deploy

chapter_hashing/hash_algorithm/index.html

@@ -1797,7 +1797,7 @@
         
   
   <span class="md-ellipsis">
-    8.3 &nbsp; Top-K 问题
+    8.3 &nbsp; Top-k 问题
   </span>
   
 
@@ -4104,7 +4104,7 @@
 <p>总而言之，我们通常选取质数作为模数，并且这个质数最好足够大，以尽可能消除周期性模式，提升哈希算法的稳健性。</p>
 <h2 id="633">6.3.3 &nbsp; 常见哈希算法<a class="headerlink" href="#633" title="Permanent link">&para;</a></h2>
 <p>不难发现，以上介绍的简单哈希算法都比较“脆弱”，远远没有达到哈希算法的设计目标。例如，由于加法和异或满足交换律，因此加法哈希和异或哈希无法区分内容相同但顺序不同的字符串，这可能会加剧哈希冲突，并引起一些安全问题。</p>
-<p>在实际中，我们通常会用一些标准哈希算法，例如 MD5、SHA-1、SHA-2、SHA-3 等。它们可以将任意长度的输入数据映射到恒定长度的哈希值。</p>
+<p>在实际中，我们通常会用一些标准哈希算法，例如 MD5、SHA-1、SHA-2 和 SHA-3 等。它们可以将任意长度的输入数据映射到恒定长度的哈希值。</p>
 <p>近一个世纪以来，哈希算法处在不断升级与优化的过程中。一部分研究人员努力提升哈希算法的性能，另一部分研究人员和黑客则致力于寻找哈希算法的安全性问题。表 6-2 展示了在实际应用中常见的哈希算法。</p>
 <ul>
 <li>MD5 和 SHA-1 已多次被成功攻击，因此它们被各类安全应用弃用。</li>
@@ -4134,10 +4134,10 @@
 </tr>
 <tr>
 <td>输出长度</td>
-<td>128 bits</td>
-<td>160 bits</td>
-<td>256/512 bits</td>
-<td>224/256/384/512 bits</td>
+<td>128 bit</td>
+<td>160 bit</td>
+<td>256/512 bit</td>
+<td>224/256/384/512 bit</td>
 </tr>
 <tr>
 <td>哈希冲突</td>
@@ -4394,7 +4394,7 @@
 </div>
 <p>在许多编程语言中，<strong>只有不可变对象才可作为哈希表的 <code>key</code></strong> 。假如我们将列表（动态数组）作为 <code>key</code> ，当列表的内容发生变化时，它的哈希值也随之改变，我们就无法在哈希表中查询到原先的 <code>value</code> 了。</p>
 <p>虽然自定义对象（比如链表节点）的成员变量是可变的，但它是可哈希的。<strong>这是因为对象的哈希值通常是基于内存地址生成的</strong>，即使对象的内容发生了变化，但它的内存地址不变，哈希值仍然是不变的。</p>
-<p>细心的你可能发现在不同控制台中运行程序时，输出的哈希值是不同的。<strong>这是因为 Python 解释器在每次启动时，都会为字符串哈希函数加入一个随机的盐（Salt）值</strong>。这种做法可以有效防止 HashDoS 攻击，提升哈希算法的安全性。</p>
+<p>细心的你可能发现在不同控制台中运行程序时，输出的哈希值是不同的。<strong>这是因为 Python 解释器在每次启动时，都会为字符串哈希函数加入一个随机的盐（salt）值</strong>。这种做法可以有效防止 HashDoS 攻击，提升哈希算法的安全性。</p>
 
 <!-- Source file information -->
 

chapter_hashing/hash_collision/index.html

@@ -1821,7 +1821,7 @@
         
   
   <span class="md-ellipsis">
-    8.3 &nbsp; Top-K 问题
+    8.3 &nbsp; Top-k 问题
   </span>
   
