
            }
        }
    }

    /* ------------------------------------------------------------ */
    // iterators

    abstract class HashIterator {
        Node<K, V> next;        // next entry to return
        Node<K, V> current;     // current entry
        int expectedModCount;  // for fast-fail
        int index;             // current slot

        HashIterator() {
            expectedModCount = modCount;
            Node<K, V>[] t = table;
            current = next = null;
            index = 0;
            if (t != null && size > 0) { // advance to first entry
                do {} while (index < t.length && (next = t[index++]) == null);
            }
        }

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

        final Node<K, V> nextNode() {
            Node<K, V>[] t;
            Node<K, V> e = next;
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();
            if (e == null)
                throw new NoSuchElementException();
            if ((next = (current = e).next) == null && (t = table) != null) {
                do {} while (index < t.length && (next = t[index++]) == null);
            }
            return e;
        }

        public final void remove() {
            Node<K, V> p = current;
            if (p == null)
                throw new IllegalStateException();
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();
            current = null;
            removeNode(p.hash, p.key, null, false, false);
            expectedModCount = modCount;
        }
    }

    final class KeyIterator extends HashIterator
            implements Iterator<K> {
        public final K next() { return nextNode().key; }
    }

    final class ValueIterator extends HashIterator
            implements Iterator<V> {
        public final V next() { return nextNode().value; }
    }

    final class EntryIterator extends HashIterator
            implements Iterator<Map.Entry<K, V>> {
        public final Map.Entry<K, V> next() { return nextNode(); }
    }

    /* ------------------------------------------------------------ */
    // spliterators

    static class HashMapSpliterator<K, V> {
        final HashMap<K, V> map;
        Node<K, V> current;          // current node
        int index;                  // current index, modified on advance/split
        int fence;                  // one past last index
        int est;                    // size estimate
        int expectedModCount;       // for comodification checks

        HashMapSpliterator(HashMap<K, V> m, int origin, 
                           int fence, int est, 
                           int expectedModCount) {
            this.map = m;
            this.index = origin;
            this.fence = fence;
            this.est = est;
            this.expectedModCount = expectedModCount;
        }

        final int getFence() { // initialize fence and size on first use
            int hi;
            if ((hi = fence) < 0) {
                HashMap<K, V> m = map;
                est = m.size;
                expectedModCount = m.modCount;
                Node<K, V>[] tab = m.table;
                hi = fence = (tab == null) ? 0 : tab.length;
            }
            return hi;
        }

        public final long estimateSize() {
            getFence(); // force init
            return (long) est;
        }
    }

    static final class KeySpliterator<K, V>
            extends HashMapSpliterator<K, V>
            implements Spliterator<K> {
        KeySpliterator(HashMap<K, V> m, int origin, int fence, int est, 
                       int expectedModCount) {
            super(m, origin, fence, est, expectedModCount);
        }

        public KeySpliterator<K, V> trySplit() {
            int hi = getFence(), lo = index, mid = (lo + hi) >>> 1;
            return (lo >= mid || current != null) ? null :
                    new KeySpliterator<>(map, lo, index = mid, est >>>= 1, 
                            expectedModCount);
        }

        public void forEachRemaining(Consumer<? super K> action) {
            int i, hi, mc;
            if (action == null)
                throw new NullPointerException();
            HashMap<K, V> m = map;
            Node<K, V>[] tab = m.table;
            if ((hi = fence) < 0) {
                mc = expectedModCount = m.modCount;
                hi = fence = (tab == null) ? 0 : tab.length;
            }
            else
                mc = expectedModCount;
            if (tab != null && tab.length >= hi &&
                    (i = index) >= 0 && (i < (index = hi) || current != null)) {
                Node<K, V> p = current;
                current = null;
                do {
                    if (p == null)
                        p = tab[i++];
                    else {
                        action.accept(p.key);
                        p = p.next;
                    }
                } while (p != null || i < hi);
                if (m.modCount != mc)
                    throw new ConcurrentModificationException();
            }
        }

        public boolean tryAdvance(Consumer<? super K> action) {
            int hi;
            if (action == null)
                throw new NullPointerException();
            Node<K, V>[] tab = map.table;
            if (tab != null && tab.length >= (hi = getFence()) && index >= 0) {
                while (current != null || index < hi) {
                    if (current == null)
                        current = tab[index++];
                    else {
                        K k = current.key;
                        current = current.next;
                        action.accept(k);
                        if (map.modCount != expectedModCount)
                            throw new ConcurrentModificationException();
                        return true;
                    }
                }
            }
            return false;
        }

