deploy

2025-07-07 06:44:57 +08:00 · 2023-06-21 19:26:17 +08:00
parent 4ed0a98f0a
commit 24541c53f1
5 changed files with 206 additions and 96 deletions
--- a/chapter_hashing/hash_algorithm/index.html
+++ b/chapter_hashing/hash_algorithm/index.html
@ -2183,23 +2183,89 @@
 <div class="tabbed-set tabbed-alternate" data-tabs="1:11"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Java</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Python</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">JavaScript</label><label for="__tabbed_1_6">TypeScript</label><label for="__tabbed_1_7">C</label><label for="__tabbed_1_8">C#</label><label for="__tabbed_1_9">Swift</label><label for="__tabbed_1_10">Zig</label><label for="__tabbed_1_11">Dart</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">simple_hash.java</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="o">[</span><span class="kd">class</span><span class="err">]{</span><span class="nc">simple_hash</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">addHash</span><span class="p">}</span>
-<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a>
-<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="o">[</span><span class="kd">class</span><span class="err">]{</span><span class="nc">simple_hash</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">mulHash</span><span class="p">}</span>
-<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a>
-<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="o">[</span><span class="kd">class</span><span class="err">]{</span><span class="nc">simple_hash</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">xorHash</span><span class="p">}</span>
-<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a>
-<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="o">[</span><span class="kd">class</span><span class="err">]{</span><span class="nc">simple_hash</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">rotHash</span><span class="p">}</span>
+<div class="highlight"><span class="filename">simple_hash.java</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 加法哈希 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">addHash</span><span class="p">(</span><span class="n">String</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-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="p">}</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="cm">/* 乘法哈希 */</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">mulHash</span><span class="p">(</span><span class="n">String</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-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="p">}</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="cm">/* 异或哈希 */</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">xorHash</span><span class="p">(</span><span class="n">String</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-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">((</span><span class="kt">int</span><span class="p">)</span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">c</span><span class="p">;</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="p">}</span>
+<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a>
+<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="cm">/* 旋转哈希 */</span>
+<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="kt">int</span><span class="w"> </span><span class="nf">rotHash</span><span class="p">(</span><span class="n">String</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-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</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="p">}</span>
+<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">simple_hash.cpp</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">addHash</span><span class="p">}</span>
-<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a>
-<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">mulHash</span><span class="p">}</span>
-<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>
-<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">xorHash</span><span class="p">}</span>
-<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a>
-<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotHash</span><span class="p">}</span>
+<div class="highlight"><span class="filename">simple_hash.cpp</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 加法哈希 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">addHash</span><span class="p">(</span><span class="n">string</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-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="n">c</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-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="p">}</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="cm">/* 乘法哈希 */</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">mulHash</span><span class="p">(</span><span class="n">string</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-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="n">c</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-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="p">}</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="cm">/* 异或哈希 */</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">xorHash</span><span class="p">(</span><span class="n">string</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-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="n">c</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-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">        </span><span class="n">cout</span><span class="o">&lt;&lt;</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">c</span><span class="o">&lt;&lt;</span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">c</span><span class="p">;</span>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="p">}</span>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a>
+<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="cm">/* 旋转哈希 */</span>
+<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="kt">int</span><span class="w"> </span><span class="nf">rotHash</span><span class="p">(</span><span class="n">string</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-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</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="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</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="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="n">c</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-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</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="p">}</span>
+<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a><span class="p">}</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
@ -2398,14 +2464,57 @@
 <li>元组的哈希值是对其中每一个元素进行哈希，然后将这些哈希值组合起来，得到单一的哈希值。</li>
 <li>对象的哈希值基于其内存地址生成。通过重写对象的哈希方法，可实现基于内容生成哈希值。</li>
 </ul>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>请注意，不同编程语言的内置哈希值计算函数的定义和方法不同。</p>
+</div>
 <div class="tabbed-set tabbed-alternate" data-tabs="2:11"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Java</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Python</label><label for="__tabbed_2_4">Go</label><label for="__tabbed_2_5">JavaScript</label><label for="__tabbed_2_6">TypeScript</label><label for="__tabbed_2_7">C</label><label for="__tabbed_2_8">C#</label><label for="__tabbed_2_9">Swift</label><label for="__tabbed_2_10">Zig</label><label for="__tabbed_2_11">Dart</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">built_in_hash.java</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
+<div class="highlight"><span class="filename">built_in_hash.java</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Integer</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="c1">// 整数 3 的哈希值为 3</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Boolean</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">bol</span><span class="p">);</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="c1">// 布尔量 true 的哈希值为 1231</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="kt">double</span><span class="w"> </span><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3.14159</span><span class="p">;</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Double</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">dec</span><span class="p">);</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="c1">// 小数 3.14159 的哈希值为 -1340954729</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="n">String</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span><span class="p">;</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str</span><span class="p">.</span><span class="na">hashCode</span><span class="p">();</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="c1">// 字符串 Hello 算法 的哈希值为 -727081396</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="n">Object</span><span class="o">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="w"> </span><span class="p">};</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashTup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">arr</span><span class="p">);</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="c1">// 数组 [12836, 小哈] 的哈希值为 1151158</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">obj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashObj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">obj</span><span class="p">.</span><span class="na">hashCode</span><span class="p">();</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="c1">// 节点对象 utils.ListNode@7dc5e7b4 的哈希值为 2110121908</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">built_in_hash.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a>
+<div class="highlight"><span class="filename">built_in_hash.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="c1">// 整数 3 的哈希值为 3</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">bol</span><span class="p">);</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="c1">// 布尔量 1 的哈希值为 1</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="kt">double</span><span class="w"> </span><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3.14159</span><span class="p">;</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="kt">double</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">dec</span><span class="p">);</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="c1">// 小数 3.14159 的哈希值为 4614256650576692846</span>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>
+<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="n">string</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span><span class="p">;</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">str</span><span class="p">);</span>
+<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="c1">// 字符串 Hello 算法 的哈希值为 15466937326284535026</span>
+<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>
+<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a><span class="c1">// 在 C++ 中，内置 std:hash() 仅提供基本数据类型的哈希值计算</span>
+<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a><span class="c1">// 数组、对象的哈希值计算需要自行实现</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">