 
@@ -3600,7 +3600,7 @@
 <!-- Page content -->
 <h1 id="62">6.2 &nbsp; 哈希冲突<a class="headerlink" href="#62" title="Permanent link">&para;</a></h1>
 <p>上一节提到，<strong>通常情况下哈希函数的输入空间远大于输出空间</strong>，因此理论上哈希冲突是不可避免的。比如，输入空间为全体整数，输出空间为数组容量大小，则必然有多个整数映射至同一桶索引。</p>
-<p>哈希冲突会导致查询结果错误，严重影响哈希表的可用性。为解决该问题，我们可以每当遇到哈希冲突就进行哈希表扩容，直至冲突消失为止。此方法简单粗暴且有效，但效率太低，因为哈希表扩容需要进行大量的数据搬运与哈希值计算。为了提升效率，我们可以采用以下策略。</p>
+<p>哈希冲突会导致查询结果错误，严重影响哈希表的可用性。为了解决该问题，每当遇到哈希冲突时，我们就进行哈希表扩容，直至冲突消失为止。此方法简单粗暴且有效，但效率太低，因为哈希表扩容需要进行大量的数据搬运与哈希值计算。为了提升效率，我们可以采用以下策略。</p>
 <ol>
 <li>改良哈希表数据结构，<strong>使得哈希表可以在出现哈希冲突时正常工作</strong>。</li>
 <li>仅在必要时，即当哈希冲突比较严重时，才执行扩容操作。</li>
@@ -3619,8 +3619,8 @@
 </ul>
 <p>链式地址存在以下局限性。</p>
 <ul>
-<li><strong>占用空间增大</strong>，链表包含节点指针，它相比数组更加耗费内存空间。</li>
-<li><strong>查询效率降低</strong>，因为需要线性遍历链表来查找对应元素。</li>
+<li><strong>占用空间增大</strong>：链表包含节点指针，它相比数组更加耗费内存空间。</li>
+<li><strong>查询效率降低</strong>：因为需要线性遍历链表来查找对应元素。</li>
 </ul>
 <p>以下代码给出了链式地址哈希表的简单实现，需要注意两点。</p>
 <ul>
@@ -3653,11 +3653,11 @@
 <a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;查询操作&quot;&quot;&quot;</span>
 <a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
 <a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>        <span class="n">bucket</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
-<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>        <span class="c1"># 遍历桶，若找到 key 则返回对应 val</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>        <span class="c1"># 遍历桶，若找到 key ，则返回对应 val</span>
 <a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">bucket</span><span class="p">:</span>
 <a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>            <span class="k">if</span> <span class="n">pair</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="n">key</span><span class="p">:</span>
 <a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>                <span class="k">return</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span>
-<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>        <span class="c1"># 若未找到 key 则返回 None</span>
+<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>        <span class="c1"># 若未找到 key ，则返回 None</span>
 <a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>        <span class="k">return</span> <span class="kc">None</span>
 <a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>
 <a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a>    <span class="k">def</span> <span class="nf">put</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
@@ -3749,13 +3749,13 @@
 <a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w">    </span><span class="cm">/* 查询操作 */</span>
 <a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="w">    </span><span class="n">string</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="w">        </span><span class="c1">// 遍历桶，若找到 key 则返回对应 val</span>
+<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="w">        </span><span class="c1">// 遍历桶，若找到 key ，则返回对应 val</span>
 <a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-42" name="__codelineno-1-42" href="#__codelineno-1-42"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
 <a id="__codelineno-1-43" name="__codelineno-1-43" href="#__codelineno-1-43"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-1-44" name="__codelineno-1-44" href="#__codelineno-1-44"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a><span class="w">        </span><span class="c1">// 若未找到 key 则返回空字符串</span>
+<a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a><span class="w">        </span><span class="c1">// 若未找到 key ，则返回空字符串</span>
 <a id="__codelineno-1-46" name="__codelineno-1-46" href="#__codelineno-1-46"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="p">;</span>
 <a id="__codelineno-1-47" name="__codelineno-1-47" href="#__codelineno-1-47"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-1-48" name="__codelineno-1-48" href="#__codelineno-1-48"></a>
@@ -3861,13 +3861,13 @@
 <a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w">    </span><span class="n">String</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
 <a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
-<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">        </span><span class="c1">// 遍历桶，若找到 key 则返回对应 val</span>
+<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">        </span><span class="c1">// 遍历桶，若找到 key ，则返回对应 val</span>
 <a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
 <a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a><span class="w">        </span><span class="c1">// 若未找到 key 则返回 null</span>
+<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a><span class="w">        </span><span class="c1">// 若未找到 key ，则返回 null</span>
 <a id="__codelineno-2-42" name="__codelineno-2-42" href="#__codelineno-2-42"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
 <a id="__codelineno-2-43" name="__codelineno-2-43" href="#__codelineno-2-43"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-2-44" name="__codelineno-2-44" href="#__codelineno-2-44"></a>
@@ -3972,13 +3972,13 @@
 <a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="w">    </span><span class="cm">/* 查询操作 */</span>
 <a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">string?</span><span class="w"> </span><span class="n">Get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a><span class="w">        </span><span class="c1">// 遍历桶，若找到 key 则返回对应 val</span>
+<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a><span class="w">        </span><span class="c1">// 遍历桶，若找到 key ，则返回对应 val</span>
 <a id="__codelineno-3-35" name="__codelineno-3-35" href="#__codelineno-3-35"></a><span class="w">        </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-36" name="__codelineno-3-36" href="#__codelineno-3-36"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-37" name="__codelineno-3-37" href="#__codelineno-3-37"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
 <a id="__codelineno-3-38" name="__codelineno-3-38" href="#__codelineno-3-38"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-3-39" name="__codelineno-3-39" href="#__codelineno-3-39"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-3-40" name="__codelineno-3-40" href="#__codelineno-3-40"></a><span class="w">        </span><span class="c1">// 若未找到 key 则返回 null</span>
+<a id="__codelineno-3-40" name="__codelineno-3-40" href="#__codelineno-3-40"></a><span class="w">        </span><span class="c1">// 若未找到 key ，则返回 null</span>
 <a id="__codelineno-3-41" name="__codelineno-3-41" href="#__codelineno-3-41"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
 <a id="__codelineno-3-42" name="__codelineno-3-42" href="#__codelineno-3-42"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-3-43" name="__codelineno-3-43" href="#__codelineno-3-43"></a>
@@ -4087,13 +4087,13 @@
 <a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">m</span><span class="w"> </span><span class="o">*</span><span class="nx">hashMapChaining</span><span class="p">)</span><span class="w"> </span><span class="nx">get</span><span class="p">(</span><span class="nx">key</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="w">    </span><span class="nx">idx</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span>
 <a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w">    </span><span class="nx">bucket</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">idx</span><span class="p">]</span>
-<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="w">    </span><span class="c1">// 遍历桶，若找到 key 则返回对应 val</span>
+<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="w">    </span><span class="c1">// 遍历桶，若找到 key ，则返回对应 val</span>
 <a id="__codelineno-4-40" name="__codelineno-4-40" href="#__codelineno-4-40"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-41" name="__codelineno-4-41" href="#__codelineno-4-41"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">p</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-42" name="__codelineno-4-42" href="#__codelineno-4-42"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">p</span><span class="p">.</span><span class="nx">val</span>
 <a id="__codelineno-4-43" name="__codelineno-4-43" href="#__codelineno-4-43"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-4-44" name="__codelineno-4-44" href="#__codelineno-4-44"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-4-45" name="__codelineno-4-45" href="#__codelineno-4-45"></a><span class="w">    </span><span class="c1">// 若未找到 key 则返回空字符串</span>
+<a id="__codelineno-4-45" name="__codelineno-4-45" href="#__codelineno-4-45"></a><span class="w">    </span><span class="c1">// 若未找到 key ，则返回空字符串</span>
 <a id="__codelineno-4-46" name="__codelineno-4-46" href="#__codelineno-4-46"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span>
 <a id="__codelineno-4-47" name="__codelineno-4-47" href="#__codelineno-4-47"></a><span class="p">}</span>
 <a id="__codelineno-4-48" name="__codelineno-4-48" href="#__codelineno-4-48"></a>
@@ -4205,13 +4205,13 @@
 <a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a>    <span class="kd">func</span> <span class="nf">get</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="nb">String</span><span class="p">?</span> <span class="p">{</span>
 <a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a>        <span class="kd">let</span> <span class="nv">index</span> <span class="p">=</span> <span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="n">key</span><span class="p">)</span>
 <a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a>        <span class="kd">let</span> <span class="nv">bucket</span> <span class="p">=</span> <span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
-<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a>        <span class="c1">// 遍历桶，若找到 key 则返回对应 val</span>
+<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a>        <span class="c1">// 遍历桶，若找到 key ，则返回对应 val</span>
 <a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="k">in</span> <span class="n">bucket</span> <span class="p">{</span>
 <a id="__codelineno-5-34" name="__codelineno-5-34" href="#__codelineno-5-34"></a>            <span class="k">if</span> <span class="n">pair</span><span class="p">.</span><span class="n">key</span> <span class="p">==</span> <span class="n">key</span> <span class="p">{</span>
 <a id="__codelineno-5-35" name="__codelineno-5-35" href="#__codelineno-5-35"></a>                <span class="k">return</span> <span class="n">pair</span><span class="p">.</span><span class="n">val</span>
 <a id="__codelineno-5-36" name="__codelineno-5-36" href="#__codelineno-5-36"></a>            <span class="p">}</span>
 <a id="__codelineno-5-37" name="__codelineno-5-37" href="#__codelineno-5-37"></a>        <span class="p">}</span>
-<a id="__codelineno-5-38" name="__codelineno-5-38" href="#__codelineno-5-38"></a>        <span class="c1">// 若未找到 key 则返回 nil</span>
+<a id="__codelineno-5-38" name="__codelineno-5-38" href="#__codelineno-5-38"></a>        <span class="c1">// 若未找到 key ，则返回 nil</span>
 <a id="__codelineno-5-39" name="__codelineno-5-39" href="#__codelineno-5-39"></a>        <span class="k">return</span> <span class="kc">nil</span>
 <a id="__codelineno-5-40" name="__codelineno-5-40" href="#__codelineno-5-40"></a>    <span class="p">}</span>
 <a id="__codelineno-5-41" name="__codelineno-5-41" href="#__codelineno-5-41"></a>
@@ -4307,13 +4307,13 @@
 <a id="__codelineno-6-29" name="__codelineno-6-29" href="#__codelineno-6-29"></a><span class="w">    </span><span class="nx">get</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-6-30" name="__codelineno-6-30" href="#__codelineno-6-30"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
 <a id="__codelineno-6-31" name="__codelineno-6-31" href="#__codelineno-6-31"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
-<a id="__codelineno-6-32" name="__codelineno-6-32" href="#__codelineno-6-32"></a><span class="w">        </span><span class="c1">// 遍历桶，若找到 key 则返回对应 val</span>
+<a id="__codelineno-6-32" name="__codelineno-6-32" href="#__codelineno-6-32"></a><span class="w">        </span><span class="c1">// 遍历桶，若找到 key ，则返回对应 val</span>