        public int characteristics() {
            return (fence < 0 || est == map.size ? Spliterator.SIZED : 0) |
                    Spliterator.DISTINCT;
        }
    }

    static final class ValueSpliterator<K, V>
            extends HashMapSpliterator<K, V>
            implements Spliterator<V> {
        ValueSpliterator(HashMap<K, V> m, int origin, int fence, int est, 
                         int expectedModCount) {
            super(m, origin, fence, est, expectedModCount);
        }

        public ValueSpliterator<K, V> trySplit() {
            int hi = getFence(), lo = index, mid = (lo + hi) >>> 1;
            return (lo >= mid || current != null) ? null :
                    new ValueSpliterator<>(map, lo, index = mid, est >>>= 1, 
                            expectedModCount);
        }

        public void forEachRemaining(Consumer<? super V> action) {
            int i, hi, mc;
            if (action == null)
                throw new NullPointerException();
            HashMap<K, V> m = map;
            Node<K, V>[] tab = m.table;
            if ((hi = fence) < 0) {
                mc = expectedModCount = m.modCount;
                hi = fence = (tab == null) ? 0 : tab.length;
            }
            else
                mc = expectedModCount;
            if (tab != null && tab.length >= hi &&
                    (i = index) >= 0 && (i < (index = hi) || current != null)) {
                Node<K, V> p = current;
                current = null;
                do {
                    if (p == null)
                        p = tab[i++];
                    else {
                        action.accept(p.value);
                        p = p.next;
                    }
                } while (p != null || i < hi);
                if (m.modCount != mc)
                    throw new ConcurrentModificationException();
            }
        }

        public boolean tryAdvance(Consumer<? super V> action) {
            int hi;
            if (action == null)
                throw new NullPointerException();
            Node<K, V>[] tab = map.table;
            if (tab != null && tab.length >= (hi = getFence()) && index >= 0) {
                while (current != null || index < hi) {
                    if (current == null)
                        current = tab[index++];
                    else {
                        V v = current.value;
                        current = current.next;
                        action.accept(v);
                        if (map.modCount != expectedModCount)
                            throw new ConcurrentModificationException();
                        return true;
                    }
                }
            }
            return false;
        }

        public int characteristics() {
            return (fence < 0 || est == map.size ? Spliterator.SIZED : 0);
        }
    }

    static final class EntrySpliterator<K, V>
            extends HashMapSpliterator<K, V>
            implements Spliterator<Map.Entry<K, V>> {
        EntrySpliterator(HashMap<K, V> m, int origin, int fence, int est, 
                         int expectedModCount) {
            super(m, origin, fence, est, expectedModCount);
        }

        public EntrySpliterator<K, V> trySplit() {
            int hi = getFence(), lo = index, mid = (lo + hi) >>> 1;
            return (lo >= mid || current != null) ? null :
                    new EntrySpliterator<>(map, lo, index = mid, est >>>= 1, 
                            expectedModCount);
        }

        public void forEachRemaining(Consumer<? super Map.Entry<K, V>> action) {
            int i, hi, mc;
            if (action == null)
                throw new NullPointerException();
            HashMap<K, V> m = map;
            Node<K, V>[] tab = m.table;
            if ((hi = fence) < 0) {
                mc = expectedModCount = m.modCount;
                hi = fence = (tab == null) ? 0 : tab.length;
            }
            else
                mc = expectedModCount;
            if (tab != null && tab.length >= hi &&
                    (i = index) >= 0 && (i < (index = hi) || current != null)) {
                Node<K, V> p = current;
                current = null;
                do {
                    if (p == null)
                        p = tab[i++];
                    else {
                        action.accept(p);
                        p = p.next;
                    }
                } while (p != null || i < hi);
                if (m.modCount != mc)
                    throw new ConcurrentModificationException();
            }
        }

        public boolean tryAdvance(Consumer<? super Map.Entry<K, V>> action) {
            int hi;
            if (action == null)
                throw new NullPointerException();
            Node<K, V>[] tab = map.table;
            if (tab != null && tab.length >= (hi = getFence()) && index >= 0) {
                while (current != null || index < hi) {
                    if (current == null)
                        current = tab[index++];
                    else {
                        Node<K, V> e = current;
                        current = current.next;
                        action.accept(e);
                        if (map.modCount != expectedModCount)
                            throw new ConcurrentModificationException();
                        return true;
                    }
                }
            }
            return false;
        }

        public int characteristics() {
            return (fence < 0 || est == map.size ? Spliterator.SIZED : 0) |
                    Spliterator.DISTINCT;
        }
    }

