<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>C++ on kenji.blog</title><link>http://kenji.blog/zh-tw/tags/c++/</link><description>Recent content in C++ on kenji.blog</description><generator>Hugo -- gohugo.io</generator><language>zh-tw</language><copyright>kenjinote</copyright><lastBuildDate>Sat, 05 Sep 2026 13:04:59 +0900</lastBuildDate><atom:link href="http://kenji.blog/zh-tw/tags/c++/index.xml" rel="self" type="application/rss+xml"/><item><title>【完全解剖】最強密碼破解演算法「GNFS」C++實作與理解</title><link>http://kenji.blog/zh-tw/p/gnfs-cpp-implementation/</link><pubDate>Sat, 05 Sep 2026 13:04:59 +0900</pubDate><guid>http://kenji.blog/zh-tw/p/gnfs-cpp-implementation/</guid><description>&lt;img src="http://kenji.blog/p/gnfs-cpp-implementation/gnfs_cpp_blog_eyecatch_1788580949217.jpg" alt="Featured image of post 【完全解剖】最強密碼破解演算法「GNFS」C++實作與理解" />&lt;h1 id="完全解剖最強密碼破解演算法gnfsc實作與理解">【完全解剖】最強密碼破解演算法「GNFS」C++實作與理解
&lt;/h1>&lt;p>支撐現代網際網路基礎的「RSA密碼學」，其堅固性仰賴於一個數學信念：「在目前的電腦技術下，要對巨大的合成數進行質因數分解實際上是不可能的」。&lt;/p>
&lt;p>然而，人類從未放棄。目前在古典電腦（非量子電腦的一般電腦）上，存在著用於進行巨大質因數分解的 &lt;strong>人類最強、最尖端的演算法&lt;/strong> 。那就是 &lt;strong>「普通數體篩法（GNFS：General Number Field Sieve）」&lt;/strong> 。&lt;/p>
&lt;p>在本篇文章中，我們將完全公開這個 GNFS 最尖端計算邏輯的 C++ 實作程式碼（使用 Boost 函式庫的多精度整數 &lt;code>boost::multiprecision&lt;/code> 進行嚴格建模），並徹底解說其背後「代數整數論」的深淵。&lt;/p>
&lt;p>請務必與原始碼一起，盡情品味數學的神秘以及用電腦科學暴力屈服它的力量。&lt;/p>
&lt;hr>
&lt;h2 id="1-gnfs-最尖端邏輯框架完整原始碼">1. GNFS 最尖端邏輯・框架（完整原始碼）
&lt;/h2>&lt;p>首先，列出本次解說的 GNFS C++ 實作全貌。實際的數體篩法（如 CADO-NFS 等）是高達數十萬行程式碼的超巨大分散式系統，但本程式碼提取了構成 GNFS 的 &lt;strong>「5個必須的管線（階段）」&lt;/strong> 進行類別設計，並在不失去數學意義的前提下，以最小配置進行了建模。&lt;/p>
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&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;iostream&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;vector&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;cmath&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;map&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;set&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;chrono&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;boost/multiprecision/cpp_int.hpp&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// 使用 Boost.Multiprecision 的多精度整數
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">boost&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">multiprecision&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// ============================================================================
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// [SOTA GNFS] General Number Field Sieve (普通數體篩法) 最尖端邏輯框架
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">//
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// 本程式碼將 CADO-NFS 等所使用的最尖端 GNFS 的 5 個管線
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// 嚴格建模為 C++ (Boost) 的類別設計。
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// ============================================================================
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">struct&lt;/span> &lt;span class="nc">Relation&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="kt">int64_t&lt;/span> &lt;span class="n">a&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="kt">int64_t&lt;/span> &lt;span class="n">b&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="kt">uint32_t&lt;/span>&lt;span class="o">&amp;gt;&lt;/span> &lt;span class="n">rational_primes&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="kt">uint32_t&lt;/span>&lt;span class="o">&amp;gt;&lt;/span> &lt;span class="n">algebraic_primes&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// ============================================================================
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// Phase 1: Polynomial Selection (KleinJung 演算法)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// ============================================================================
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>&lt;span class="k">class&lt;/span> &lt;span class="nc">PolynomialSelector&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">public&lt;/span>&lt;span class="o">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="kt">int&lt;/span> &lt;span class="n">degree&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">cpp_int&lt;/span>&lt;span class="o">&amp;gt;&lt;/span> &lt;span class="n">f&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="c1">// 代數側多項式 f(x)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">cpp_int&lt;/span>&lt;span class="o">&amp;gt;&lt;/span> &lt;span class="n">g&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="c1">// 有理側多項式 g(x) = x - m
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">cpp_int&lt;/span> &lt;span class="n">m&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">PolynomialSelector&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="kt">int&lt;/span> &lt;span class="n">d&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="o">:&lt;/span> &lt;span class="n">degree&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">d&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 基於 base-m 展開產生初始多項式 (實際上會使用更高階的晶格基底歸約 LLL)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="kt">void&lt;/span> &lt;span class="nf">select&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="k">const&lt;/span> &lt;span class="n">cpp_int&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="n">N&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;[Phase 1] Polynomial Selection (Degree &amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">degree&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;) starting...&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 簡易的 base-m 展開 (d次)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// m = N^(1/d)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">cpp_int&lt;/span> &lt;span class="n">N_copy&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">N&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">m&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 簡易的 m 近似值計算 (不使用 Boost 函式的近似)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">cpp_int&lt;/span> &lt;span class="n">low&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">high&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">N&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">while&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">low&lt;/span> &lt;span class="o">&amp;lt;=&lt;/span> &lt;span class="n">high&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">cpp_int&lt;/span> &lt;span class="n">mid&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">low&lt;/span> &lt;span class="o">+&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">high&lt;/span> &lt;span class="o">-&lt;/span> &lt;span class="n">low&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="o">/&lt;/span> &lt;span class="mi">2&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">cpp_int&lt;/span> &lt;span