 <a id="__codelineno-6-33" name="__codelineno-6-33" href="#__codelineno-6-33"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-6-34" name="__codelineno-6-34" href="#__codelineno-6-34"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-6-35" name="__codelineno-6-35" href="#__codelineno-6-35"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
 <a id="__codelineno-6-36" name="__codelineno-6-36" href="#__codelineno-6-36"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-6-37" name="__codelineno-6-37" href="#__codelineno-6-37"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-6-38" name="__codelineno-6-38" href="#__codelineno-6-38"></a><span class="w">        </span><span class="c1">// 若未找到 key 则返回 null</span>
+<a id="__codelineno-6-38" name="__codelineno-6-38" href="#__codelineno-6-38"></a><span class="w">        </span><span class="c1">// 若未找到 key ，则返回 null</span>
 <a id="__codelineno-6-39" name="__codelineno-6-39" href="#__codelineno-6-39"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
 <a id="__codelineno-6-40" name="__codelineno-6-40" href="#__codelineno-6-40"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-6-41" name="__codelineno-6-41" href="#__codelineno-6-41"></a>
@@ -4413,13 +4413,13 @@
 <a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w">    </span><span class="nx">get</span><span class="p">(</span><span class="nx">key</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">);</span>
 <a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
-<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="w">        </span><span class="c1">// 遍历桶，若找到 key 则返回对应 val</span>
+<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="w">        </span><span class="c1">// 遍历桶，若找到 key ，则返回对应 val</span>
 <a id="__codelineno-7-33" name="__codelineno-7-33" href="#__codelineno-7-33"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-7-34" name="__codelineno-7-34" href="#__codelineno-7-34"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-7-35" name="__codelineno-7-35" href="#__codelineno-7-35"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
 <a id="__codelineno-7-36" name="__codelineno-7-36" href="#__codelineno-7-36"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-7-37" name="__codelineno-7-37" href="#__codelineno-7-37"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-7-38" name="__codelineno-7-38" href="#__codelineno-7-38"></a><span class="w">        </span><span class="c1">// 若未找到 key 则返回 null</span>
+<a id="__codelineno-7-38" name="__codelineno-7-38" href="#__codelineno-7-38"></a><span class="w">        </span><span class="c1">// 若未找到 key ，则返回 null</span>
 <a id="__codelineno-7-39" name="__codelineno-7-39" href="#__codelineno-7-39"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
 <a id="__codelineno-7-40" name="__codelineno-7-40" href="#__codelineno-7-40"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-7-41" name="__codelineno-7-41" href="#__codelineno-7-41"></a>
@@ -4519,13 +4519,13 @@
 <a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="w">  </span><span class="kt">String</span><span class="o">?</span><span class="w"> </span><span class="kd">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
 <a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
-<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="w">    </span><span class="c1">// 遍历桶，若找到 key 则返回对应 val</span>
+<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="w">    </span><span class="c1">// 遍历桶，若找到 key ，则返回对应 val</span>
 <a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-8-35" name="__codelineno-8-35" href="#__codelineno-8-35"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
 <a id="__codelineno-8-36" name="__codelineno-8-36" href="#__codelineno-8-36"></a><span class="w">      </span><span class="p">}</span>
 <a id="__codelineno-8-37" name="__codelineno-8-37" href="#__codelineno-8-37"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-8-38" name="__codelineno-8-38" href="#__codelineno-8-38"></a><span class="w">    </span><span class="c1">// 若未找到 key 则返回 null</span>
+<a id="__codelineno-8-38" name="__codelineno-8-38" href="#__codelineno-8-38"></a><span class="w">    </span><span class="c1">// 若未找到 key ，则返回 null</span>
 <a id="__codelineno-8-39" name="__codelineno-8-39" href="#__codelineno-8-39"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
 <a id="__codelineno-8-40" name="__codelineno-8-40" href="#__codelineno-8-40"></a><span class="w">  </span><span class="p">}</span>
 <a id="__codelineno-8-41" name="__codelineno-8-41" href="#__codelineno-8-41"></a>
@@ -4639,7 +4639,7 @@
 <a id="__codelineno-9-43" name="__codelineno-9-43" href="#__codelineno-9-43"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-9-44" name="__codelineno-9-44" href="#__codelineno-9-44"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-9-45" name="__codelineno-9-45" href="#__codelineno-9-45"></a>
-<a id="__codelineno-9-46" name="__codelineno-9-46" href="#__codelineno-9-46"></a><span class="w">        </span><span class="c1">// 若未找到 key 则返回 None</span>
+<a id="__codelineno-9-46" name="__codelineno-9-46" href="#__codelineno-9-46"></a><span class="w">        </span><span class="c1">// 若未找到 key ，则返回 None</span>
 <a id="__codelineno-9-47" name="__codelineno-9-47" href="#__codelineno-9-47"></a><span class="w">        </span><span class="nb">None</span>
 <a id="__codelineno-9-48" name="__codelineno-9-48" href="#__codelineno-9-48"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-9-49" name="__codelineno-9-49" href="#__codelineno-9-49"></a>
@@ -4705,14 +4705,14 @@
 <a id="__codelineno-9-109" name="__codelineno-9-109" href="#__codelineno-9-109"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
 <a id="__codelineno-9-110" name="__codelineno-9-110" href="#__codelineno-9-110"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">&amp;</span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
 <a id="__codelineno-9-111" name="__codelineno-9-111" href="#__codelineno-9-111"></a>
-<a id="__codelineno-9-112" name="__codelineno-9-112" href="#__codelineno-9-112"></a><span class="w">        </span><span class="c1">// 遍历桶，若找到 key 则返回对应 val</span>
+<a id="__codelineno-9-112" name="__codelineno-9-112" href="#__codelineno-9-112"></a><span class="w">        </span><span class="c1">// 遍历桶，若找到 key ，则返回对应 val</span>
 <a id="__codelineno-9-113" name="__codelineno-9-113" href="#__codelineno-9-113"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-114" name="__codelineno-9-114" href="#__codelineno-9-114"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-9-115" name="__codelineno-9-115" href="#__codelineno-9-115"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="o">&amp;</span><span class="n">pair</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-9-116" name="__codelineno-9-116" href="#__codelineno-9-116"></a><span class="w">            </span><span class="p">}</span>
 <a id="__codelineno-9-117" name="__codelineno-9-117" href="#__codelineno-9-117"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-9-118" name="__codelineno-9-118" href="#__codelineno-9-118"></a>
-<a id="__codelineno-9-119" name="__codelineno-9-119" href="#__codelineno-9-119"></a><span class="w">        </span><span class="c1">// 若未找到 key 则返回 None</span>
+<a id="__codelineno-9-119" name="__codelineno-9-119" href="#__codelineno-9-119"></a><span class="w">        </span><span class="c1">// 若未找到 key ，则返回 None</span>
 <a id="__codelineno-9-120" name="__codelineno-9-120" href="#__codelineno-9-120"></a><span class="w">        </span><span class="nb">None</span>
 <a id="__codelineno-9-121" name="__codelineno-9-121" href="#__codelineno-9-121"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-9-122" name="__codelineno-9-122" href="#__codelineno-9-122"></a><span class="p">}</span>
@@ -4776,7 +4776,7 @@
 <a id="__codelineno-10-55" name="__codelineno-10-55" href="#__codelineno-10-55"></a><span class="cm">/* 查询操作 */</span>
 <a id="__codelineno-10-56" name="__codelineno-10-56" href="#__codelineno-10-56"></a><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="nf">get</span><span class="p">(</span><span class="n">HashMapChaining</span><span class="w"> </span><span class="o">*</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-10-57" name="__codelineno-10-57" href="#__codelineno-10-57"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">hashMap</span><span class="p">,</span><span class="w"> </span><span class="n">key</span><span class="p">);</span>
-<a id="__codelineno-10-58" name="__codelineno-10-58" href="#__codelineno-10-58"></a><span class="w">    </span><span class="c1">// 遍历桶，若找到 key 则返回对应 val</span>
+<a id="__codelineno-10-58" name="__codelineno-10-58" href="#__codelineno-10-58"></a><span class="w">    </span><span class="c1">// 遍历桶，若找到 key ，则返回对应 val</span>
 <a id="__codelineno-10-59" name="__codelineno-10-59" href="#__codelineno-10-59"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
 <a id="__codelineno-10-60" name="__codelineno-10-60" href="#__codelineno-10-60"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-10-61" name="__codelineno-10-61" href="#__codelineno-10-61"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -4784,7 +4784,7 @@
 <a id="__codelineno-10-63" name="__codelineno-10-63" href="#__codelineno-10-63"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-10-64" name="__codelineno-10-64" href="#__codelineno-10-64"></a><span class="w">        </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
 <a id="__codelineno-10-65" name="__codelineno-10-65" href="#__codelineno-10-65"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-10-66" name="__codelineno-10-66" href="#__codelineno-10-66"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="p">;</span><span class="w"> </span><span class="c1">// 若未找到 key 则返回空字符串</span>
+<a id="__codelineno-10-66" name="__codelineno-10-66" href="#__codelineno-10-66"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="p">;</span><span class="w"> </span><span class="c1">// 若未找到 key ，则返回空字符串</span>
 <a id="__codelineno-10-67" name="__codelineno-10-67" href="#__codelineno-10-67"></a><span class="p">}</span>
 <a id="__codelineno-10-68" name="__codelineno-10-68" href="#__codelineno-10-68"></a>
 <a id="__codelineno-10-69" name="__codelineno-10-69" href="#__codelineno-10-69"></a><span class="cm">/* 添加操作 */</span>
@@ -4888,24 +4888,24 @@
 </div>
 <p>值得注意的是，当链表很长时，查询效率 <span class="arithmatex">\(O(n)\)</span> 很差。<strong>此时可以将链表转换为“AVL 树”或“红黑树”</strong>，从而将查询操作的时间复杂度优化至 <span class="arithmatex">\(O(\log n)\)</span> 。</p>
 <h2 id="622">6.2.2 &nbsp; 开放寻址<a class="headerlink" href="#622" title="Permanent link">&para;</a></h2>
-<p>「开放寻址 open addressing」不引入额外的数据结构，而是通过“多次探测”来处理哈希冲突，探测方式主要包括线性探测、平方探测、多次哈希等。</p>
+<p>「开放寻址 open addressing」不引入额外的数据结构，而是通过“多次探测”来处理哈希冲突，探测方式主要包括线性探测、平方探测和多次哈希等。</p>
 <p>下面以线性探测为例，介绍开放寻址哈希表的工作机制。</p>
 <h3 id="1">1. &nbsp; 线性探测<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
 <p>线性探测采用固定步长的线性搜索来进行探测，其操作方法与普通哈希表有所不同。</p>
 <ul>
 <li><strong>插入元素</strong>：通过哈希函数计算桶索引，若发现桶内已有元素，则从冲突位置向后线性遍历（步长通常为 <span class="arithmatex">\(1\)</span> ），直至找到空桶，将元素插入其中。</li>
-<li><strong>查找元素</strong>：若发现哈希冲突，则使用相同步长向后线性遍历，直到找到对应元素，返回 <code>value</code> 即可；如果遇到空桶，说明目标元素不在哈希表中，返回 <span class="arithmatex">\(\text{None}\)</span> 。</li>
+<li><strong>查找元素</strong>：若发现哈希冲突，则使用相同步长向后进行线性遍历，直到找到对应元素，返回 <code>value</code> 即可；如果遇到空桶，说明目标元素不在哈希表中，返回 <code>None</code> 。</li>
 </ul>
 <p>图 6-6 展示了开放寻址（线性探测）哈希表的键值对分布。根据此哈希函数，最后两位相同的 <code>key</code> 都会被映射到相同的桶。而通过线性探测，它们被依次存储在该桶以及之下的桶中。</p>
-<p><a class="glightbox" href="../hash_collision.assets/hash_table_linear_probing.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="开放寻址和线性探测" class="animation-figure" src="../hash_collision.assets/hash_table_linear_probing.png" /></a></p>
-<p align="center"> 图 6-6 &nbsp; 开放寻址和线性探测 </p>
+<p><a class="glightbox" href="../hash_collision.assets/hash_table_linear_probing.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="开放寻址（线性探测）哈希表的键值对分布" class="animation-figure" src="../hash_collision.assets/hash_table_linear_probing.png" /></a></p>
+<p align="center"> 图 6-6 &nbsp; 开放寻址（线性探测）哈希表的键值对分布 </p>
 
