• HashMap分析


    1.HashMap简介

    HashMap基于哈希表的Map接口实现。是以key-value存储形式存在。线程不安全。key和value都可以为null,无序

    JDK1.8之前由数组+链表组成,数组是HashMap主体,链表则主要是为了解决哈希冲突(两个对象调用的hashCode方法计算的哈希码值一致导致计算的数组索引值相同)而存在的(“拉链法”解决冲突),JDK1.8之后,当链表长度大于阈值(或者红黑树的边界值,默认为8)并且当前数组的长度大于64时,此时此索引位置上的所有数据改为使用红黑树存储。加入红黑树可以使查询效率更高。

    补充:为了提高效率,将链表转换为红黑树前会判断,即使阈值大于8,但是数组长度小于64,此时并不会将链表变为红黑树,而是选择进行数组扩容。

    2.HashMap集合底层的数据结构

    JDK1.8之前,数组+链表

    JDK1.8之后,数组+链表+红黑树

    问题1:

    1、哈希表底层采用何种算法计算hash值?还有哪些算法可以计算出hash值?
    底层采用的key的hashCode方法的值结合数组长度进行无符号右移(>>>)、按位异或(^)计算hash值,按位与(&)计算出索引

    static final int hash(Object key) {
          int h;
          return (key == null) ? 0 : (h = key.hashCode()) ^ (h >>> 16);
     }
    //其中n为数组长度
    (n - 1) & hash

    还可以采用:平方取中法,取余数、伪随机数法

    2.当两个对象的hashCode相等时会怎么样?

    会产生哈希碰撞,通过调用equals方法比较key的内容是否相同,相同则替换旧的value,不然就连接到链表后面,链表长度超过阈值8转为红黑树。

    3.在不断的添加数据的过程中,会涉及到扩容问题,当超出临界值时扩容,默认的扩容方式为扩充为原来的2倍,并将原有的数据复制过来。

    4.1.8之后为什么引入红黑树,这样不是使结构更加复杂了吗?为什么阈值大于8转化成红黑树?

     

    说明:

    • size表示HashMap中K-V的实时数量,不是数组的长度
    • threshold(临界值)=capacity(容量)*loadFactor(加载因子)。这个值是当前已占用数组长度的最大值。size超过这个临界值就重新resize(扩容),扩容后的HashMap容量是之前容量的两倍

    3.HashMap继承关系

    public class HashMap<K,V> extends AbstractMap<K,V>
        implements Map<K,V>, Cloneable, Serializable {
    
        private static final long serialVersionUID = 362498820763181265L;
    public abstract class AbstractMap<K,V> implements Map<K,V> {
        /**
         * Sole constructor.  (For invocation by subclass constructors, typically
         * implicit.)
         */
        protected AbstractMap() {
        }

    4.HashMap集合类的成员

    4.1成员变量

    1、序列化版本号

    private static final long serialVersionUID = 362498820763181265L;

    2、集合的初始化容量(必须是2的n次幂)

      /**
         * The default initial capacity - MUST be a power of two.
         */
        static final int DEFAULT_INITIAL_CAPACITY = 1 << 4; // aka 16

    问题:为什么大小必须是2的n次幂?

    存储高效,尽量减少碰撞,在(length-1)&hash求索引的时候更均匀。

     

     

     问题:如果传入的容量默认不是2的幂,假如是10,会怎么样呢?

    底层通过一些列的右移和或运算,把给定值变成比它大的最小的2的次数值,比如给10变成16,给17变成32。

    //对传入容量进行右移位运算后进行或运算
    //一共进行5次或运算,可以将当前数字中二进制最高位1的右边全部变成1,最后+1后返回
    static final int tableSizeFor(int cap) {
            //这里-1的目的是使得找到的目标值大于或等于原值
            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;
        }

    完整例子:

     

     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);
        }

    3、默认的负载因子

    static final float DEFAULT_LOAD_FACTOR = 0.75f;

    4、集合最大容量

    static final int MAXIMUM_CAPACITY = 1 << 30;

    5、链表转红黑树的阈值

    static final int TREEIFY_THRESHOLD = 8;

    问题:为什么是8?

