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算法无处不在
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算法是什么
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计算复杂度
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计算复杂度
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空间复杂度
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权衡时间与空间
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数据结构简介
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链表引入
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二叉树引入
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线性探测
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多次哈希
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二叉树常见类型
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冒泡排序
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插入排序
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快速排序
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归并排序
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链表引入
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开放寻址
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线性探测
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多次哈希
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M20.71 7.04c.39-.39.39-1.04 0-1.41l-2.34-2.34c-.37-.39-1.02-.39-1.41 0l-1.84 1.83 3.75 3.75M3 17.25V21h3.75L17.81 9.93l-3.75-3.75L3 17.25Z" / > < / svg >
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< h1 id = "_1" > 哈希冲突处理< a class = "headerlink" href = "#_1" title = "Permanent link" > ¶ < / a > < / h1 >
< p > 理想情况下，哈希函数应该为每个输入产生唯一的输出，使得 key 和 value 一一对应。而实际上，往往存在不同 key 对应相同 value 的情况，这种情况被称为「哈希冲突 Hash Collision」。< / p >
< p > < strong > 哈希冲突会严重影响哈希表的实用性< / strong > 。试想一下，如果在哈希表中总是查找到错误的结果，那么我们肯定不会继续使用这样的数据结构了。< / p >
2022-12-12 17:53:31 +00:00
< div class = "admonition question" >
< p class = "admonition-title" > 为什么会出现哈希冲突？< / p >
< p > 因为 < strong > 哈希函数的输入空间往往远大于输出空间< / strong > ，所以不可避免地会出现多个输入产生相同输出的情况。比如，输入空间是全体整数，输出空间是一个固定大小的桶（数组）的索引范围，那么必定会有多个整数同时映射到一个桶索引。< / p >
< / div >
< p > 虽然理论上哈希冲突难以避免，< strong > 但我们仍然可以在数据结构层面上缓解哈希冲突所带来的负面影响< / strong > ，尽量保证哈希表的增删查改操作效率。< / p >
< p > 常见的哈希冲突的解决方案有「链式地址」和「开放寻址」。< / p >
2022-12-12 17:36:54 +00:00
< h2 id = "_2" > 链式地址< a class = "headerlink" href = "#_2" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 「链式地址」通过引入链表来解决哈希冲突问题，代价是占用空间变大，因为链表或二叉树包含结点指针，相比于数组更加耗费内存空间。< / p >
< h3 id = "_3" > 链表引入< a class = "headerlink" href = "#_3" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 在原始哈希表中，一个桶地址只能存储一个元素（即键值对）。< strong > 考虑将桶地址内的单个元素转变成一个链表，将所有冲突元素都存储在一个链表中< / strong > ，此时哈希表操作方法为：< / p >
< ul >
< li > < strong > 查询元素：< / strong > 先将 key 输入到哈希函数得到桶地址（即访问链表头部），再遍历链表来确定对应的 value 。< / li >
< li > < strong > 添加元素：< / strong > 先通过哈希函数访问链表头部，再将元素直接添加到链表头部即可。< / li >
< li > < strong > 删除元素：< / strong > 同样先访问链表头部，再遍历链表查找对应元素，删除之即可。< / li >
< / ul >
< p > （图）< / p >
< h3 id = "_4" > 二叉树引入< a class = "headerlink" href = "#_4" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 引入链表虽然解决了哈希冲突，但查询效率也随之降低了，因为需要线性查找（即遍历链表）来确认对应元素。为了缓解此问题，< strong > 当某个桶地址内的链表太长时，可以把链表转化为「平衡二叉搜索树」< / strong > ，将时间复杂度降低至 < span class = "arithmatex" > \(O(\log n)\)< / span > 。< / p >
< div class = "admonition note" >
< p class = "admonition-title" > 工业界方案< / p >
< p > Java 使用了链式地址来解决哈希冲突。在 JDK 1.8 之后， HashMap 内长度大于 8 的链表会被转化为「红黑树」，以提升查找性能。< / p >
< / div >
< h2 id = "_5" > 开放寻址< a class = "headerlink" href = "#_5" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 「开放寻址」不引入额外数据结构，而是通过 “向后探测” 来解决哈希冲突。根据探测方法的不同，主要分为 < strong > 线性探测、平方探测、多次哈希< / strong > 。< / p >
