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typeof="WebPage" data-v-1ae4ad7a><!--[-->通过位运算快速生成所有的子序列<!--]--><!----></a><!----><meta property="name" content="通过位运算快速生成所有的子序列" data-v-1ae4ad7a><meta property="position" content="5" data-v-1ae4ad7a></li><!--]--></ol></nav><!--[--><!--]--><!--[--><h1 class="vp-doc-title page-title" data-v-ba8d1a1e><!----> 通过位运算快速生成所有的子序列 <!----></h1><div class="vp-doc-meta" data-v-ba8d1a1e><!--[--><!--]--><p class="reading-time" data-v-ba8d1a1e><span class="vpi-books icon" data-v-ba8d1a1e></span><span data-v-ba8d1a1e>约 667 字</span><span data-v-ba8d1a1e>大约 2 分钟</span></p><!----><!--[--><!--]--><p class="create-time" data-v-ba8d1a1e><span class="vpi-clock icon" data-v-ba8d1a1e></span><span data-v-ba8d1a1e>2026-01-09</span></p></div><!--]--><!--[--><!--]--><div class="_archives_ea20bdda-0d49-4472-a647-2e305a930d11_ external-link-icon-enabled vp-doc plume-content" vp-content data-v-23f6ad98><!--[--><!--]--><div data-v-23f6ad98><h2 id="一、子序列的本质" tabindex="-1"><a class="header-anchor" href="#一、子序列的本质"><span>一、子序列的本质</span></a></h2><p>子序列是从原字符串中选择任意数量的字符（可以是 0 个、1 个、...、所有字符），且保持这些字符的原始顺序形成的字符串。</p><p>例如：原字符串 <code>"abc"</code> 的子序列包括 <code>"a"</code>, <code>"b"</code>, <code>"c"</code>, <code>"ab"</code>, <code>"ac"</code>, <code>"bc"</code>, <code>"abc"</code> 和空字符串 <code>""</code>（共 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>2</mn><mn>3</mn></msup><mo>=</mo><mn>8</mn></mrow><annotation encoding="application/x-tex">2^3 = 8</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">8</span></span></span></span> 种可能性）。</p><h2 id="二、位掩码-bitmask-的引入" tabindex="-1"><a class="header-anchor" href="#二、位掩码-bitmask-的引入"><span>二、位掩码（Bitmask）的引入</span></a></h2><p>假设字符串长度为 <code>n</code>，我们可以用一个 <code>n</code> 位的二进制数来表示是否选择某个字符：</p><ul><li>二进制数的每一位对应原字符串的一个字符。</li><li>如果某一位是 <code>1</code>，表示选择对应的字符；如果是 <code>0</code>，表示不选择。</li></ul><p>例如，对于字符串 <code>"abc"</code>（<code>n=3</code>）：</p><table><thead><tr><th style="text-align:left;">二进制数</th><th style="text-align:left;">十进制</th><th style="text-align:left;">选择情况</th><th style="text-align:left;">生成子序列</th></tr></thead><tbody><tr><td style="text-align:left;"><code>101</code></td><td style="text-align:left;">5</td><td style="text-align:left;">选择第 1 个字符 "a" 和第 3 个字符 "c"</td><td style="text-align:left;"><code>"ac"</code></td></tr><tr><td style="text-align:left;"><code>010</code></td><td style="text-align:left;">2</td><td style="text-align:left;">选择第 2 个字符 "b"</td><td style="text-align:left;"><code>"b"</code></td></tr></tbody></table><h2 id="三、遍历所有可能的二进制数" tabindex="-1"><a class="header-anchor" href="#三、遍历所有可能的二进制数"><span>三、遍历所有可能的二进制数</span></a></h2><p>所有可能的二进制数范围是 <code>0</code>（全 0）到 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">2^n - 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7477em;vertical-align:-0.0833em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span>（全 1）。例如，<code>n=3</code> 时：</p><ul><li>范围是 <code>000</code> (0) 到 <code>111</code> (7)，共 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>2</mn><mn>3</mn></msup><mo>=</mo><mn>8</mn></mrow><annotation encoding="application/x-tex">2^3 = 8</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">8</span></span></span></span> 种可能。</li><li>每个二进制数对应一种子序列选择方式。</li><li>如果包含 <code>000</code> (0)，对应空字符串 <code>""</code>。若不需要空字符串，可以从 <code>1</code> 开始遍历。</li></ul><h2 id="四、如何将二进制数转换为子序列" tabindex="-1"><a class="header-anchor" href="#四、如何将二进制数转换为子序列"><span>四、如何将二进制数转换为子序列？</span></a></h2><h3 id="_1-外层循环-遍历所有可能的二进制数" tabindex="-1"><a class="header-anchor" href="#_1-外层循环-遍历所有可能的二进制数"><span>1. 外层循环：遍历所有可能的二进制数</span></a></h3><p>对于 <code>n=3</code>，遍历 <code>1</code> (<code>001</code>) 到 <code>7</code> (<code>111</code>)。</p><h3 id="_2-内层循环-检查每一位是否为-1" tabindex="-1"><a class="header-anchor" href="#_2-内层循环-检查每一位是否为-1"><span>2. 内层循环：检查每一位是否为 1</span></a></h3><ul><li>对于每个二进制数 <code>mask</code>，遍历其每一位 <code>i</code>（从 <code>0</code> 到 <code>n-1</code>）。</li><li>如果 <code>mask</code> 的第 <code>i</code> 位是 <code>1</code>（即 <code>mask & (1 << i)</code> 为真），则将原字符串的第 <code>i</code> 个字符加入子序列。</li></ul><h2 id="五、代码示例" tabindex="-1"><a class="header-anchor" href="#五、代码示例"><span>五、代码示例</span></a></h2><div class="language-python line-numbers-mode" data-highlighter="shiki" data-ext="python" style="--shiki-light:#393a34;--shiki-dark:#dbd7caee;--shiki-light-bg:#ffffff;--shiki-dark-bg:#121212;"><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code class="language-python"><span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">def</span><span style="--shiki-light:#59873A;--shiki-dark:#80A665;"> get_all_subsequences</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">s</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">):</span></span>
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||