    TreeNode占用空间是普通Node的两倍,空间和时间的权衡,同时如果为8,log(8)=3小于链表的平均8/2=4

      /* 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)* /

    还有一种解释方式:

    6、红黑树转链表的阈值

    static final int UNTREEIFY_THRESHOLD = 6;

    7、链表转红黑树时数组的大小的阈值,即数组大小大于这个数字时,链表长度大于8才会转为红黑树

    static final int MIN_TREEIFY_CAPACITY = 64;

    8、table用来初始化数组(大小是2的n次幂)

    transient Node<K,V>[] table;

     9、用来存放缓存(遍历的时候使用)

    transient Set<Map.Entry<K,V>> entrySet;

    10、HashMap中存放元素的个数(重点)

    transient int size;

    11、记录HashMap的修改次数

    transient int modCount;

    12、临界值(如果存放元素大小大于该值,则进行扩容)

    int threshold;

    13、哈希表的加载因子(重点)

    final float loadFactor

    说明:

    loadFactor加载因子,可以表示HashMap的舒米程度,影响hash操作到同一个数组位置的概率,默认0.75,不建议修改

    4.2构造方法

     1、构造一个空的HashMap,默认初始容量(16)和默认负载因子(0.75)

     public HashMap() {
            this.loadFactor = DEFAULT_LOAD_FACTOR; // all other fields defaulted
        }

    2、构造一个具有指定的出是容来那个和默认负载因子(0.75)的HashMap

      public HashMap(int initialCapacity) {
            this(initialCapacity, DEFAULT_LOAD_FACTOR);
        }

    3、构造一个具有指定初始容量和负载因子的HashMap

       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;
            //根据初始值返回一个2的n次数字,赋给阈值,在put方法中会对此值进行重新运算
            this.threshold = tableSizeFor(initialCapacity);
        }

    4、包含另一个Map的构造函数

        public HashMap(Map<? extends K, ? extends V> m) {
            this.loadFactor = DEFAULT_LOAD_FACTOR;
            putMapEntries(m, false);
        }
        final void putMapEntries(Map<? extends K, ? extends V> m, boolean evict) {
            int s = m.size();
            if (s > 0) {
                if (table == null) { // pre-size
                    //+1的目的是获取更大的容量,减少数组的扩容次数
                    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);
                }
            }
        }

    4.3成员方法

    增加方法(put)

    1)先判断数组是否未初始化,如果没有初始化,则进行一次初始化操作(扩容),同时将数组大小赋给n

    2)找到具体的桶,并判断此位置是否有元素,如果没有元素,则创建一个Node直接插入

    3)如果出现冲突

    ​ 1)如果为红黑树节点,调用红黑树方法插入数据

    ​ 2)如果为普通节点,插入链表末尾,并且长度达到临界值时,将链表转为红黑树

    4)如果桶中存在重复的键,将该键替换新值value

    5)size大于阈值threshold,进行扩容

     /**
         * 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 <tt>key</tt>, or
         *         <tt>null</tt> if there was no mapping for <tt>key</tt>.
         *         (A <tt>null</tt> return can also indicate that the map
         *         previously associated <tt>null</tt> with <tt>key</tt>.)
         */
        public V put(K key, V value) {
            return putVal(hash(key), key, value, false, true);
        }

     

     /**
         * 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.
         */
        static final int hash(Object key) {
            int h;
            return (key == null) ? 0 : (h = key.hashCode()) ^ (h >>> 16);
        }

