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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_preface/installation/" class="md-nav__link">
|
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编程环境安装
|
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</li>
|
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<li class="md-nav__item">
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一起参与创作
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|
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</ul>
|
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</nav>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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<label class="md-nav__link" for="__nav_2">
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<nav class="md-nav" aria-label="引言" data-md-level="1">
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数组与链表
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|
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<a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
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数组（Array）
|
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</a>
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</li>
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<li class="md-nav__item">
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链表（LinkedList）
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</li>
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<li class="md-nav__item">
|
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<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
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列表（List）
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|
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<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
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小结
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<label class="md-nav__link" for="__nav_6">
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栈与队列
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" aria-label="栈与队列" data-md-level="1">
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栈与队列
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</label>
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<li class="md-nav__item">
|
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<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
|
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栈（Stack）
|
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</a>
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</li>
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<li class="md-nav__item">
|
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<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
|
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队列（Queue）
|
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</a>
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</li>
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
|
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双向队列（Deque）
|
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</a>
|
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</li>
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<li class="md-nav__item">
|
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<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
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小结
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</ul>
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</nav>
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<li class="md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested">
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<label class="md-nav__link" for="__nav_7">
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散列表
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" aria-label="散列表" data-md-level="1">
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<span class="md-nav__icon md-icon"></span>
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散列表
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
|
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<a href="../hash_map/" class="md-nav__link">
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哈希表（HashMap）
|
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</a>
|
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</li>
|
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<label class="md-nav__link md-nav__link--active" for="__toc">
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哈希冲突处理
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<a href="./" class="md-nav__link md-nav__link--active">
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哈希冲突处理
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<nav class="md-nav md-nav--secondary" aria-label="目录">
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<nav class="md-nav" aria-label="链式地址">
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<a href="#_3" class="md-nav__link">
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<li class="md-nav__item">
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<a href="#_4" class="md-nav__link">
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二叉树引入
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</li>
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</nav>
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<li class="md-nav__item">
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<a href="#_5" class="md-nav__link">
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开放寻址
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<nav class="md-nav" aria-label="开放寻址">
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<ul class="md-nav__list">
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<a href="#_6" class="md-nav__link">
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线性探测
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|
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<a href="#_7" class="md-nav__link">
|
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多次哈希
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<li class="md-nav__item">
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<a href="../summary/" class="md-nav__link">
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小结
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</nav>
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<label class="md-nav__link" for="__nav_8">
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二叉树
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" aria-label="二叉树" data-md-level="1">
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<span class="md-nav__icon md-icon"></span>
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二叉树
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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二叉树（Binary Tree）
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</a>
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</li>
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<li class="md-nav__item">
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二叉树常见类型
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二叉搜索树
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|
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开放寻址
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线性探测
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|
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多次哈希
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<article class="md-content__inner md-typeset">
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<a href="https://github.com/krahets/hello-algo/tree/master/docs/chapter_hashing/hash_collision.md" title="编辑此页" class="md-content__button md-icon">
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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>
|
||
<p>然而，即使我们设计了一个足够好的「哈希函数」，却仍然无法杜绝哈希冲突问题，这是因为：</p>
|
||
<ul>
|
||
<li>哈希表的桶的大小（地址范围）是有限的，只要数据量足够大，理论上一定会出现冲突；</li>
|
||
<li>哈希函数很难使键值对完全均匀分布，这也增大了冲突发生的可能性。</li>
|
||
</ul>
|
||
<p>虽然理论上哈希冲突无法避免，但我们仍然可以在数据结构与算法的层面缓解冲突问题，尽量保证哈希表的增删查改操作效率。<strong>常见的哈希冲突的解决方案有「链式地址」和「开放寻址」</strong>。</p>
|
||
<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>
|
||
|
||
|
||
|
||
|
||
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<h2 id="__comments">评论</h2>
|
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