基于版本jdk1.7.0_80

java.util.LinkedHashMap

代码如下

/*
* Copyright (c) 2000, 2010, Oracle and/or its affiliates. All rights reserved.
* ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*/ package java.util;
import java.io.*; /**
* <p>Hash table and linked list implementation of the <tt>Map</tt> interface,
* with predictable iteration order. This implementation differs from
* <tt>HashMap</tt> in that it maintains a doubly-linked list running through
* all of its entries. This linked list defines the iteration ordering,
* which is normally the order in which keys were inserted into the map
* (<i>insertion-order</i>). Note that insertion order is not affected
* if a key is <i>re-inserted</i> into the map. (A key <tt>k</tt> is
* reinserted into a map <tt>m</tt> if <tt>m.put(k, v)</tt> is invoked when
* <tt>m.containsKey(k)</tt> would return <tt>true</tt> immediately prior to
* the invocation.)
*
* <p>This implementation spares its clients from the unspecified, generally
* chaotic ordering provided by {@link HashMap} (and {@link Hashtable}),
* without incurring the increased cost associated with {@link TreeMap}. It
* can be used to produce a copy of a map that has the same order as the
* original, regardless of the original map's implementation:
* <pre>
* void foo(Map m) {
* Map copy = new LinkedHashMap(m);
* ...
* }
* </pre>
* This technique is particularly useful if a module takes a map on input,
* copies it, and later returns results whose order is determined by that of
* the copy. (Clients generally appreciate having things returned in the same
* order they were presented.)
*
* <p>A special {@link #LinkedHashMap(int,float,boolean) constructor} is
* provided to create a linked hash map whose order of iteration is the order
* in which its entries were last accessed, from least-recently accessed to
* most-recently (<i>access-order</i>). This kind of map is well-suited to
* building LRU caches. Invoking the <tt>put</tt> or <tt>get</tt> method
* results in an access to the corresponding entry (assuming it exists after
* the invocation completes). The <tt>putAll</tt> method generates one entry
* access for each mapping in the specified map, in the order that key-value
* mappings are provided by the specified map's entry set iterator. <i>No
* other methods generate entry accesses.</i> In particular, operations on
* collection-views do <i>not</i> affect the order of iteration of the backing
* map.
*
* <p>The {@link #removeEldestEntry(Map.Entry)} method may be overridden to
* impose a policy for removing stale mappings automatically when new mappings
* are added to the map.
*
* <p>This class provides all of the optional <tt>Map</tt> operations, and
* permits null elements. Like <tt>HashMap</tt>, it provides constant-time
* performance for the basic operations (<tt>add</tt>, <tt>contains</tt> and
* <tt>remove</tt>), assuming the hash function disperses elements
* properly among the buckets. Performance is likely to be just slightly
* below that of <tt>HashMap</tt>, due to the added expense of maintaining the
* linked list, with one exception: Iteration over the collection-views
* of a <tt>LinkedHashMap</tt> requires time proportional to the <i>size</i>
* of the map, regardless of its capacity. Iteration over a <tt>HashMap</tt>
* is likely to be more expensive, requiring time proportional to its
* <i>capacity</i>.
*
* <p>A linked hash map has two parameters that affect its performance:
* <i>initial capacity</i> and <i>load factor</i>. They are defined precisely
* as for <tt>HashMap</tt>. Note, however, that the penalty for choosing an
* excessively high value for initial capacity is less severe for this class
* than for <tt>HashMap</tt>, as iteration times for this class are unaffected
* by capacity.
*
* <p><strong>Note that this implementation is not synchronized.</strong>
* If multiple threads access a linked hash map concurrently, and at least
* one of the threads modifies the map structurally, it <em>must</em> be
* synchronized externally. This is typically accomplished by
* synchronizing on some object that naturally encapsulates the map.
*
* 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 LinkedHashMap(...));</pre>
*
* A structural modification is any operation that adds or deletes one or more
* mappings or, in the case of access-ordered linked hash maps, affects
* iteration order. In insertion-ordered linked hash maps, merely changing
* the value associated with a key that is already contained in the map is not
* a structural modification. <strong>In access-ordered linked hash maps,
* merely querying the map with <tt>get</tt> is a structural
* modification.</strong>)
*
* <p>The iterators returned by the <tt>iterator</tt> method of the collections
* returned by all of this class's collection view methods are
* <em>fail-fast</em>: if the map is structurally modified at any time after
* the iterator is created, in any way except through the iterator's own
