build_notes_simengweb/assets/index.html-CrJDOkEe.js

import{_ as i,c as a,a as n,o as t}from"./app-CyezZKiD.js";const e={};function l(p,s){return t(),a("div",null,[...s[0]||(s[0]=[n(`<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>&quot;abc&quot;</code> 的子序列包括 <code>&quot;a&quot;</code>, <code>&quot;b&quot;</code>, <code>&quot;c&quot;</code>, <code>&quot;ab&quot;</code>, <code>&quot;ac&quot;</code>, <code>&quot;bc&quot;</code>, <code>&quot;abc&quot;</code> 和空字符串 <code>&quot;&quot;</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>&quot;abc&quot;</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 &quot;a&quot; 和第 3 个字符 &quot;c&quot;</td><td style="text-align:left;"><code>&quot;ac&quot;</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 &quot;b&quot;</td><td style="text-align:left;"><code>&quot;b&quot;</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>&quot;&quot;</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 &amp; (1 &lt;&lt; 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>
<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;"> &lt;&lt;</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;">&amp;</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;"> &lt;&lt;</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;">&#39;&#39;</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>
<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;">&quot;</span><span style="--shiki-light:#B56959;--shiki-dark:#C98A7D;">abc</span><span style="--shiki-light:#B5695977;--shiki-dark:#C98A7D77;">&quot;</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">))</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># 输出: [&#39;a&#39;, &#39;b&#39;, &#39;ab&#39;, &#39;c&#39;, &#39;ac&#39;, &#39;bc&#39;, &#39;abc&#39;]</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>
<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>
<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;"> &lt;&lt;</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;"> &quot;&quot;</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;">&amp;</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;"> &lt;&lt;</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>
<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>`,21)])])}const k=i(e,[["render",l]]),d=JSON.parse('{"path":"/archives/ea20bdda-0d49-4472-a647-2e305a930d11/","title":"通过位运算快速生成所有的子序列","lang":"zh-CN","frontmatter":{"title":"通过位运算快速生成所有的子序列","createTime":"2026/01/09 16:15:00","cover":"/images/elysia/10.jpg","coverStyle":{"layout":"right"},"permalink":"/archives/ea20bdda-0d49-4472-a647-2e305a930d11/","description":"一、子序列的本质 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。 例如：原字符串 \\"abc\\" 的子序列包括 \\"a\\", \\"b\\", \\"c\\", \\"ab\\", \\"ac\\", \\"bc\\", \\"abc\\" 和空字符串 \\"\\"（共 23=8 种可能性）。 二、位掩码（Bitmask）的引入 假设字符串...","head":[["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"通过位运算快速生成所有的子序列\\",\\"image\\":[\\"https://www.simengweb.com/images/elysia/10.jpg\\"],\\"dateModified\\":\\"2026-01-09T08:42:22.000Z\\",\\"author\\":[]}"],["meta",{"property":"og:url","content":"https://www.simengweb.com/archives/ea20bdda-0d49-4472-a647-2e305a930d11/"}],["meta",{"property":"og:site_name","content":"仲夏夜之梦"}],["meta",{"property":"og:title","content":"通过位运算快速生成所有的子序列"}],["meta",{"property":"og:description","content":"一、子序列的本质 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。 例如：原字符串 \\"abc\\" 的子序列包括 \\"a\\", \\"b\\", \\"c\\", \\"ab\\", \\"ac\\", \\"bc\\", \\"abc\\" 和空字符串 \\"\\"（共 23=8 种可能性）。 二、位掩码（Bitmask）的引入 假设字符串..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:image","content":"https://www.simengweb.com/images/elysia/10.jpg"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"og:updated_time","content":"2026-01-09T08:42:22.000Z"}],["meta",{"name":"twitter:card","content":"summary_large_image"}],["meta",{"name":"twitter:image:src","content":"https://www.simengweb.com/images/elysia/10.jpg"}],["meta",{"name":"twitter:image:alt","content":"通过位运算快速生成所有的子序列"}],["meta",{"property":"article:modified_time","content":"2026-01-09T08:42:22.000Z"}]]},"readingTime":{"minutes":2.22,"words":667},"git":{"createdTime":1767948142000,"updatedTime":1767948142000,"contributors":[{"name":"祀梦","username":"","email":"3501646051@qq.com","commits":1,"avatar":"https://gravatar.com/avatar/6406a81eeddc359cf3d3ce018797689fc6d014ff06215c27d0210b42e8f5a8ab?d=retro"}]},"autoDesc":true,"filePathRelative":"blog/technology/bitwise-subsequences.md","headers":[],"categoryList":[{"id":"126ac9","sort":10000,"name":"blog"},{"id":"750eb7","sort":10005,"name":"technology"}]}');export{k as comp,d as data};