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> n </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> len</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">s</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span></span>
|
||
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> subsequences </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> []</span></span>
|
||
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"> # 遍历 1 到 2^n - 1 (排除空字符串)</span></span>
|
||
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mask </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> <<</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> n</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">):</span></span>
|
||
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> subseq </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> []</span></span>
|
||
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> i </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">n</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">):</span></span>
|
||
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"> # 检查 mask 的第 i 位是否为 1</span></span>
|
||
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> if</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mask </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">&</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> <<</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> i</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">):</span></span>
|
||
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> subseq</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">.</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">append</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">s</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">i</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">])</span></span>
|
||
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> subsequences</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">.</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">append</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#B5695977;--shiki-dark:#C98A7D77;">''</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">.</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">join</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">subseq</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">))</span></span>
|
||
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> return</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> subsequences</span></span>
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||
<span class="line"></span>
|
||
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># 测试</span></span>
|
||
<span class="line"><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">print</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">get_all_subsequences</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#B5695977;--shiki-dark:#C98A7D77;">"</span><span style="--shiki-light:#B56959;--shiki-dark:#C98A7D;">abc</span><span style="--shiki-light:#B5695977;--shiki-dark:#C98A7D77;">"</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">))</span></span>
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||
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># 输出: ['a', 'b', 'ab', 'c', 'ac', 'bc', 'abc']</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="六、应用场景" tabindex="-1"><a class="header-anchor" href="#六、应用场景"><span>六、应用场景</span></a></h2><p>在处理类似 <strong>X 质数</strong> 的问题时，我们需要检查一个数字的所有数字子序列。通过这种位运算的方式，可以非常高效地生成所有组合并进行判断。</p><div class="language-python line-numbers-mode" data-highlighter="shiki" data-ext="python" style="--shiki-light:#393a34;--shiki-dark:#dbd7caee;--shiki-light-bg:#ffffff;--shiki-dark-bg:#121212;"><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code class="language-python"><span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">def</span><span style="--shiki-light:#59873A;--shiki-dark:#80A665;"> solve_x_prime</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">num</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">):</span></span>
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||
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> s </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> str</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">num</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span></span>
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||
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> n </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> len</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">s</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span></span>
|
||
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mask </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> <<</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> n</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">):</span></span>