     

    final V putVal(int hash, K key, V value, boolean onlyIfAbsent,
                       boolean evict) {
            //初始化一个tab以及一个Node
            Node<K,V>[] tab; Node<K,V> p; int n, i;
            //此处才进行tab的初始化。tab为空或者数组大小为0,对数组进行初始化操作,并将数组大小赋给n
            if ((tab = table) == null || (n = tab.length) == 0)
                n = (tab = resize()).length;
            //通过hash与数组大小-1的与运算计算出所在桶位置的元素p,如果p为null,创建一个
            //新节点直接插入,如果出现冲突,进入分支判断
            if ((p = tab[i = (n - 1) & hash]) == null)
                tab[i] = newNode(hash, key, value, null);
            else {
                Node<K,V> e; K k;
                //如果插入的元素的hash值与p相等以及p的key与要插入的key相同,将p(原位置节点)赋给e;
                if (p.hash == hash &&
                    ((k = p.key) == key || (key != null && key.equals(k))))
                    e = p;
                //p为红黑树节点,则调用putTreeVal插入数据,如果为覆盖,则e为旧节点
                else if (p instanceof TreeNode)
                    e = ((TreeNode<K,V>)p).putTreeVal(this, tab, hash, key, value);
                else {
                    //链表节点
                    for (int binCount = 0; ; ++binCount) {
                        //找到链表的尾结点,此时e==null,p为链表的最后一个节点
                        if ((e = p.next) == null) {
                            //在末尾处创建一个节点赋给p.next,此时e仍为null
                            p.next = newNode(hash, key, value, null);
                            //如果找到当前节点时已经循环了7次,即该链表在插入元素大小为8,将链表转为红黑树
                            if (binCount >= TREEIFY_THRESHOLD - 1) // -1 for 1st
                                //链表转红黑树,传入tab数组以及该键的hash值(可计算出数组的具体索引)
                                treeifyBin(tab, hash);
                            break;
                        }
                        //如果找到了具有相同key的元素,也停止寻找
                        if (e.hash == hash &&
                            ((k = e.key) == key || (key != null && key.equals(k))))
                            break;
                        p = e;
                    }
                }
                //若此时e不为null,说明找到了一个具有相同key的值
                if (e != null) { // existing mapping for key
                    //保存一下旧节点的value值
                    V oldValue = e.value;
                    //是否要改变之前存在值(默认为false)或者之前存在的值为null,将value进行一个覆盖
                    if (!onlyIfAbsent || oldValue == null)
                        e.value = value;
                    //回调相关方法,HashMap该方法默认实现为空,LinkedHashMap在此会进行一些处理
                    afterNodeAccess(e);
                    //返回旧值,不会进行下面的修改次数以及元素个数增加操作
                    return oldValue;
                }
            }
            //记录下map的修改次数
            ++modCount;
            //如果元素个数大于了阈值,进行扩容操作
            if (++size > threshold)
                resize();
            afterNodeInsertion(evict);
            return null;
        }

     

     

     

    链表转红黑树(treeifyBin)

    //tab为数组名,hash为hash值
    if (binCount >= TREEIFY_THRESHOLD - 1) // -1 for 1st
                                treeifyBin(tab, hash);
                            break;
    /**
      * 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;
            //如果tab数组为空或者tab数组大小小于链表转红黑树的最小要求值,则进行扩容操作
            if (tab == null || (n = tab.length) < MIN_TREEIFY_CAPACITY)
                resize();
            //拿到当前要转换的桶的起始节点
            else if ((e = tab[index = (n - 1) & hash]) != null) {
                //初始化头结点和尾结点
                TreeNode<K,V> hd = null, tl = null;
                //循环将链表结点转化为红黑树结点
                do {
                    //利用链表结点来创建一个树结点
                    TreeNode<K,V> p = replacementTreeNode(e, null);
                    //如果tl为null,表示红黑树还没有结点,将p赋给头结点
                    if (tl == null)
                        hd = p;
                    //将p节点与尾结点相连
                    else {
                        p.prev = tl;
                        tl.next = p;
                    }
                    //更新尾节点
                    tl = p;
                } while ((e = e.next) != null);
                if ((tab[index] = hd) != null)
                    //将各个树结点转化为红黑树
                    hd.treeify(tab);
            }
        }

    扩容方法(resize)