* <tt>remove</tt> 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.
*
* <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 <tt>ConcurrentModificationException</tt> 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>
*
* <p>This class is a member of the
* <a href="{@docRoot}/../technotes/guides/collections/index.html">
* Java Collections Framework</a>.
*
* @param <K> the type of keys maintained by this map
* @param <V> the type of mapped values
*
* @author Josh Bloch
* @see Object#hashCode()
* @see Collection
* @see Map
* @see HashMap
* @see TreeMap
* @see Hashtable
* @since 1.4
*/ public class LinkedHashMap<K,V>
extends HashMap<K,V>
implements Map<K,V>
{ private static final long serialVersionUID = 3801124242820219131L; /**
* The head of the doubly linked list.
*/
private transient Entry<K,V> header; /**
* The iteration ordering method for this linked hash map: <tt>true</tt>
* for access-order, <tt>false</tt> for insertion-order.
*
* @serial
*/
private final boolean accessOrder; /**
* Constructs an empty insertion-ordered <tt>LinkedHashMap</tt> instance
* 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 LinkedHashMap(int initialCapacity, float loadFactor) {
super(initialCapacity, loadFactor);
accessOrder = false;
} /**
* Constructs an empty insertion-ordered <tt>LinkedHashMap</tt> instance
* with the specified initial capacity and a default load factor (0.75).
*
* @param initialCapacity the initial capacity
* @throws IllegalArgumentException if the initial capacity is negative
*/
public LinkedHashMap(int initialCapacity) {
super(initialCapacity);
accessOrder = false;
} /**
* Constructs an empty insertion-ordered <tt>LinkedHashMap</tt> instance
* with the default initial capacity (16) and load factor (0.75).
*/
public LinkedHashMap() {
super();
accessOrder = false;
} /**
* Constructs an insertion-ordered <tt>LinkedHashMap</tt> instance with
* the same mappings as the specified map. The <tt>LinkedHashMap</tt>
* instance is created with a default load factor (0.75) and an initial
* capacity sufficient to hold the mappings in the specified map.
*
* @param m the map whose mappings are to be placed in this map
* @throws NullPointerException if the specified map is null
*/
public LinkedHashMap(Map<? extends K, ? extends V> m) {
super(m);
accessOrder = false;
} /**
* Constructs an empty <tt>LinkedHashMap</tt> instance with the
* specified initial capacity, load factor and ordering mode.
*
* @param initialCapacity the initial capacity
* @param loadFactor the load factor
* @param accessOrder the ordering mode - <tt>true</tt> for
* access-order, <tt>false</tt> for insertion-order
* @throws IllegalArgumentException if the initial capacity is negative
* or the load factor is nonpositive
*/
public LinkedHashMap(int initialCapacity,
float loadFactor,
boolean accessOrder) {
super(initialCapacity, loadFactor);
this.accessOrder = accessOrder;
} /**
* Called by superclass constructors and pseudoconstructors (clone,
* readObject) before any entries are inserted into the map. Initializes
* the chain.
*/
@Override
void init() {
header = new Entry<>(-1, null, null, null);
header.before = header.after = header;
} /**
* Transfers all entries to new table array. This method is called
* by superclass resize. It is overridden for performance, as it is
* faster to iterate using our linked list.
*/
@Override
void transfer(HashMap.Entry[] newTable, boolean rehash) {
int newCapacity = newTable.length;
for (Entry<K,V> e = header.after; e != header; e = e.after) {
if (rehash)
e.hash = (e.key == null) ? 0 : hash(e.key);
int index = indexFor(e.hash, newCapacity);
e.next = newTable[index];
newTable[index] = e;
}
} /**
* Returns <tt>true</tt> 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 <tt>true</tt> if this map maps one or more keys to the
* specified value
*/
public boolean containsValue(Object value) {
// Overridden to take advantage of faster iterator
if (value==null) {
for (Entry e = header.after; e != header; e = e.after)
if (e.value==null)
return true;
} else {
for (Entry e = header.after; e != header; e = e.after)
if (value.equals(e.value))
return true;
}
return false;
} /**
* 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.
*/
public V get(Object key) {
Entry<K,V> e = (Entry<K,V>)getEntry(key);
if (e == null)
return null;
e.recordAccess(this);
return e.value;
} /**
* Removes all of the mappings from this map.
* The map will be empty after this call returns.
*/
public void clear() {
super.clear();
header.before = header.after = header;
} /**
* LinkedHashMap entry.
*/
private static class Entry<K,V> extends HashMap.Entry<K,V> {
// These fields comprise the doubly linked list used for iteration.
Entry<K,V> before, after; Entry(int hash, K key, V value, HashMap.Entry<K,V> next) {
super(hash, key, value, next);
} /**
* Removes this entry from the linked list.
*/
private void remove() {
before.after = after;
after.before = before;
} /**
* Inserts this entry before the specified existing entry in the list.