 <p>然而，<strong>线性探测容易产生“聚集现象”</strong>。具体来说，数组中连续被占用的位置越长，这些连续位置发生哈希冲突的可能性越大，从而进一步促使该位置的聚堆生长，形成恶性循环，最终导致增删查改操作效率劣化。</p>
-<p>值得注意的是，<strong>我们不能在开放寻址哈希表中直接删除元素</strong>。这是因为删除元素会在数组内产生一个空桶 <span class="arithmatex">\(\text{None}\)</span> ，而当查询元素时，线性探测到该空桶就会返回，因此在该空桶之下的元素都无法再被访问到，程序可能误判这些元素不存在。</p>
+<p>值得注意的是，<strong>我们不能在开放寻址哈希表中直接删除元素</strong>。这是因为删除元素会在数组内产生一个空桶 <code>None</code> ，而当查询元素时，线性探测到该空桶就会返回，因此在该空桶之下的元素都无法再被访问到，程序可能误判这些元素不存在。</p>
 <p><a class="glightbox" href="../hash_collision.assets/hash_table_open_addressing_deletion.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="在开放寻址中删除元素导致的查询问题" class="animation-figure" src="../hash_collision.assets/hash_table_open_addressing_deletion.png" /></a></p>
 <p align="center"> 图 6-7 &nbsp; 在开放寻址中删除元素导致的查询问题 </p>
 