    /* ------------------------------------------------------------ */
    // LinkedHashMap support


    /*
     * The following package-protected methods are designed to be
     * overridden by LinkedHashMap, but not by any other subclass.
     * Nearly all other internal methods are also package-protected
     * but are declared final, so can be used by LinkedHashMap, view
     * classes, and HashSet.
     */

    // Create a regular (non-tree) node
    Node<K, V> newNode(int hash, K key, V value, Node<K, V> next) {
        return new Node<>(hash, key, value, next);
    }

    // For conversion from TreeNodes to plain nodes
    Node<K, V> replacementNode(Node<K, V> p, Node<K, V> next) {
        return new Node<>(p.hash, p.key, p.value, next);
    }

    // Create a tree bin node
    TreeNode<K, V> newTreeNode(int hash, K key, V value, Node<K, V> next) {
        return new TreeNode<>(hash, key, value, next);
    }

    // For treeifyBin
    TreeNode<K, V> replacementTreeNode(Node<K, V> p, Node<K, V> next) {
        return new TreeNode<>(p.hash, p.key, p.value, next);
    }

    /**
     * Reset to initial default state.  Called by clone and readObject.
     */
    void reinitialize() {
        table = null;
        entrySet = null;
        keySet = null;
        values = null;
        modCount = 0;
        threshold = 0;
        size = 0;
    }

    // Callbacks to allow LinkedHashMap post-actions
    void afterNodeAccess(Node<K, V> p) { }
    void afterNodeInsertion(boolean evict) { }
    void afterNodeRemoval(Node<K, V> p) { }

    // Called only from writeObject, to ensure compatible ordering.
    void internalWriteEntries(java.io.ObjectOutputStream s) throws IOException {
        Node<K, V>[] tab;
        if (size > 0 && (tab = table) != null) {
            for (Node<K, V> e : tab) {
                for (; e != null; e = e.next) {
                    s.writeObject(e.key);
                    s.writeObject(e.value);
                }
            }
        }
    }

    /* ------------------------------------------------------------ */
    // Tree bins

    /**
     * Entry for Tree bins. Extends LinkedHashMap.Entry (which in turn
     * extends Node) so can be used as extension of either regular or
     * linked node.
     */
    static final class TreeNode<K, V> extends LinkedHashMap.Entry<K, V> {
        TreeNode<K, V> parent;  // red-black tree links
        TreeNode<K, V> left;
        TreeNode<K, V> right;
        TreeNode<K, V> prev;    // needed to unlink next upon deletion
        boolean red;
        TreeNode(int hash, K key, V val, Node<K, V> next) {
            super(hash, key, val, next);
        }

        /**
         * Returns root of tree containing this node.
         */
        final TreeNode<K, V> root() {
            for (TreeNode<K, V> r = this, p;;) {
                if ((p = r.parent) == null)
                    return r;
                r = p;
            }
        }

        /**
         * Ensures that the given root is the first node of its bin.
         */
        static <K, V> void moveRootToFront(Node<K, V>[] tab, TreeNode<K, V> root) {
            int n;
            if (root != null && tab != null && (n = tab.length) > 0) {
                int index = (n - 1) & root.hash;
                TreeNode<K, V> first = (TreeNode<K, V>)tab[index];
                if (root != first) {
                    Node<K, V> rn;
                    tab[index] = root;
                    TreeNode<K, V> rp = root.prev;
                    if ((rn = root.next) != null)
                        ((TreeNode<K, V>)rn).prev = rp;
                    if (rp != null)
                        rp.next = rn;
                    if (first != null)
                        first.prev = root;
                    root.next = first;
                    root.prev = null;
                }
                assert checkInvariants(root);
            }
        }

