CS_learn/hello-algo
1
0
Fork 0
mirror of https://github.com/krahets/hello-algo.git synced 2026-07-16 11:02:09 +08:00
Code Issues Packages Projects Releases Wiki Activity

deploy

Browse Source
This commit is contained in:
krahets
2023-12-28 17:18:44 +08:00
parent 5e0d7327db
commit b8a5bd790b
114 changed files with 860 additions and 863 deletions
Download Patch File Download Diff File Expand all files Collapse all files

24
chapter_hashing/hash_map/index.html
View File

@@ -1788,7 +1788,7 @@
<span class="md-ellipsis">
8.3 &nbsp; Top-K 问题
8.3 &nbsp; Top-k 问题
</span>
@@ -3533,7 +3533,7 @@
<!-- Page content -->
<h1 id="61">6.1 &nbsp; 哈希表<a class="headerlink" href="#61" title="Permanent link">&para;</a></h1>
<p>「哈希表 hash table」，又称「散列表」，其通过建立键 <code>key</code> 与值 <code>value</code> 之间的映射，实现高效的元素查询。具体而言，我们向哈希表输入一个键 <code>key</code> ，则可以在 <span class="arithmatex">\(O(1)\)</span> 时间内获取对应的值 <code>value</code> 。</p>
<p>「哈希表 hash table」，又称「散列表」，它通过建立键 <code>key</code> 与值 <code>value</code> 之间的映射，实现高效的元素查询。具体而言，我们向哈希表中输入一个键 <code>key</code> ，则可以在 <span class="arithmatex">\(O(1)\)</span> 时间内获取对应的值 <code>value</code> 。</p>
<p>如图 6-1 所示，给定 <span class="arithmatex">\(n\)</span> 个学生，每个学生都有“姓名”和“学号”两项数据。假如我们希望实现“输入一个学号，返回对应的姓名”的查询功能，则可以采用图 6-1 所示的哈希表来实现。</p>
<p><a class="glightbox" href="../hash_map.assets/hash_table_lookup.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="哈希表的抽象表示" class="animation-figure" src="../hash_map.assets/hash_table_lookup.png" /></a></p>
<p align="center"> 图 6-1 &nbsp; 哈希表的抽象表示 </p>
@@ -3596,7 +3596,7 @@
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;小鸭&quot;</span>
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="c1"># 查询操作</span>
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="c1"># 向哈希表输入键 key ，得到值 value</span>
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="c1"># 向哈希表中输入键 key ，得到值 value</span>
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="n">name</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="n">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span>
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="c1"># 删除操作</span>
@@ -3617,7 +3617,7 @@
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="n">map</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span><span class="p">;</span>
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a>
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="cm">/* 查询操作 */</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="c1">// 向哈希表输入键 key ，得到值 value</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="c1">// 向哈希表中输入键 key ，得到值 value</span>
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="n">string</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">];</span>
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a>
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="cm">/* 删除操作 */</span>
@@ -3638,7 +3638,7 @@
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">10583</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span><span class="p">);</span>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a>
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="cm">/* 查询操作 */</span>
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="c1">// 向哈希表输入键 key ，得到值 value</span>
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="c1">// 向哈希表中输入键 key ，得到值 value</span>
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="n">String</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">15937</span><span class="p">);</span>
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a>
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="cm">/* 删除操作 */</span>
@@ -3659,7 +3659,7 @@
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="p">};</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="cm">/* 查询操作 */</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="c1">// 向哈希表输入键 key ，得到值 value</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="c1">// 向哈希表中输入键 key ，得到值 value</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="kt">string</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">[</span><span class="m">15937</span><span class="p">];</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="cm">/* 删除操作 */</span>
@@ -3680,7 +3680,7 @@
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* 查询操作 */</span>
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="c1">// 向哈希表输入键 key ，得到值 value</span>
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="c1">// 向哈希表中输入键 key ，得到值 value</span>
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="nx">name</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span>
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a>
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="cm">/* 删除操作 */</span>
@@ -3701,7 +3701,7 @@
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="bp">map</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span> <span class="p">=</span> <span class="s">&quot;小鸭&quot;</span>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* 查询操作 */</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="c1">// 向哈希表输入键 key ，得到值 value</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="c1">// 向哈希表中输入键 key ，得到值 value</span>
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="kd">let</span> <span class="nv">name</span> <span class="p">=</span> <span class="bp">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="o">!</span>
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="cm">/* 删除操作 */</span>
@@ -3721,7 +3721,7 @@
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">10583</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小鸭&#39;</span><span class="p">);</span>
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a>
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="cm">/* 查询操作 */</span>
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="c1">// 向哈希表输入键 key ，得到值 value</span>
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="c1">// 向哈希表中输入键 key ，得到值 value</span>
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="kd">let</span><span class="w"> </span><span class="nx">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="mf">15937</span><span class="p">);</span>
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a>
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="cm">/* 删除操作 */</span>
@@ -3743,7 +3743,7 @@
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">map</span><span class="p">);</span>
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a>
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="cm">/* 查询操作 */</span>
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="c1">// 向哈希表输入键 key ，得到值 value</span>
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="c1">// 向哈希表中输入键 key ，得到值 value</span>
<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="kd">let</span><span class="w"> </span><span class="nx">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="mf">15937</span><span class="p">);</span>
<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n输入学号 15937 ，查询到姓名 &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">name</span><span class="p">);</span>
<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a>
@@ -3767,7 +3767,7 @@
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="n">map</span><span class="p">[</span><span class="m">10583</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;小鸭&quot;</span><span class="p">;</span>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a>
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="cm">/* 查询操作 */</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="c1">// 向哈希表输入键 key ，得到值 value</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="c1">// 向哈希表中输入键 key ，得到值 value</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="kt">String</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">[</span><span class="m">15937</span><span class="p">];</span>
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a>
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="cm">/* 删除操作 */</span>
@@ -5123,7 +5123,7 @@
<p><a class="glightbox" href="../hash_map.assets/hash_table_reshash.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="哈希表扩容" class="animation-figure" src="../hash_map.assets/hash_table_reshash.png" /></a></p>
<p align="center"> 图 6-4 &nbsp; 哈希表扩容 </p>
<p>类似于数组扩容，哈希表扩容需将所有键值对从原哈希表迁移至新哈希表，非常耗时；并且由于哈希表容量 <code>capacity</code> 改变，我们需要通过哈希函数来重新计算所有键值对的存储位置，这进一步提高了扩容过程的计算开销。为此，编程语言通常会预留足够大的哈希表容量，防止频繁扩容。</p>
<p>类似于数组扩容，哈希表扩容需将所有键值对从原哈希表迁移至新哈希表，非常耗时；并且由于哈希表容量 <code>capacity</code> 改变，我们需要通过哈希函数来重新计算所有键值对的存储位置，这进一步增加了扩容过程的计算开销。为此，编程语言通常会预留足够大的哈希表容量，防止频繁扩容。</p>
<p>「负载因子 load factor」是哈希表的一个重要概念，其定义为哈希表的元素数量除以桶数量，用于衡量哈希冲突的严重程度，<strong>也常作为哈希表扩容的触发条件</strong>。例如在 Java 中，当负载因子超过 <span class="arithmatex">\(0.75\)</span> 时，系统会将哈希表扩容至原先的 <span class="arithmatex">\(2\)</span> 倍。</p>
<!-- Source file information -->