-<p>为了解决该问题，我们可以采用「懒删除 lazy deletion」机制：它不直接从哈希表中移除元素，<strong>而是利用一个常量 <code>TOMBSTONE</code> 来标记这个桶</strong>。在该机制下，<span class="arithmatex">\(\text{None}\)</span> 和 <code>TOMBSTONE</code> 都代表空桶，都可以放置键值对。但不同的是，线性探测到 <code>TOMBSTONE</code> 时应该继续遍历，因为其之下可能还存在键值对。</p>
+<p>为了解决该问题，我们可以采用「懒删除 lazy deletion」机制：它不直接从哈希表中移除元素，<strong>而是利用一个常量 <code>TOMBSTONE</code> 来标记这个桶</strong>。在该机制下，<code>None</code> 和 <code>TOMBSTONE</code> 都代表空桶，都可以放置键值对。但不同的是，线性探测到 <code>TOMBSTONE</code> 时应该继续遍历，因为其之下可能还存在键值对。</p>
 <p>然而，<strong>懒删除可能会加速哈希表的性能退化</strong>。这是因为每次删除操作都会产生一个删除标记，随着 <code>TOMBSTONE</code> 的增加，搜索时间也会增加，因为线性探测可能需要跳过多个 <code>TOMBSTONE</code> 才能找到目标元素。</p>
 <p>为此，考虑在线性探测中记录遇到的首个 <code>TOMBSTONE</code> 的索引，并将搜索到的目标元素与该 <code>TOMBSTONE</code> 交换位置。这样做的好处是当每次查询或添加元素时，元素会被移动至距离理想位置（探测起始点）更近的桶，从而优化查询效率。</p>
 <p>以下代码实现了一个包含懒删除的开放寻址（线性探测）哈希表。为了更加充分地使用哈希表的空间，我们将哈希表看作一个“环形数组”，当越过数组尾部时，回到头部继续遍历。</p>
@@ -4938,9 +4938,9 @@
 <a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a>        <span class="n">first_tombstone</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
 <a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a>        <span class="c1"># 线性探测，当遇到空桶时跳出</span>
 <a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a>        <span class="k">while</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a>            <span class="c1"># 若遇到 key ，返回对应桶索引</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a>            <span class="c1"># 若遇到 key ，返回对应的桶索引</span>
 <a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a>            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="n">key</span><span class="p">:</span>
-<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a>                <span class="c1"># 若之前遇到了删除标记，则将键值对移动至该索引</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a>                <span class="c1"># 若之前遇到了删除标记，则将键值对移动至该索引处</span>
 <a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a>                <span class="k">if</span> <span class="n">first_tombstone</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
 <a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a>                    <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">first_tombstone</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
 <a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a>                    <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span>
@@ -4949,7 +4949,7 @@
 <a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a>            <span class="c1"># 记录遇到的首个删除标记</span>
 <a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a>            <span class="k">if</span> <span class="n">first_tombstone</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">is</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">:</span>
 <a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a>                <span class="n">first_tombstone</span> <span class="o">=</span> <span class="n">index</span>
-<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a>            <span class="c1"># 计算桶索引，越过尾部返回头部</span>
+<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a>            <span class="c1"># 计算桶索引，越过尾部则返回头部</span>
 <a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a>            <span class="n">index</span> <span class="o">=</span> <span class="p">(</span><span class="n">index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
 <a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a>        <span class="c1"># 若 key 不存在，则返回添加点的索引</span>
 <a id="__codelineno-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a>        <span class="k">return</span> <span class="n">index</span> <span class="k">if</span> <span class="n">first_tombstone</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> <span class="k">else</span> <span class="n">first_tombstone</span>
@@ -5054,9 +5054,9 @@
 <a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
 <a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a><span class="w">        </span><span class="c1">// 线性探测，当遇到空桶时跳出</span>
 <a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a><span class="w">            </span><span class="c1">// 若遇到 key ，返回对应桶索引</span>
+<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a><span class="w">            </span><span class="c1">// 若遇到 key ，返回对应的桶索引</span>
 <a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a><span class="w">                </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引</span>
+<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a><span class="w">                </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引处</span>
 <a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a><span class="w">                    </span><span class="n">buckets</span><span class="p">[</span><span class="n">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
 <a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a><span class="w">                    </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
@@ -5068,7 +5068,7 @@
 <a id="__codelineno-13-53" name="__codelineno-13-53" href="#__codelineno-13-53"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-13-54" name="__codelineno-13-54" href="#__codelineno-13-54"></a><span class="w">                </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
 <a id="__codelineno-13-55" name="__codelineno-13-55" href="#__codelineno-13-55"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-13-56" name="__codelineno-13-56" href="#__codelineno-13-56"></a><span class="w">            </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
+<a id="__codelineno-13-56" name="__codelineno-13-56" href="#__codelineno-13-56"></a><span class="w">            </span><span class="c1">// 计算桶索引，越过尾部则返回头部</span>
 <a id="__codelineno-13-57" name="__codelineno-13-57" href="#__codelineno-13-57"></a><span class="w">            </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
 <a id="__codelineno-13-58" name="__codelineno-13-58" href="#__codelineno-13-58"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-13-59" name="__codelineno-13-59" href="#__codelineno-13-59"></a><span class="w">        </span><span class="c1">// 若 key 不存在，则返回添加点的索引</span>
@@ -5181,9 +5181,9 @@
 <a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
 <a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w">        </span><span class="c1">// 线性探测，当遇到空桶时跳出</span>
 <a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">            </span><span class="c1">// 若遇到 key ，返回对应桶索引</span>
+<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">            </span><span class="c1">// 若遇到 key ，返回对应的桶索引</span>
 <a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w">                </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引</span>
+<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w">                </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引处</span>
 <a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w">                    </span><span class="n">buckets</span><span class="o">[</span><span class="n">firstTombstone</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">;</span>
 <a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w">                    </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
@@ -5195,7 +5195,7 @@
 <a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w">                </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
 <a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a><span class="w">            </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
+<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a><span class="w">            </span><span class="c1">// 计算桶索引，越过尾部则返回头部</span>
 <a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w">            </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
 <a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a><span class="w">        </span><span class="c1">// 若 key 不存在，则返回添加点的索引</span>
@@ -5306,9 +5306,9 @@
 <a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
 <a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">        </span><span class="c1">// 线性探测，当遇到空桶时跳出</span>
 <a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">            </span><span class="c1">// 若遇到 key ，返回对应桶索引</span>
+<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">            </span><span class="c1">// 若遇到 key ，返回对应的桶索引</span>
 <a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">                </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引</span>
+<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">                </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引处</span>
 <a id="__codelineno-15-35" name="__codelineno-15-35" href="#__codelineno-15-35"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-36" name="__codelineno-15-36" href="#__codelineno-15-36"></a><span class="w">                    </span><span class="n">buckets</span><span class="p">[</span><span class="n">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
 <a id="__codelineno-15-37" name="__codelineno-15-37" href="#__codelineno-15-37"></a><span class="w">                    </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
@@ -5320,7 +5320,7 @@
 <a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w">                </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
 <a id="__codelineno-15-45" name="__codelineno-15-45" href="#__codelineno-15-45"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">            </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
+<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">            </span><span class="c1">// 计算桶索引，越过尾部则返回头部</span>
 <a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a><span class="w">            </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
 <a id="__codelineno-15-48" name="__codelineno-15-48" href="#__codelineno-15-48"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w">        </span><span class="c1">// 若 key 不存在，则返回添加点的索引</span>
@@ -5441,7 +5441,7 @@
 <a id="__codelineno-16-39" name="__codelineno-16-39" href="#__codelineno-16-39"></a><span class="w">    </span><span class="nx">idx</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span>
 <a id="__codelineno-16-40" name="__codelineno-16-40" href="#__codelineno-16-40"></a><span class="w">    </span><span class="c1">// 线性探测，从 index 开始向后遍历</span>
 <a id="__codelineno-16-41" name="__codelineno-16-41" href="#__codelineno-16-41"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">capacity</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-16-42" name="__codelineno-16-42" href="#__codelineno-16-42"></a><span class="w">        </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
+<a id="__codelineno-16-42" name="__codelineno-16-42" href="#__codelineno-16-42"></a><span class="w">        </span><span class="c1">// 计算桶索引，越过尾部则返回头部</span>
 <a id="__codelineno-16-43" name="__codelineno-16-43" href="#__codelineno-16-43"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="nx">idx</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">capacity</span>
 <a id="__codelineno-16-44" name="__codelineno-16-44" href="#__codelineno-16-44"></a><span class="w">        </span><span class="c1">// 若遇到空桶，说明无此 key ，则返回 null</span>
 <a id="__codelineno-16-45" name="__codelineno-16-45" href="#__codelineno-16-45"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="p">{})</span><span class="w"> </span><span class="p">{</span>
@@ -5452,7 +5452,7 @@
 <a id="__codelineno-16-50" name="__codelineno-16-50" href="#__codelineno-16-50"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">j</span><span class="p">].</span><span class="nx">val</span>