*/
private void addBefore(Entry<K,V> existingEntry) {
after = existingEntry;
before = existingEntry.before;
before.after = this;
after.before = this;
} /**
* This method is invoked by the superclass whenever the value
* of a pre-existing entry is read by Map.get or modified by Map.set.
* If the enclosing Map is access-ordered, it moves the entry
* to the end of the list; otherwise, it does nothing.
*/
void recordAccess(HashMap<K,V> m) {
LinkedHashMap<K,V> lm = (LinkedHashMap<K,V>)m;
if (lm.accessOrder) {
lm.modCount++;
remove();
addBefore(lm.header);
}
} void recordRemoval(HashMap<K,V> m) {
remove();
}
} private abstract class LinkedHashIterator<T> implements Iterator<T> {
Entry<K,V> nextEntry = header.after;
Entry<K,V> lastReturned = null; /**
* The modCount value that the iterator believes that the backing
* List should have. If this expectation is violated, the iterator
* has detected concurrent modification.
*/
int expectedModCount = modCount; public boolean hasNext() {
return nextEntry != header;
} public void remove() {
if (lastReturned == null)
throw new IllegalStateException();
if (modCount != expectedModCount)
throw new ConcurrentModificationException(); LinkedHashMap.this.remove(lastReturned.key);
lastReturned = null;
expectedModCount = modCount;
} Entry<K,V> nextEntry() {
if (modCount != expectedModCount)
throw new ConcurrentModificationException();
if (nextEntry == header)
throw new NoSuchElementException(); Entry<K,V> e = lastReturned = nextEntry;
nextEntry = e.after;
return e;
}
} private class KeyIterator extends LinkedHashIterator<K> {
public K next() { return nextEntry().getKey(); }
} private class ValueIterator extends LinkedHashIterator<V> {
public V next() { return nextEntry().value; }
} private class EntryIterator extends LinkedHashIterator<Map.Entry<K,V>> {
public Map.Entry<K,V> next() { return nextEntry(); }
} // These Overrides alter the behavior of superclass view iterator() methods
Iterator<K> newKeyIterator() { return new KeyIterator(); }
Iterator<V> newValueIterator() { return new ValueIterator(); }
Iterator<Map.Entry<K,V>> newEntryIterator() { return new EntryIterator(); } /**
* This override alters behavior of superclass put method. It causes newly
* allocated entry to get inserted at the end of the linked list and
* removes the eldest entry if appropriate.
*/
void addEntry(int hash, K key, V value, int bucketIndex) {
super.addEntry(hash, key, value, bucketIndex); // Remove eldest entry if instructed
Entry<K,V> eldest = header.after;
if (removeEldestEntry(eldest)) {
removeEntryForKey(eldest.key);
}
} /**
* This override differs from addEntry in that it doesn't resize the
* table or remove the eldest entry.
*/
void createEntry(int hash, K key, V value, int bucketIndex) {
HashMap.Entry<K,V> old = table[bucketIndex];
Entry<K,V> e = new Entry<>(hash, key, value, old);
table[bucketIndex] = e;
e.addBefore(header);
size++;
} /**
* Returns <tt>true</tt> if this map should remove its eldest entry.
* This method is invoked by <tt>put</tt> and <tt>putAll</tt> after
* inserting a new entry into the map. It provides the implementor
* with the opportunity to remove the eldest entry each time a new one
* is added. This is useful if the map represents a cache: it allows
* the map to reduce memory consumption by deleting stale entries.
*
* <p>Sample use: this override will allow the map to grow up to 100
* entries and then delete the eldest entry each time a new entry is
* added, maintaining a steady state of 100 entries.
* <pre>
* private static final int MAX_ENTRIES = 100;
*
* protected boolean removeEldestEntry(Map.Entry eldest) {
* return size() > MAX_ENTRIES;
* }
* </pre>
*
* <p>This method typically does not modify the map in any way,
* instead allowing the map to modify itself as directed by its
* return value. It <i>is</i> permitted for this method to modify
* the map directly, but if it does so, it <i>must</i> return
* <tt>false</tt> (indicating that the map should not attempt any
* further modification). The effects of returning <tt>true</tt>
* after modifying the map from within this method are unspecified.
*
* <p>This implementation merely returns <tt>false</tt> (so that this
* map acts like a normal map - the eldest element is never removed).
*
* @param eldest The least recently inserted entry in the map, or if
* this is an access-ordered map, the least recently accessed
* entry. This is the entry that will be removed it this
* method returns <tt>true</tt>. If the map was empty prior
* to the <tt>put</tt> or <tt>putAll</tt> invocation resulting
* in this invocation, this will be the entry that was just
* inserted; in other words, if the map contains a single
* entry, the eldest entry is also the newest.
* @return <tt>true</tt> if the eldest entry should be removed
* from the map; <tt>false</tt> if it should be retained.
*/
protected boolean removeEldestEntry(Map.Entry<K,V> eldest) {
return false;
}
}