class="n">p&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">for&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="kt">int&lt;/span> &lt;span class="n">i&lt;/span>&lt;span class="o">=&lt;/span>&lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="n">i&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">degree&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="o">++&lt;/span>&lt;span class="n">i&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="n">p&lt;/span> &lt;span class="o">*=&lt;/span> &lt;span class="n">mid&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">p&lt;/span> &lt;span class="o">&amp;lt;=&lt;/span> &lt;span class="n">N&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span> &lt;span class="n">m&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">mid&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="n">low&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">mid&lt;/span> &lt;span class="o">+&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">else&lt;/span> &lt;span class="p">{&lt;/span> &lt;span class="n">high&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">mid&lt;/span> &lt;span class="o">-&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">f&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">resize&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">degree&lt;/span> &lt;span class="o">+&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">cpp_int&lt;/span> &lt;span class="n">temp&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">N&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">for&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="kt">int&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">&amp;lt;=&lt;/span> &lt;span class="n">degree&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="o">++&lt;/span>&lt;span class="n">i&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">f&lt;/span>&lt;span class="p">[&lt;/span>&lt;span class="n">i&lt;/span>&lt;span class="p">]&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">temp&lt;/span> &lt;span class="o">%&lt;/span> &lt;span class="n">m&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">temp&lt;/span> &lt;span class="o">/=&lt;/span> &lt;span class="n">m&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">g&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="p">{&lt;/span>&lt;span class="o">-&lt;/span>&lt;span class="n">m&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">};&lt;/span> &lt;span class="c1">// g(x) = x - m
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34; -&amp;gt; m = &amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">m&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34; -&amp;gt; f(x) = &amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">for&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="kt">int&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">degree&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">&amp;gt;=&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="o">--&lt;/span>&lt;span class="n">i&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">f&lt;/span>&lt;span class="p">[&lt;/span>&lt;span class="n">i&lt;/span>&lt;span class="p">]&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;x^&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">i&lt;/span> &lt;span class="o">&amp;gt;&lt;/span> &lt;span class="mi">0&lt;/span> &lt;span class="o">?&lt;/span> &lt;span class="s">&amp;#34; + &amp;#34;&lt;/span> &lt;span class="o">:&lt;/span> &lt;span class="s">&amp;#34;&amp;#34;&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;&lt;/span>&lt;span class="se">\n&lt;/span>&lt;span class="s">[Phase 1] Complete.&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// ============================================================================
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// Phase 2: Lattice Sieving (晶格篩法)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// ============================================================================
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// 近年的 GNFS 已不再使用 Line Sieve (直線篩法)，而是以 Franke-Kleinjung 等人的
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// 特殊 q 晶格篩法 (Special-q Lattice Sieving) 為業界標準。
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>&lt;span class="k">class&lt;/span> &lt;span class="nc">LatticeSieve&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="kt">uint32_t&lt;/span> &lt;span class="n">rational_bound&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="kt">uint32_t&lt;/span> &lt;span class="n">algebraic_bound&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="kt">uint32_t&lt;/span>&lt;span class="o">&amp;gt;&lt;/span> &lt;span class="n">rational_fb&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="kt">uint32_t&lt;/span>&lt;span class="o">&amp;gt;&lt;/span> &lt;span class="n">algebraic_fb&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">public&lt;/span>&lt;span class="o">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">LatticeSieve&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="kt">uint32_t&lt;/span> &lt;span class="n">rb&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="kt">uint32_t&lt;/span> &lt;span class="n">ab&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="o">:&lt;/span> &lt;span class="n">rational_bound&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">rb&lt;/span>&lt;span class="p">),&lt;/span> &lt;span class="n">algebraic_bound&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">ab&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="kt">void&lt;/span> &lt;span class="nf">generate_factor_bases&lt;/span>&lt;span class="p">()&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;[Phase 2] Generating Factor Bases (Rational Bound: &amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">rational_bound&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;, Algebraic Bound: &amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">algebraic_bound&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;)&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// (省略) 實際上會進行質數生成與勒讓德符號等的篩選
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">Relation&lt;/span>&lt;span class="o">&amp;gt;&lt;/span> &lt;span class="n">sieve&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="k">const&lt;/span> &lt;span class="n">PolynomialSelector&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="n">poly&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;[Phase 2] Special-q Lattice Sieving active...&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">Relation&lt;/span>&lt;span class="o">&amp;gt;&lt;/span> &lt;span class="n">relations&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 模擬實作：實際的晶格篩法會以區塊為單位掃描數百 GB 的記憶體空間
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// 將 (a, b) 的數對映射到每個特殊質數 q 的晶格 (a = i*q + j*...) 上，
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// 執行將快取效率提升到極限的篩法 (Sieve)。