 <a id="__codelineno-16-51" name="__codelineno-16-51" href="#__codelineno-16-51"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-16-52" name="__codelineno-16-52" href="#__codelineno-16-52"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-16-53" name="__codelineno-16-53" href="#__codelineno-16-53"></a><span class="w">    </span><span class="c1">// 若未找到 key 则返回空字符串</span>
+<a id="__codelineno-16-53" name="__codelineno-16-53" href="#__codelineno-16-53"></a><span class="w">    </span><span class="c1">// 若未找到 key ，则返回空字符串</span>
 <a id="__codelineno-16-54" name="__codelineno-16-54" href="#__codelineno-16-54"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span>
 <a id="__codelineno-16-55" name="__codelineno-16-55" href="#__codelineno-16-55"></a><span class="p">}</span>
 <a id="__codelineno-16-56" name="__codelineno-16-56" href="#__codelineno-16-56"></a>
@@ -5465,7 +5465,7 @@
 <a id="__codelineno-16-63" name="__codelineno-16-63" href="#__codelineno-16-63"></a><span class="w">    </span><span class="nx">idx</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">hashFunc</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span>
 <a id="__codelineno-16-64" name="__codelineno-16-64" href="#__codelineno-16-64"></a><span class="w">    </span><span class="c1">// 线性探测，从 index 开始向后遍历</span>
 <a id="__codelineno-16-65" name="__codelineno-16-65" href="#__codelineno-16-65"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">capacity</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-16-66" name="__codelineno-16-66" href="#__codelineno-16-66"></a><span class="w">        </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
+<a id="__codelineno-16-66" name="__codelineno-16-66" href="#__codelineno-16-66"></a><span class="w">        </span><span class="c1">// 计算桶索引，越过尾部则返回头部</span>
 <a id="__codelineno-16-67" name="__codelineno-16-67" href="#__codelineno-16-67"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="nx">idx</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">capacity</span>
 <a id="__codelineno-16-68" name="__codelineno-16-68" href="#__codelineno-16-68"></a><span class="w">        </span><span class="c1">// 若遇到空桶、或带有删除标记的桶，则将键值对放入该桶</span>
 <a id="__codelineno-16-69" name="__codelineno-16-69" href="#__codelineno-16-69"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="p">{})</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">removed</span><span class="w"> </span><span class="p">{</span>
@@ -5490,7 +5490,7 @@
 <a id="__codelineno-16-88" name="__codelineno-16-88" href="#__codelineno-16-88"></a><span class="w">    </span><span class="c1">// 遍历桶，从中删除键值对</span>
 <a id="__codelineno-16-89" name="__codelineno-16-89" href="#__codelineno-16-89"></a><span class="w">    </span><span class="c1">// 线性探测，从 index 开始向后遍历</span>
 <a id="__codelineno-16-90" name="__codelineno-16-90" href="#__codelineno-16-90"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">capacity</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-16-91" name="__codelineno-16-91" href="#__codelineno-16-91"></a><span class="w">        </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
+<a id="__codelineno-16-91" name="__codelineno-16-91" href="#__codelineno-16-91"></a><span class="w">        </span><span class="c1">// 计算桶索引，越过尾部则返回头部</span>
 <a id="__codelineno-16-92" name="__codelineno-16-92" href="#__codelineno-16-92"></a><span class="w">        </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="nx">idx</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">capacity</span>
 <a id="__codelineno-16-93" name="__codelineno-16-93" href="#__codelineno-16-93"></a><span class="w">        </span><span class="c1">// 若遇到空桶，说明无此 key ，则直接返回</span>
 <a id="__codelineno-16-94" name="__codelineno-16-94" href="#__codelineno-16-94"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">m</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="p">(</span><span class="nx">pair</span><span class="p">{})</span><span class="w"> </span><span class="p">{</span>
@@ -5570,9 +5570,9 @@
 <a id="__codelineno-17-33" name="__codelineno-17-33" href="#__codelineno-17-33"></a>        <span class="kd">var</span> <span class="nv">firstTombstone</span> <span class="p">=</span> <span class="o">-</span><span class="mi">1</span>
 <a id="__codelineno-17-34" name="__codelineno-17-34" href="#__codelineno-17-34"></a>        <span class="c1">// 线性探测，当遇到空桶时跳出</span>
 <a id="__codelineno-17-35" name="__codelineno-17-35" href="#__codelineno-17-35"></a>        <span class="k">while</span> <span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
-<a id="__codelineno-17-36" name="__codelineno-17-36" href="#__codelineno-17-36"></a>            <span class="c1">// 若遇到 key ，返回对应桶索引</span>
+<a id="__codelineno-17-36" name="__codelineno-17-36" href="#__codelineno-17-36"></a>            <span class="c1">// 若遇到 key ，返回对应的桶索引</span>
 <a id="__codelineno-17-37" name="__codelineno-17-37" href="#__codelineno-17-37"></a>            <span class="k">if</span> <span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="n">key</span> <span class="p">==</span> <span class="n">key</span> <span class="p">{</span>
-<a id="__codelineno-17-38" name="__codelineno-17-38" href="#__codelineno-17-38"></a>                <span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引</span>
+<a id="__codelineno-17-38" name="__codelineno-17-38" href="#__codelineno-17-38"></a>                <span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引处</span>
 <a id="__codelineno-17-39" name="__codelineno-17-39" href="#__codelineno-17-39"></a>                <span class="k">if</span> <span class="n">firstTombstone</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span> <span class="p">{</span>
 <a id="__codelineno-17-40" name="__codelineno-17-40" href="#__codelineno-17-40"></a>                    <span class="n">buckets</span><span class="p">[</span><span class="n">firstTombstone</span><span class="p">]</span> <span class="p">=</span> <span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
 <a id="__codelineno-17-41" name="__codelineno-17-41" href="#__codelineno-17-41"></a>                    <span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="p">=</span> <span class="n">TOMBSTONE</span>
@@ -5584,7 +5584,7 @@
 <a id="__codelineno-17-47" name="__codelineno-17-47" href="#__codelineno-17-47"></a>            <span class="k">if</span> <span class="n">firstTombstone</span> <span class="p">==</span> <span class="o">-</span><span class="mi">1</span> <span class="o">&amp;&amp;</span> <span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="p">==</span> <span class="n">TOMBSTONE</span> <span class="p">{</span>
 <a id="__codelineno-17-48" name="__codelineno-17-48" href="#__codelineno-17-48"></a>                <span class="n">firstTombstone</span> <span class="p">=</span> <span class="n">index</span>
 <a id="__codelineno-17-49" name="__codelineno-17-49" href="#__codelineno-17-49"></a>            <span class="p">}</span>
-<a id="__codelineno-17-50" name="__codelineno-17-50" href="#__codelineno-17-50"></a>            <span class="c1">// 计算桶索引，越过尾部返回头部</span>
+<a id="__codelineno-17-50" name="__codelineno-17-50" href="#__codelineno-17-50"></a>            <span class="c1">// 计算桶索引，越过尾部则返回头部</span>
 <a id="__codelineno-17-51" name="__codelineno-17-51" href="#__codelineno-17-51"></a>            <span class="n">index</span> <span class="p">=</span> <span class="p">(</span><span class="n">index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="n">capacity</span>
 <a id="__codelineno-17-52" name="__codelineno-17-52" href="#__codelineno-17-52"></a>        <span class="p">}</span>
 <a id="__codelineno-17-53" name="__codelineno-17-53" href="#__codelineno-17-53"></a>        <span class="c1">// 若 key 不存在，则返回添加点的索引</span>
@@ -5699,9 +5699,9 @@
 <a id="__codelineno-18-33" name="__codelineno-18-33" href="#__codelineno-18-33"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
 <a id="__codelineno-18-34" name="__codelineno-18-34" href="#__codelineno-18-34"></a><span class="w">        </span><span class="c1">// 线性探测，当遇到空桶时跳出</span>
 <a id="__codelineno-18-35" name="__codelineno-18-35" href="#__codelineno-18-35"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-18-36" name="__codelineno-18-36" href="#__codelineno-18-36"></a><span class="w">            </span><span class="c1">// 若遇到 key ，返回对应桶索引</span>
+<a id="__codelineno-18-36" name="__codelineno-18-36" href="#__codelineno-18-36"></a><span class="w">            </span><span class="c1">// 若遇到 key ，返回对应的桶索引</span>
 <a id="__codelineno-18-37" name="__codelineno-18-37" href="#__codelineno-18-37"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">].</span><span class="nx">key</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-18-38" name="__codelineno-18-38" href="#__codelineno-18-38"></a><span class="w">                </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引</span>
+<a id="__codelineno-18-38" name="__codelineno-18-38" href="#__codelineno-18-38"></a><span class="w">                </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引处</span>
 <a id="__codelineno-18-39" name="__codelineno-18-39" href="#__codelineno-18-39"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-18-40" name="__codelineno-18-40" href="#__codelineno-18-40"></a><span class="w">                    </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
 <a id="__codelineno-18-41" name="__codelineno-18-41" href="#__codelineno-18-41"></a><span class="w">                    </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">TOMBSTONE</span><span class="p">;</span>
@@ -5716,7 +5716,7 @@
 <a id="__codelineno-18-50" name="__codelineno-18-50" href="#__codelineno-18-50"></a><span class="w">            </span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-18-51" name="__codelineno-18-51" href="#__codelineno-18-51"></a><span class="w">                </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span>
 <a id="__codelineno-18-52" name="__codelineno-18-52" href="#__codelineno-18-52"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-18-53" name="__codelineno-18-53" href="#__codelineno-18-53"></a><span class="w">            </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
+<a id="__codelineno-18-53" name="__codelineno-18-53" href="#__codelineno-18-53"></a><span class="w">            </span><span class="c1">// 计算桶索引，越过尾部则返回头部</span>
 <a id="__codelineno-18-54" name="__codelineno-18-54" href="#__codelineno-18-54"></a><span class="w">            </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">capacity</span><span class="p">;</span>
 <a id="__codelineno-18-55" name="__codelineno-18-55" href="#__codelineno-18-55"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-18-56" name="__codelineno-18-56" href="#__codelineno-18-56"></a><span class="w">        </span><span class="c1">// 若 key 不存在，则返回添加点的索引</span>
@@ -5840,9 +5840,9 @@
 <a id="__codelineno-19-33" name="__codelineno-19-33" href="#__codelineno-19-33"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
 <a id="__codelineno-19-34" name="__codelineno-19-34" href="#__codelineno-19-34"></a><span class="w">        </span><span class="c1">// 线性探测，当遇到空桶时跳出</span>
 <a id="__codelineno-19-35" name="__codelineno-19-35" href="#__codelineno-19-35"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-19-36" name="__codelineno-19-36" href="#__codelineno-19-36"></a><span class="w">            </span><span class="c1">// 若遇到 key ，返回对应桶索引</span>