代码量493,因为只是做了一些扩展

1. 接口分析

LinkedHashMap继承于HashMap(只是对HashMap做了一些扩展,以及部分函数更高效的实现)

Map接口

2. 实现原理

额外加了一个双向环形链表,用来记录Map内元素被最后一次访问的次序,链表节点定义如下

    private static class Entry<K,V> extends HashMap.Entry<K,V> {
// These fields comprise the doubly linked list used for iteration.
Entry<K,V> before, after; Entry(int hash, K key, V value, HashMap.Entry<K,V> next) {
super(hash, key, value, next);
}
}

3. 链表的更新

重写了HashMap.addEntry方法

    void addEntry(int hash, K key, V value, int bucketIndex) {
super.addEntry(hash, key, value, bucketIndex);//调用父类的HashMap.addEntry来维护table // Remove eldest entry if instructed
Entry<K,V> eldest = header.after;//获取HashMap中最长时间无人访问的节点,然后根据removeEldestEntry方法的返回结果决定是否将这个节点移除
if (removeEldestEntry(eldest)) {//removeEldestEntry方法可以在LinkedHashMap的子类中实现
removeEntryForKey(eldest.key);
}
}

重写了HashMap.createEntry方法

    void createEntry(int hash, K key, V value, int bucketIndex) {
HashMap.Entry<K,V> old = table[bucketIndex];
Entry<K,V> e = new Entry<>(hash, key, value, old);//创建LinkedHashMap.Entry节点
table[bucketIndex] = e;//头插法将新节点插入table
e.addBefore(header);//将新节点插入LinkedHashMap维护的链表
size++;
}