< h3 id = "_6" > 线性探测< a class = "headerlink" href = "#_6" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 「线性探测」使用固定步长的线性查找来解决哈希冲突。< / p >
< p > < strong > 插入元素：< / strong > 如果出现哈希冲突，则从冲突位置向后线性遍历（步长一般取 1 ），直到找到一个空位，则将元素插入到该空位中。< / p >
< p > < strong > 查找元素：< / strong > 若出现哈希冲突，则使用相同步长执行线性查找，会遇到两种情况：< / p >
< ol >
< li > 找到对应元素，返回 value 即可；< / li >
< li > 若遇到空位，则说明查找键值对不在哈希表中；< / li >
< / ol >
< p > （图）< / p >
< p > 线性探测有以下缺陷：< / p >
< ul >
< li > < strong > 不能直接删除元素< / strong > 。删除元素会导致桶内出现一个空位，在查找其他元素时，该空位有可能导致程序认为元素不存在（即上述第 < code > 2.< / code > 种情况）。因此需要借助一个标志位来标记删除元素。< / li >
< li > < strong > 容易产生聚集< / strong > 。桶内被占用的连续位置越长，这些连续位置发生哈希冲突的可能性越大，从而进一步促进这一位置的 “聚堆生长” ，最终导致增删查改操作效率的劣化。< / li >
< / ul >
< h3 id = "_7" > 多次哈希< a class = "headerlink" href = "#_7" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 顾名思义，「多次哈希」的思路是基于多个哈希函数 < span class = "arithmatex" > \(f_1(x)\)< / span > , < span class = "arithmatex" > \(f_2(x)\)< / span > , < span class = "arithmatex" > \(f_3(x)\)< / span > , < span class = "arithmatex" > \(\cdots\)< / span > 进行探测。< / p >
< p > < strong > 插入元素：< / strong > 若哈希函数 < span class = "arithmatex" > \(f_1(x)\)< / span > 出现冲突，则尝试 < span class = "arithmatex" > \(f_2(x)\)< / span > ，以此类推……直到找到空位后插入元素。< / p >
< p > < strong > 查找元素：< / strong > 以相同的哈希函数顺序查找，存在两种情况：< / p >
< ol >
< li > 找到目标元素，则返回之；< / li >
< li > 到空位或已尝试所有哈希函数，说明哈希表中无此元素；< / li >
< / ol >
< p > 相比于「线性探测」，「多次哈希」方法更不容易产生聚集，代价是多个哈希函数增加了额外计算量。< / p >
< h2 id = "__comments" > 评论< / h2 >
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<!-- Synchronize Giscus theme with palette -->
< script >
var giscus = document.querySelector("script[src*=giscus]")
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}
})
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< script > var tabs = _ _md _get ( "__tabs" ) ; if ( Array . isArray ( tabs ) ) e : for ( var set of document . querySelectorAll ( ".tabbed-set" ) ) { var tab , labels = set . querySelector ( ".tabbed-labels" ) ; for ( tab of tabs ) for ( var label of labels . getElementsByTagName ( "label" ) ) if ( label . innerText . trim ( ) === tab ) { var input = document . getElementById ( label . htmlFor ) ; input . checked = ! 0 ; continue e } } < / script >
< / div >
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< footer class = "md-footer" >
< div class = "md-footer-meta md-typeset" >
< div class = "md-footer-meta__inner md-grid" >
< div class = "md-copyright" >
< div class = "md-copyright__highlight" >
Copyright © 2020 - 2022 Krahets
< / div >
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< div class = "md-social" >
< a href = "https://github.com/krahets" target = "_blank" rel = "noopener" title = "github.com" class = "md-social__link" >
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< / a >
< / div >
< / div >
< / div >
< / footer >
< / div >
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< div class = "md-dialog__inner md-typeset" > < / div >
< / div >
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< script src = "../../assets/javascripts/bundle.f1ef77e2.min.js" > < / script >
< script src = "../../javascripts/mathjax.js" > < / script >
< script src = "https://polyfill.io/v3/polyfill.min.js?features=es6" > < / script >
< script src = "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js" > < / script >
< / body >
< / html >