+<a id="__codelineno-19-36" name="__codelineno-19-36" href="#__codelineno-19-36"></a><span class="w">            </span><span class="c1">// 若遇到 key ，返回对应的桶索引</span>
 <a id="__codelineno-19-37" name="__codelineno-19-37" href="#__codelineno-19-37"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="nx">key</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-19-38" name="__codelineno-19-38" href="#__codelineno-19-38"></a><span class="w">                </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引</span>
+<a id="__codelineno-19-38" name="__codelineno-19-38" href="#__codelineno-19-38"></a><span class="w">                </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引处</span>
 <a id="__codelineno-19-39" name="__codelineno-19-39" href="#__codelineno-19-39"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-40" name="__codelineno-19-40" href="#__codelineno-19-40"></a><span class="w">                    </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">];</span>
 <a id="__codelineno-19-41" name="__codelineno-19-41" href="#__codelineno-19-41"></a><span class="w">                    </span><span class="k">this</span><span class="p">.</span><span class="nx">buckets</span><span class="p">[</span><span class="nx">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">TOMBSTONE</span><span class="p">;</span>
@@ -5857,7 +5857,7 @@
 <a id="__codelineno-19-50" name="__codelineno-19-50" href="#__codelineno-19-50"></a><span class="w">            </span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-51" name="__codelineno-19-51" href="#__codelineno-19-51"></a><span class="w">                </span><span class="nx">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">index</span><span class="p">;</span>
 <a id="__codelineno-19-52" name="__codelineno-19-52" href="#__codelineno-19-52"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-19-53" name="__codelineno-19-53" href="#__codelineno-19-53"></a><span class="w">            </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
+<a id="__codelineno-19-53" name="__codelineno-19-53" href="#__codelineno-19-53"></a><span class="w">            </span><span class="c1">// 计算桶索引，越过尾部则返回头部</span>
 <a id="__codelineno-19-54" name="__codelineno-19-54" href="#__codelineno-19-54"></a><span class="w">            </span><span class="nx">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">capacity</span><span class="p">;</span>
 <a id="__codelineno-19-55" name="__codelineno-19-55" href="#__codelineno-19-55"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-19-56" name="__codelineno-19-56" href="#__codelineno-19-56"></a><span class="w">        </span><span class="c1">// 若 key 不存在，则返回添加点的索引</span>
@@ -5977,9 +5977,9 @@
 <a id="__codelineno-20-29" name="__codelineno-20-29" href="#__codelineno-20-29"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
 <a id="__codelineno-20-30" name="__codelineno-20-30" href="#__codelineno-20-30"></a><span class="w">    </span><span class="c1">// 线性探测，当遇到空桶时跳出</span>
 <a id="__codelineno-20-31" name="__codelineno-20-31" href="#__codelineno-20-31"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-20-32" name="__codelineno-20-32" href="#__codelineno-20-32"></a><span class="w">      </span><span class="c1">// 若遇到 key ，返回对应桶索引</span>
+<a id="__codelineno-20-32" name="__codelineno-20-32" href="#__codelineno-20-32"></a><span class="w">      </span><span class="c1">// 若遇到 key ，返回对应的桶索引</span>
 <a id="__codelineno-20-33" name="__codelineno-20-33" href="#__codelineno-20-33"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">!</span><span class="p">.</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-20-34" name="__codelineno-20-34" href="#__codelineno-20-34"></a><span class="w">        </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引</span>
+<a id="__codelineno-20-34" name="__codelineno-20-34" href="#__codelineno-20-34"></a><span class="w">        </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引处</span>
 <a id="__codelineno-20-35" name="__codelineno-20-35" href="#__codelineno-20-35"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-20-36" name="__codelineno-20-36" href="#__codelineno-20-36"></a><span class="w">          </span><span class="n">_buckets</span><span class="p">[</span><span class="n">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
 <a id="__codelineno-20-37" name="__codelineno-20-37" href="#__codelineno-20-37"></a><span class="w">          </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_TOMBSTONE</span><span class="p">;</span>
@@ -5991,7 +5991,7 @@
 <a id="__codelineno-20-43" name="__codelineno-20-43" href="#__codelineno-20-43"></a><span class="w">      </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">_buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">_TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-20-44" name="__codelineno-20-44" href="#__codelineno-20-44"></a><span class="w">        </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
 <a id="__codelineno-20-45" name="__codelineno-20-45" href="#__codelineno-20-45"></a><span class="w">      </span><span class="p">}</span>
-<a id="__codelineno-20-46" name="__codelineno-20-46" href="#__codelineno-20-46"></a><span class="w">      </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
+<a id="__codelineno-20-46" name="__codelineno-20-46" href="#__codelineno-20-46"></a><span class="w">      </span><span class="c1">// 计算桶索引，越过尾部则返回头部</span>
 <a id="__codelineno-20-47" name="__codelineno-20-47" href="#__codelineno-20-47"></a><span class="w">      </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">_capacity</span><span class="p">;</span>
 <a id="__codelineno-20-48" name="__codelineno-20-48" href="#__codelineno-20-48"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-20-49" name="__codelineno-20-49" href="#__codelineno-20-49"></a><span class="w">    </span><span class="c1">// 若 key 不存在，则返回添加点的索引</span>
@@ -6125,7 +6125,7 @@
 <a id="__codelineno-21-52" name="__codelineno-21-52" href="#__codelineno-21-52"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">first_tombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-21-53" name="__codelineno-21-53" href="#__codelineno-21-53"></a><span class="w">                </span><span class="n">first_tombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
 <a id="__codelineno-21-54" name="__codelineno-21-54" href="#__codelineno-21-54"></a><span class="w">            </span><span class="p">}</span>
-<a id="__codelineno-21-55" name="__codelineno-21-55" href="#__codelineno-21-55"></a><span class="w">            </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
+<a id="__codelineno-21-55" name="__codelineno-21-55" href="#__codelineno-21-55"></a><span class="w">            </span><span class="c1">// 计算桶索引，越过尾部则返回头部</span>
 <a id="__codelineno-21-56" name="__codelineno-21-56" href="#__codelineno-21-56"></a><span class="w">            </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">capacity</span><span class="p">;</span>
 <a id="__codelineno-21-57" name="__codelineno-21-57" href="#__codelineno-21-57"></a><span class="w">        </span><span class="p">}</span>
 <a id="__codelineno-21-58" name="__codelineno-21-58" href="#__codelineno-21-58"></a><span class="w">        </span><span class="c1">// 若 key 不存在，则返回添加点的索引</span>
@@ -6261,9 +6261,9 @@
 <a id="__codelineno-22-50" name="__codelineno-22-50" href="#__codelineno-22-50"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
 <a id="__codelineno-22-51" name="__codelineno-22-51" href="#__codelineno-22-51"></a><span class="w">    </span><span class="c1">// 线性探测，当遇到空桶时跳出</span>
 <a id="__codelineno-22-52" name="__codelineno-22-52" href="#__codelineno-22-52"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-22-53" name="__codelineno-22-53" href="#__codelineno-22-53"></a><span class="w">        </span><span class="c1">// 若遇到 key ，返回对应桶索引</span>
+<a id="__codelineno-22-53" name="__codelineno-22-53" href="#__codelineno-22-53"></a><span class="w">        </span><span class="c1">// 若遇到 key ，返回对应的桶索引</span>
 <a id="__codelineno-22-54" name="__codelineno-22-54" href="#__codelineno-22-54"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-22-55" name="__codelineno-22-55" href="#__codelineno-22-55"></a><span class="w">            </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引</span>
+<a id="__codelineno-22-55" name="__codelineno-22-55" href="#__codelineno-22-55"></a><span class="w">            </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引处</span>
 <a id="__codelineno-22-56" name="__codelineno-22-56" href="#__codelineno-22-56"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-22-57" name="__codelineno-22-57" href="#__codelineno-22-57"></a><span class="w">                </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
 <a id="__codelineno-22-58" name="__codelineno-22-58" href="#__codelineno-22-58"></a><span class="w">                </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="p">;</span>
@@ -6275,7 +6275,7 @@
 <a id="__codelineno-22-64" name="__codelineno-22-64" href="#__codelineno-22-64"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-22-65" name="__codelineno-22-65" href="#__codelineno-22-65"></a><span class="w">            </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
 <a id="__codelineno-22-66" name="__codelineno-22-66" href="#__codelineno-22-66"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-22-67" name="__codelineno-22-67" href="#__codelineno-22-67"></a><span class="w">        </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
+<a id="__codelineno-22-67" name="__codelineno-22-67" href="#__codelineno-22-67"></a><span class="w">        </span><span class="c1">// 计算桶索引，越过尾部则返回头部</span>
 <a id="__codelineno-22-68" name="__codelineno-22-68" href="#__codelineno-22-68"></a><span class="w">        </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">hashMap</span><span class="o">-&gt;</span><span class="n">capacity</span><span class="p">;</span>
 <a id="__codelineno-22-69" name="__codelineno-22-69" href="#__codelineno-22-69"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-22-70" name="__codelineno-22-70" href="#__codelineno-22-70"></a><span class="w">    </span><span class="c1">// 若 key 不存在，则返回添加点的索引</span>
@@ -6392,8 +6392,8 @@
 <h3 id="3">3. &nbsp; 多次哈希<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
 <p>顾名思义，多次哈希方法使用多个哈希函数 <span class="arithmatex">\(f_1(x)\)</span>、<span class="arithmatex">\(f_2(x)\)</span>、<span class="arithmatex">\(f_3(x)\)</span>、<span class="arithmatex">\(\dots\)</span> 进行探测。</p>
 <ul>
-<li><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，直到找到空桶后插入元素。</li>
-<li><strong>查找元素</strong>：在相同的哈希函数顺序下进行查找，直到找到目标元素时返回；若遇到空桶或已尝试所有哈希函数，说明哈希表中不存在该元素，则返回 <span class="arithmatex">\(\text{None}\)</span> 。</li>
+<li><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。</li>
+<li><strong>查找元素</strong>：在相同的哈希函数顺序下进行查找，直到找到目标元素时返回；若遇到空位或已尝试所有哈希函数，说明哈希表中不存在该元素，则返回 <code>None</code> 。</li>
 </ul>
 <p>与线性探测相比，多次哈希方法不易产生聚集，但多个哈希函数会带来额外的计算量。</p>
 <div class="admonition tip">
@@ -6403,9 +6403,9 @@
 <h2 id="623">6.2.3 &nbsp; 编程语言的选择<a class="headerlink" href="#623" title="Permanent link">&para;</a></h2>
 <p>各种编程语言采取了不同的哈希表实现策略，下面举几个例子。</p>
 <ul>
-<li>Python 采用开放寻址。字典 dict 使用伪随机数进行探测。</li>
-<li>Java 采用链式地址。自 JDK 1.8 以来，当 HashMap 内数组长度达到 64 且链表长度达到 8 时，链表会转换为红黑树以提升查找性能。</li>
-<li>Go 采用链式地址。Go 规定每个桶最多存储 8 个键值对，超出容量则连接一个溢出桶。当溢出桶过多时，会执行一次特殊的等量扩容操作，以确保性能。</li>
+<li>Python 采用开放寻址。字典 <code>dict</code> 使用伪随机数进行探测。</li>
+<li>Java 采用链式地址。自 JDK 1.8 以来，当 <code>HashMap</code> 内数组长度达到 64 且链表长度达到 8 时，链表会转换为红黑树以提升查找性能。</li>
+<li>Go 采用链式地址。Go 规定每个桶最多存储 8 个键值对，超出容量则连接一个溢出桶；当溢出桶过多时，会执行一次特殊的等量扩容操作，以确保性能。</li>
 </ul>
 