        /**
         * Finds the node starting at root p with the given hash and key.
         * The kc argument caches comparableClassFor(key) upon first use
         * comparing keys.
         */
        final TreeNode<K, V> find(int h, Object k, Class<?> kc) {
            TreeNode<K, V> p = this;
            do {
                int ph, dir; K pk;
                TreeNode<K, V> pl = p.left, pr = p.right, q;
                if ((ph = p.hash) > h)
                    p = pl;
                else if (ph < h)
                    p = pr;
                else if ((pk = p.key) == k || (k != null && k.equals(pk)))
                    return p;
                else if (pl == null)
                    p = pr;
                else if (pr == null)
                    p = pl;
                else if ((kc != null ||
                        (kc = comparableClassFor(k)) != null) &&
                        (dir = compareComparables(kc, k, pk)) != 0)
                    p = (dir < 0) ? pl : pr;
                else if ((q = pr.find(h, k, kc)) != null)
                    return q;
                else
                    p = pl;
            } while (p != null);
            return null;
        }

        /**
         * Calls find for root node.
         */
        final TreeNode<K, V> getTreeNode(int h, Object k) {
            return ((parent != null) ? root() : this).find(h, k, null);
        }

        /**
         * Tie-breaking utility for ordering insertions when equal
         * hashCodes and non-comparable. We don't require a total
         * order, just a consistent insertion rule to maintain
         * equivalence across rebalancings. Tie-breaking further than
         * necessary simplifies testing a bit.
         */
        static int tieBreakOrder(Object a, Object b) {
            int d;
            if (a == null || b == null ||
                    (d = a.getClass().getName().
                            compareTo(b.getClass().getName())) == 0)
                d = (System.identityHashCode(a) <= System.identityHashCode(b) ?
                        -1 : 1);
            return d;
        }

        /**
         * Forms tree of the nodes linked from this node.
         * @return root of tree
         */
        final void treeify(Node<K, V>[] tab) {
            TreeNode<K, V> root = null;
            for (TreeNode<K, V> x = this, next; x != null; x = next) {
                next = (TreeNode<K, V>)x.next;
                x.left = x.right = null;
                if (root == null) {
                    x.parent = null;
                    x.red = false;
                    root = x;
                }
                else {
                    K k = x.key;
                    int h = x.hash;
                    Class<?> kc = null;
                    for (TreeNode<K, V> p = root;;) {
                        int dir, ph;
                        K pk = p.key;
                        if ((ph = p.hash) > h)
                            dir = -1;
                        else if (ph < h)
                            dir = 1;
                        else if ((kc == null &&
                                (kc = comparableClassFor(k)) == null) ||
                                (dir = compareComparables(kc, k, pk)) == 0)
                            dir = tieBreakOrder(k, pk);

                        TreeNode<K, V> xp = p;
                        if ((p = (dir <= 0) ? p.left : p.right) == null) {
                            x.parent = xp;
                            if (dir <= 0)
                                xp.left = x;
                            else
                                xp.right = x;
                            root = balanceInsertion(root, x);
                            break;
                        }
                    }
                }
            }
            moveRootToFront(tab, root);
        }

        /**
         * Returns a list of non-TreeNodes replacing those linked from
         * this node.
         */
        final Node<K, V> untreeify(HashMap<K, V> map) {
            Node<K, V> hd = null, tl = null;
            for (Node<K, V> q = this; q != null; q = q.next) {
                Node<K, V> p = map.replacementNode(q, null);
                if (tl == null)
                    hd = p;
                else
                    tl.next = p;
                tl = p;
            }
            return hd;
        }

        /**
         * Tree version of putVal.
         */
        final TreeNode<K, V> putTreeVal(HashMap<K, V> map, Node<K, V>[] tab, 
                                       int h, K k, V v) {
            Class<?> kc = null;
            boolean searched = false;
            TreeNode<K, V> root = (parent != null) ? root() : this;
            for (TreeNode<K, V> p = root;;) {
                int dir, ph; K pk;
                if ((ph = p.hash) > h)
                    dir = -1;
                else if (ph < h)
                    dir = 1;
                else if ((pk = p.key) == k || (k != null && k.equals(pk)))
                    return p;
                else if ((kc == null &&
                        (kc = comparableClassFor(k)) == null) ||
                        (dir = compareComparables(kc, k, pk)) == 0) {
                    if (!searched) {
                        TreeNode<K, V> q, ch;
                        searched = true;
                        if (((ch = p.left) != null &&
                                (q = ch.find(h, k, kc)) != null) ||
                                ((ch = p.right) != null &&
                                        (q = ch.find(h, k, kc)) != null))
                            return q;
                    }
                    dir = tieBreakOrder(k, pk);
                }