|
||
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> subseq_str </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#B5695977;--shiki-dark:#C98A7D77;"> ""</span></span>
|
||
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> i </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">n</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">):</span></span>
|
||
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> if</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mask </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">&</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> <<</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> i</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">):</span></span>
|
||
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> subseq_str </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">+=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> s</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">i</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]</span></span>
|
||
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> </span></span>
|
||
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"> # 将生成的子序列转换为整数并判断是否为质数</span></span>
|
||
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> p </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> int</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">subseq_str</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span></span>
|
||
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> if</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> is_prime</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">p</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">):</span></span>
|
||
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> return</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> True</span></span>
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<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> return</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> False</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div></div><!----><!----><!----></div></main><footer class="vp-doc-footer" data-v-23f6ad98 data-v-7138e2cb><!--[--><!--]--><!----><div class="contributors" aria-label="Contributors" data-v-7138e2cb><span class="contributors-label" data-v-7138e2cb>贡献者: </span><span class="contributors-info" data-v-7138e2cb><!--[--><!--[--><span class="contributor" data-v-7138e2cb>祀梦</span><!----><!--]--><!--]--></span></div><nav class="prev-next" data-v-7138e2cb><div class="pager" data-v-7138e2cb><a class="vp-link link pager-link prev" href="/archives/d0ad06b9-d675-461c-a8ce-f47baeeb291d/" data-v-7138e2cb><!--[--><span class="desc" data-v-7138e2cb>上一页</span><span class="title" data-v-7138e2cb>码蹄杯 2024 年真题集详解</span><!--]--><!----></a></div><div class="pager" data-v-7138e2cb><a class="vp-link link pager-link next" href="/archives/1325a3bf-91d7-43ff-9630-e894549e12c1/" data-v-7138e2cb><!--[--><span class="desc" data-v-7138e2cb>下一页</span><span class="title" data-v-7138e2cb>快速幂算法详解</span><!--]--><!----></a></div></nav></footer><div id="comment" class="waline-wrapper vp-comment" vp-comment darkmode="false" style="display:block;" data-v-23f6ad98><!----></div><!--[--><!--]--></div></div></div><!--[--><!--]--></div></div><!--]--><button style="display:none;" type="button" class="vp-back-to-top" aria-label="back to top" data-v-f73ca3da data-v-bcf8d9a6><span class="percent" data-allow-mismatch data-v-bcf8d9a6>0%</span><span class="show icon vpi-back-to-top" data-v-bcf8d9a6></span><svg aria-hidden="true" data-v-bcf8d9a6><circle cx="50%" cy="50%" data-allow-mismatch style="stroke-dasharray:calc(0% - 12.566370614359172px) calc(314.1592653589793% - 12.566370614359172px);" data-v-bcf8d9a6></circle></svg></button><svg style="display:none;" xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewbox="0 0 24 24" aria-label="sign down" class="vp-sign-down" aria-hidden="true" data-v-f73ca3da data-v-900978de><g fill="none" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round" stroke-width="2.5" data-v-900978de><path d="m19 11l-7 6l-7-6" data-v-900978de></path><path d="m19 5l-7 6l-7-6" opacity="0.6" data-v-900978de></path></g></svg><footer class="vp-footer" vp-footer data-v-f73ca3da data-v-400675cf><!--[--><div class="container" data-v-400675cf><p class="message" data-v-400675cf>愿每一份温柔都被世界珍藏 ✨</p><p class="copyright" data-v-400675cf><a href="https://beian.miit.gov.cn/" target="_blank" aria-label="gongan filing address">沪ICP备2023010022号-1</a>©2025祀梦的个人博客</p></div><!--]--></footer><!--[--><!--]--><!--]--></div><!----><!--]--><!--[--><!--]--><!--]--></div><script type="module" src="/assets/app-CyezZKiD.js" defer></script></body></html> |