 <!-- Source file information -->

chapter_hashing/hash_map/index.html

@@ -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 -->

chapter_hashing/index.html

@@ -1721,7 +1721,7 @@
         
   
   <span class="md-ellipsis">
-    8.3 &nbsp; Top-K 问题
+    8.3 &nbsp; Top-k 问题
   </span>
   
 

chapter_hashing/summary/index.html

@@ -1779,7 +1779,7 @@
         
   
   <span class="md-ellipsis">
-    8.3 &nbsp; Top-K 问题
+    8.3 &nbsp; Top-k 问题
   </span>
   
 
@@ -3556,7 +3556,7 @@
 </div>
 <div class="admonition question">
 <p class="admonition-title">为什么哈希表扩容能够缓解哈希冲突？</p>
-<p>哈希函数的最后一步往往是对数组长度 <span class="arithmatex">\(n\)</span> 取余，让输出值落在数组索引范围内；在扩容后，数组长度 <span class="arithmatex">\(n\)</span> 发生变化，而 <code>key</code> 对应的索引也可能发生变化。原先落在同一个桶的多个 <code>key</code> ，在扩容后可能会被分配到多个桶中，从而实现哈希冲突的缓解。</p>
+<p>哈希函数的最后一步往往是对数组长度 <span class="arithmatex">\(n\)</span> 取模（取余），让输出值落在数组索引范围内；在扩容后，数组长度 <span class="arithmatex">\(n\)</span> 发生变化，而 <code>key</code> 对应的索引也可能发生变化。原先落在同一个桶的多个 <code>key</code> ，在扩容后可能会被分配到多个桶中，从而实现哈希冲突的缓解。</p>
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