                TreeNode<K, V> xp = p;
                if ((p = (dir <= 0) ? p.left : p.right) == null) {
                    Node<K, V> xpn = xp.next;
                    TreeNode<K, V> x = map.newTreeNode(h, k, v, xpn);
                    if (dir <= 0)
                        xp.left = x;
                    else
                        xp.right = x;
                    xp.next = x;
                    x.parent = x.prev = xp;
                    if (xpn != null)
                        ((TreeNode<K, V>)xpn).prev = x;
                    moveRootToFront(tab, balanceInsertion(root, x));
                    return null;
                }
            }
        }

        /**
         * Removes the given node, that must be present before this call.
         * This is messier than typical red-black deletion code because we
         * cannot swap the contents of an interior node with a leaf
         * successor that is pinned by "next" pointers that are accessible
         * independently during traversal. So instead we swap the tree
         * linkages. If the current tree appears to have too few nodes, 
         * the bin is converted back to a plain bin. (The test triggers
         * somewhere between 2 and 6 nodes, depending on tree structure).
         */
        final void removeTreeNode(HashMap<K, V> map, Node<K, V>[] tab, 
                                  boolean movable) {
            int n;
            if (tab == null || (n = tab.length) == 0)
                return;
            int index = (n - 1) & hash;
            TreeNode<K, V> first = (TreeNode<K, V>)tab[index], root = first, rl;
            TreeNode<K, V> succ = (TreeNode<K, V>)next, pred = prev;
            if (pred == null)
                tab[index] = first = succ;
            else
                pred.next = succ;
            if (succ != null)
                succ.prev = pred;
            if (first == null)
                return;
            if (root.parent != null)
                root = root.root();
            if (root == null || root.right == null ||
                    (rl = root.left) == null || rl.left == null) {
                tab[index] = first.untreeify(map);  // too small
                return;
            }
            TreeNode<K, V> p = this, pl = left, pr = right, replacement;
            if (pl != null && pr != null) {
                TreeNode<K, V> s = pr, sl;
                while ((sl = s.left) != null) // find successor
                    s = sl;
                boolean c = s.red; s.red = p.red; p.red = c; // swap colors
                TreeNode<K, V> sr = s.right;
                TreeNode<K, V> pp = p.parent;
                if (s == pr) { // p was s's direct parent
                    p.parent = s;
                    s.right = p;
                }
                else {
                    TreeNode<K, V> sp = s.parent;
                    if ((p.parent = sp) != null) {
                        if (s == sp.left)
                            sp.left = p;
                        else
                            sp.right = p;
                    }
                    if ((s.right = pr) != null)
                        pr.parent = s;
                }
                p.left = null;
                if ((p.right = sr) != null)
                    sr.parent = p;
                if ((s.left = pl) != null)
                    pl.parent = s;
                if ((s.parent = pp) == null)
                    root = s;
                else if (p == pp.left)
                    pp.left = s;
                else
                    pp.right = s;
                if (sr != null)
                    replacement = sr;
                else
                    replacement = p;
            }
            else if (pl != null)
                replacement = pl;
            else if (pr != null)
                replacement = pr;
            else
                replacement = p;
            if (replacement != p) {
                TreeNode<K, V> pp = replacement.parent = p.parent;
                if (pp == null)
                    root = replacement;
                else if (p == pp.left)
                    pp.left = replacement;
                else
                    pp.right = replacement;
                p.left = p.right = p.parent = null;
            }

            TreeNode<K, V> r = p.red ? root : balanceDeletion(root, replacement);

            if (replacement == p) {  // detach
                TreeNode<K, V> pp = p.parent;
                p.parent = null;
                if (pp != null) {
                    if (p == pp.left)
                        pp.left = null;
                    else if (p == pp.right)
                        pp.right = null;
                }
            }
            if (movable)
                moveRootToFront(tab, r);
        }