重写了HashMap.get方法,get的时候会调用LinkedHashMap.recordAccess方法

    public V get(Object key) {
Entry<K,V> e = (Entry<K,V>)getEntry(key);
if (e == null)
return null;
e.recordAccess(this);
return e.value;
} void recordAccess(HashMap<K,V> m) {
LinkedHashMap<K,V> lm = (LinkedHashMap<K,V>)m;
if (lm.accessOrder) {
lm.modCount++;
remove();
addBefore(lm.header);
}
}

4. HashMap中某些方法更高效的实现

重写了HashMap.transfer/HashMap.containValue方法,因为现在可以直接用维护的链表来遍历Map内的所有元素了,无需操作table,可以减少开销

    void transfer(HashMap.Entry[] newTable, boolean rehash) {
int newCapacity = newTable.length;
for (Entry<K,V> e = header.after; e != header; e = e.after) {
if (rehash)
e.hash = (e.key == null) ? 0 : hash(e.key);
int index = indexFor(e.hash, newCapacity);
e.next = newTable[index];
newTable[index] = e;
}
} public boolean containsValue(Object value) {
// Overridden to take advantage of faster iterator
if (value==null) {
for (Entry e = header.after; e != header; e = e.after)
if (e.value==null)
return true;
} else {
for (Entry e = header.after; e != header; e = e.after)
if (value.equals(e.value))
return true;
}
return false;
}

5. 新的迭代器

LinkedHashMap中有一个新的迭代器LinkedHashIterator,这个迭代器会利用LinkedHashMap维护的链表进行迭代,迭代结果的次序是Map内元素最后一次被访问的次序,跟HashMap等容器相同,在迭代器建立后如果再次修改原LinkedHashMap,会抛出ConcurrentModificationException。

    private abstract class LinkedHashIterator<T> implements Iterator<T> {
Entry<K,V> nextEntry = header.after;
Entry<K,V> lastReturned = null; /**
* The modCount value that the iterator believes that the backing
* List should have. If this expectation is violated, the iterator
* has detected concurrent modification.
*/
int expectedModCount = modCount; public boolean hasNext() {
return nextEntry != header;
} public void remove() {
if (lastReturned == null)
throw new IllegalStateException();
if (modCount != expectedModCount)
throw new ConcurrentModificationException(); LinkedHashMap.this.remove(lastReturned.key);
lastReturned = null;
expectedModCount = modCount;
} Entry<K,V> nextEntry() {
if (modCount != expectedModCount)
throw new ConcurrentModificationException();
if (nextEntry == header)
throw new NoSuchElementException(); Entry<K,V> e = lastReturned = nextEntry;
nextEntry = e.after;
return e;
}
}

6. 实际作用

最直接的想法就是可以用LinkedHashMap来实现LRU Cache,在初始化的时候,为Cache设定一个阈值,当Cache内的元素数量到达这个阈值后,自动踢出最长时间没有被使用过的对象

点了一下子类之后发现,Druid等框架中确实有LRUCache的实现类继承于LinkedHashMap

JDK7集合框架源码阅读(四) LinkedHashMap的更多相关文章

  1. JDK7集合框架源码阅读(五) Hashtable

    基于版本jdk1.7.0_80 java.util.Hashtable 代码如下 /* * Copyright (c) 1994, 2011, Oracle and/or its affiliates ...

  2. JDK7集合框架源码阅读(二) LinkedList

    基于版本jdk1.7.0_80 java.util.LinkedList 代码如下 /* * Copyright (c) 1997, 2011, Oracle and/or its affiliate ...

  3. JDK7集合框架源码阅读(六) HashSet与LinkedHashSet

    基于版本jdk1.7.0_80 java.util.HashSet java.util.LinkedHashSet 代码如下 HashSet,312行 /* * Copyright (c) 1997, ...

  4. JDK7集合框架源码阅读(七) ArrayDeque

    基于版本jdk1.7.0_80 java.util.ArrayDeque 代码如下 /* * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to li ...