     数组初始化以及数组元素个数大于阈值时进行扩容操作,一部分索引会增加原数组长度大小的长度(用到了高位1),一部分仍保持原索引(高位为0)

    举个例子:

     

     /**
         * 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.
         *
         * @return the table
         */
        final Node<K,V>[] resize() {
            //将旧数组进行保存
            Node<K,V>[] oldTab = table;
            //保存旧数组的长度
            int oldCap = (oldTab == null) ? 0 : oldTab.length;
            //保存旧数组的阈值
            int oldThr = threshold;
            //定义新的长度和阈值
            int newCap, newThr = 0;
            if (oldCap > 0) {
                //数组已经达到最大容量,直接返回
                if (oldCap >= MAXIMUM_CAPACITY) {
                    threshold = Integer.MAX_VALUE;
                    return oldTab;
                }
                //新数组长度为旧数组长度*2
                else if ((newCap = oldCap << 1) < MAXIMUM_CAPACITY &&
                         oldCap >= DEFAULT_INITIAL_CAPACITY)
                    //阈值同样*2
                    newThr = oldThr << 1; // double threshold
            }
            else if (oldThr > 0) // initial capacity was placed in threshold
                newCap = oldThr;
            else {
                // zero initial threshold signifies using defaults,默认的初始化操作
                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);
            }
            //将新的阈值赋给成员变量
            threshold = newThr;
            //创建一个新的数组,大小为newCap
            @SuppressWarnings({"rawtypes","unchecked"})
                Node<K,V>[] newTab = (Node<K,V>[])new Node[newCap];
            table = newTab;
            //将旧数组元素放入到新数组中
            if (oldTab != null) {
                for (int j = 0; j < oldCap; ++j) {
                    Node<K,V> e;
                    if ((e = oldTab[j]) != null) {
                        oldTab[j] = null;
                        //如果当前索引只有一个节点
                        if (e.next == null)
                            newTab[e.hash & (newCap - 1)] = e;
                        else if (e instanceof TreeNode)
                            ((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;

    删除方法(remove)

     /**
         * 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 <tt>key</tt>, or
         *         <tt>null</tt> if there was no mapping for <tt>key</tt>.
         *         (A <tt>null</tt> return can also indicate that the map
         *         previously associated <tt>null</tt> with <tt>key</tt>.)
         */
        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;
                //初始节点为要找的节点,赋值给node
                if (p.hash == hash &&
                    ((k = p.key) == key || (key != null && key.equals(k))))
                    node = p;
                //向下找节点
                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);
                    }
                }
                //删除操作
                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;
        }

    查找方法(get)

        /**
         * 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 &&
                (first = tab[(n - 1) & hash]) != null) {
                if (first.hash == hash && // always check first node
                    ((k = first.key) == key || (key != null && key.equals(k))))
                    return first;
                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;
        }

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

    遍历HashMap集合的几种方式

    1、分别遍历Key和Values

    for(String key:map.keySet()){
        System.out.println(key);
    }
    for(Object value:map.values()){
        System.out.println(value);
    }

    2、迭代器(增强for循环)

    Iterator<Map.Entry<String, Integer>> iterator = map.entrySet().iterator();
    while(iterator.hasNext()){
        Map.Entry<String, Integer> next = iterator.next();
        System.out.println(next.getKey()+":"+next.getValue());
    }

    3、通过get方式(不建议使用)

    Set<String> keySet=map.keySet();
    for(String str:keySet){
        System.out.println(str+"==="+map.get(str))
    }

    4、jdk8以后采用Map接口的默认方法forEach

    map.forEach((k,v)->{
        System.out.println(k+":"+v);
    });

    HashMap的初始化设计

     为了尽可能的避免hashmap的扩容操作,提高性能,如果明确知道存储的数据量大小I时,初始化值如下

    Map<String,String> map=new HashMap<>(initialCapacity);
    
    initialCapacity=(需要存储的元素个数/负载因子)+1

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  • 原文地址:https://www.cnblogs.com/xinmomoyan/p/12313875.html
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