        /**
         * Splits nodes in a tree bin into lower and upper tree bins, 
         * or untreeifies if now too small. Called only from resize;
         * see above discussion about split bits and indices.
         *
         * @param map the map
         * @param tab the table for recording bin heads
         * @param index the index of the table being split
         * @param bit the bit of hash to split on
         */
        final void split(HashMap<K, V> map, Node<K, V>[] tab, int index, int bit) {
            TreeNode<K, V> b = this;
            // Relink into lo and hi lists, preserving order
            TreeNode<K, V> loHead = null, loTail = null;
            TreeNode<K, V> hiHead = null, hiTail = null;
            int lc = 0, hc = 0;
            for (TreeNode<K, V> e = b, next; e != null; e = next) {
                next = (TreeNode<K, V>)e.next;
                e.next = null;
                if ((e.hash & bit) == 0) {
                    if ((e.prev = loTail) == null)
                        loHead = e;
                    else
                        loTail.next = e;
                    loTail = e;
                    ++lc;
                }
                else {
                    if ((e.prev = hiTail) == null)
                        hiHead = e;
                    else
                        hiTail.next = e;
                    hiTail = e;
                    ++hc;
                }
            }

            if (loHead != null) {
                if (lc <= UNTREEIFY_THRESHOLD)
                    tab[index] = loHead.untreeify(map);
                else {
                    tab[index] = loHead;
                    if (hiHead != null) // (else is already treeified)
                        loHead.treeify(tab);
                }
            }
            if (hiHead != null) {
                if (hc <= UNTREEIFY_THRESHOLD)
                    tab[index + bit] = hiHead.untreeify(map);
                else {
                    tab[index + bit] = hiHead;
                    if (loHead != null)
                        hiHead.treeify(tab);
                }
            }
        }

        /* ------------------------------------------------------------ */
        // Red-black tree methods, all adapted from CLR

        static <K, V> TreeNode<K, V> rotateLeft(TreeNode<K, V> root, 
                                              TreeNode<K, V> p) {
            TreeNode<K, V> r, pp, rl;
            if (p != null && (r = p.right) != null) {
                if ((rl = p.right = r.left) != null)
                    rl.parent = p;
                if ((pp = r.parent = p.parent) == null)
                    (root = r).red = false;
                else if (pp.left == p)
                    pp.left = r;
                else
                    pp.right = r;
                r.left = p;
                p.parent = r;
            }
            return root;
        }

        static <K, V> TreeNode<K, V> rotateRight(TreeNode<K, V> root, 
                                               TreeNode<K, V> p) {
            TreeNode<K, V> l, pp, lr;
            if (p != null && (l = p.left) != null) {
                if ((lr = p.left = l.right) != null)
                    lr.parent = p;
                if ((pp = l.parent = p.parent) == null)
                    (root = l).red = false;
                else if (pp.right == p)
                    pp.right = l;
                else
                    pp.left = l;
                l.right = p;
                p.parent = l;
            }
            return root;
        }

        static <K, V> TreeNode<K, V> balanceInsertion(TreeNode<K, V> root, 
                                                    TreeNode<K, V> x) {
            x.red = true;
            for (TreeNode<K, V> xp, xpp, xppl, xppr;;) {
                if ((xp = x.parent) == null) {
                    x.red = false;
                    return x;
                }
                else if (!xp.red || (xpp = xp.parent) == null)
                    return root;
                if (xp == (xppl = xpp.left)) {
                    if ((xppr = xpp.right) != null && xppr.red) {
                        xppr.red = false;
                        xp.red = false;
                        xpp.red = true;
                        x = xpp;
                    }
                    else {
                        if (x == xp.right) {
                            root = rotateLeft(root, x = xp);
                            xpp = (xp = x.parent) == null ? null : xp.parent;
                        }
                        if (xp != null) {
                            xp.red = false;
                            if (xpp != null) {
                                xpp.red = true;
                                root = rotateRight(root, xpp);
                            }
                        }
                    }
                }
                else {
                    if (xppl != null && xppl.red) {
                        xppl.red = false;
                        xp.red = false;
                        xpp.red = true;
                        x = xpp;
                    }
                    else {
                        if (x == xp.left) {
                            root = rotateRight(root, x = xp);
                            xpp = (xp = x.parent) == null ? null : xp.parent;
                        }
                        if (xp != null) {
                            xp.red = false;
                            if (xpp != null) {
                                xpp.red = true;
                                root = rotateLeft(root, xpp);
                            }
                        }
                    }
                }
            }
        }