  5. JDK7集合框架源码阅读(一) ArrayList

    基于版本jdk1.7.0_80 java.util.ArrayList 代码如下 /* * Copyright (c) 1997, 2013, Oracle and/or its affiliates ...

  6. JDK7集合框架源码阅读(三) HashMap

    基于版本jdk1.7.0_80 java.util.HashMap 代码如下 /* * Copyright (c) 1997, 2010, Oracle and/or its affiliates. ...

  7. Java集合框架源码(四)——Vector

    第1部分 Vector介绍 Vector简介 Vector 是矢量队列,它是JDK1.0版本添加的类.继承于AbstractList,实现了List, RandomAccess, Cloneable这 ...

  8. 【java集合框架源码剖析系列】java源码剖析之HashSet

    注:博主java集合框架源码剖析系列的源码全部基于JDK1.8.0版本.本博客将从源码角度带领大家学习关于HashSet的知识. 一HashSet的定义: public class HashSet&l ...

  9. 【java集合框架源码剖析系列】java源码剖析之HashMap

    前言:之所以打算写java集合框架源码剖析系列博客是因为自己反思了一下阿里内推一面的失败(估计没过,因为写此博客已距阿里巴巴一面一个星期),当时面试完之后感觉自己回答的挺好的,而且据面试官最后说的这几 ...

随机推荐

  1. python语言中threading.Thread类的使用方法

    1. 编程语言里面的任务和线程是很重要的一个功能.在python里面,线程的创建有两种方式,其一使用Thread类创建 # 导入Python标准库中的Thread模块 from threading i ...

  2. nohup 重定向的问题-- 费元星 站长

    费元星 大牛 以前只知道使用nohup可以让一个程序后台执行,但是生成的日志文件都放到nohup.out中了,不能自己指定,尤其是在同一个目录下我需要让两个甚至多个程序都要后台执行时,这样看日志就比较 ...

  3. 《Cracking the Coding Interview》——第4章:树和图——题目8

    2014-03-19 05:04 题目:给定两棵二叉树T1和T2,判断T2是否是T1的子树.子树的定义是,以T1的某个节点(可以是T1的根)作为根节点,得到的这棵树和T2一模一样. 解法:首先可以根据 ...

  4. MySQL高可用之MHA安装

      Preface       MasterHA is a tool which can be used in MySQL HA architecture.I'm gonna implement it ...

  5. 关于在虚拟机上安装iOS所遇到的问题

    先配一张成功的图片: 要想实现上图所示的,就要安装 unlocker206, 安装完unlocker206 不用改里面的内容!!!看到**经验上说还要改内容,结果我试了很多次,根本不行,其实问题不在改 ...

  6. Linux网络运维相关

    删除特殊的用户和用户组 userdel games group games   关闭不需要的服务 chkconfig chkconfig --level 345 bluetooth off   删减系 ...

  7. Sprint 站立会议(个人)

    昨天做: 开Sprint会议确定并绘制Backlog. 今天做: 系统主窗体格局 编程环境搭建(部分) 遇到问题: 缺乏经验,没有好的总体规划. 团队博客园:http://www.cnblogs.co ...

  8. 那些牛掰的 HTML5的API(二)

    1:视频播放器 2:地理定位 我们的支持html5 的浏览器给我们提供一个接口(api),可以用来获取你当前的位置. 主要是通过geolocation(地理位置),对象 ,去访问硬件,来获取到经纬度. ...

  9. web自动化测试:watir+minitest(四)

    脚本连跑: rake是ruby中的一个构建工具,和make很像.允许用ruby来写rakefile. 我们使用rake以任务的方式来运行我们的脚本集. 新建Rakefile文件,写入如下内容: req ...

  10. GYM - 101620 J.Justified Jungle

    题意: 给出一棵树,删掉其中一些边,要求生成的每个子树节点数一样.输出所有可以删掉的边数. 题解: 以节点1为根,预处理每个子树的大小.对于每个n的因数x,还需满足子树为他倍数的点够n/x个,那么删的 ...