        static <K, V> TreeNode<K, V> balanceDeletion(TreeNode<K, V> root, 
                                                   TreeNode<K, V> x) {
            for (TreeNode<K, V> xp, xpl, xpr;;)  {
                if (x == null || x == root)
                    return root;
                else if ((xp = x.parent) == null) {
                    x.red = false;
                    return x;
                }
                else if (x.red) {
                    x.red = false;
                    return root;
                }
                else if ((xpl = xp.left) == x) {
                    if ((xpr = xp.right) != null && xpr.red) {
                        xpr.red = false;
                        xp.red = true;
                        root = rotateLeft(root, xp);
                        xpr = (xp = x.parent) == null ? null : xp.right;
                    }
                    if (xpr == null)
                        x = xp;
                    else {
                        TreeNode<K, V> sl = xpr.left, sr = xpr.right;
                        if ((sr == null || !sr.red) &&
                                (sl == null || !sl.red)) {
                            xpr.red = true;
                            x = xp;
                        }
                        else {
                            if (sr == null || !sr.red) {
                                if (sl != null)
                                    sl.red = false;
                                xpr.red = true;
                                root = rotateRight(root, xpr);
                                xpr = (xp = x.parent) == null ?
                                        null : xp.right;
                            }
                            if (xpr != null) {
                                xpr.red = (xp == null) ? false : xp.red;
                                if ((sr = xpr.right) != null)
                                    sr.red = false;
                            }
                            if (xp != null) {
                                xp.red = false;
                                root = rotateLeft(root, xp);
                            }
                            x = root;
                        }
                    }
                }
                else { // symmetric
                    if (xpl != null && xpl.red) {
                        xpl.red = false;
                        xp.red = true;
                        root = rotateRight(root, xp);
                        xpl = (xp = x.parent) == null ? null : xp.left;
                    }
                    if (xpl == null)
                        x = xp;
                    else {
                        TreeNode<K, V> sl = xpl.left, sr = xpl.right;
                        if ((sl == null || !sl.red) &&
                                (sr == null || !sr.red)) {
                            xpl.red = true;
                            x = xp;
                        }
                        else {
                            if (sl == null || !sl.red) {
                                if (sr != null)
                                    sr.red = false;
                                xpl.red = true;
                                root = rotateLeft(root, xpl);
                                xpl = (xp = x.parent) == null ?
                                        null : xp.left;
                            }
                            if (xpl != null) {
                                xpl.red = (xp == null) ? false : xp.red;
                                if ((sl = xpl.left) != null)
                                    sl.red = false;
                            }
                            if (xp != null) {
                                xp.red = false;
                                root = rotateRight(root, xp);
                            }
                            x = root;
                        }
                    }
                }
            }
        }

        /**
         * Recursive invariant check
         */
        static <K, V> boolean checkInvariants(TreeNode<K, V> t) {
            TreeNode<K, V> tp = t.parent, tl = t.left, tr = t.right, 
                    tb = t.prev, tn = (TreeNode<K, V>)t.next;
            if (tb != null && tb.next != t)
                return false;
            if (tn != null && tn.prev != t)
                return false;
            if (tp != null && t != tp.left && t != tp.right)
                return false;
            if (tl != null && (tl.parent != t || tl.hash > t.hash))
                return false;
            if (tr != null && (tr.parent != t || tr.hash < t.hash))
                return false;
            if (t.red && tl != null && tl.red && tr != null && tr.red)
                return false;
            if (tl != null && !checkInvariants(tl))
                return false;
            if (tr != null && !checkInvariants(tr))
                return false;
            return true;
        }
    }

}

4. 泊松分布

是一种统计与概率学里常见到的离散概率分布.
以下连接内容仅供参考:
http://www.ruanyifeng.com/blog/2015/06/poisson-distribution.html
待继续研究

5. Todo

• 泊松分布
• 红黑树
• 再次阅读源码

6. Resource

• http://www.cnblogs.com/killbug/p/7679043.html
• http://www.cnblogs.com/leesf456/p/5242233.html
• https://blog.csdn.net/u011240877/article/details/53358305
• https://blog.csdn.net/u011642663/article/details/49853087