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 為了展示，加入一個虛擬的 Relation (關係)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">Relation&lt;/span> &lt;span class="n">r&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="n">r&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">a&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">17&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="n">r&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">b&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">3&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">r&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">rational_primes&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="p">{&lt;/span>&lt;span class="mi">2&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">5&lt;/span>&lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">r&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">algebraic_primes&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="p">{&lt;/span>&lt;span class="mi">3&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">7&lt;/span>&lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">relations&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">push_back&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">r&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;[Phase 2] Found &amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">relations&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">size&lt;/span>&lt;span class="p">()&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34; relations.&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="n">relations&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// ============================================================================
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// Phase 3: Filtering (奇異點清除與派系合併)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// ============================================================================
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>&lt;span class="k">class&lt;/span> &lt;span class="nc">Filter&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">public&lt;/span>&lt;span class="o">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="kt">void&lt;/span> &lt;span class="n">reduce_matrix&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">Relation&lt;/span>&lt;span class="o">&amp;gt;&amp;amp;&lt;/span> &lt;span class="n">relations&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;[Phase 3] Filtering Relations...&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 1. Singleton removal (刪除只出現過一次的質數的 Relation)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// 2. Clique merging (為使稀疏矩陣變密集而合併 Relation)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// 實際上會使用 Union-Find 等演算法，將數億行的矩陣壓縮到數百萬行。
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;[Phase 3] Matrix size reduced optimally.&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// ============================================================================
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// Phase 4: Linear Algebra over GF(2) (Block Wiedemann 法)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// ============================================================================
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>&lt;span class="k">class&lt;/span> &lt;span class="nc">LinearAlgebraGF2&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">public&lt;/span>&lt;span class="o">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 在近年的超級電腦環境中，相較於 Block Lanczos 法，更適合分散式運算的
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// Block Wiedemann 法 (Coppersmith 實作) 被作為最尖端技術使用。
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="kt">int&lt;/span>&lt;span class="o">&amp;gt;&amp;gt;&lt;/span> &lt;span class="n">solve_nullspace&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="k">const&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">Relation&lt;/span>&lt;span class="o">&amp;gt;&amp;amp;&lt;/span> &lt;span class="n">relations&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;[Phase 4] Block Wiedemann algorithm over GF(2) starting...&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 反覆進行稀疏矩陣 (Sparse Matrix) 與向量的乘法運算，
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// 找到多個滿足 M * x = 0 mod 2 的解向量 (核, Kernel)。
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="kt">int&lt;/span>&lt;span class="o">&amp;gt;&amp;gt;&lt;/span> &lt;span class="n">dependencies&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="c1">// 依賴關係列表
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// 虛擬資料
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">dependencies&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">push_back&lt;/span>&lt;span class="p">({&lt;/span>&lt;span class="mi">0&lt;/span>&lt;span class="p">});&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;[Phase 4] Found &amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">dependencies&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">size&lt;/span>&lt;span class="p">()&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34; linear dependencies (perfect squares).&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="n">dependencies&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// ============================================================================
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// Phase 5: Algebraic Square Root (代數平方根)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// ============================================================================
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>&lt;span class="k">class&lt;/span> &lt;span class="nc">AlgebraicSquareRoot&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">public&lt;/span>&lt;span class="o">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="kt">void&lt;/span> &lt;span class="n">compute_and_factor&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="k">const&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">Relation&lt;/span>&lt;span class="o">&amp;gt;&amp;amp;&lt;/span> &lt;span class="n">relations&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="k">const&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="kt">int&lt;/span>&lt;span class="o">&amp;gt;&amp;amp;&lt;/span> &lt;span class="n">dep&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="k">const&lt;/span> &lt;span class="n">cpp_int&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="n">N&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;[Phase 5] Algebraic Square Root computation...&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 1. 有理側的平方根 V 的計算 (單純的整數運算)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">cpp_int&lt;/span> &lt;span class="n">V&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// V = sqrt( prod(a - bm) ) mod N
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 2. 代數側的平方根 gamma 的計算 (Montgomery&amp;#39;s method 等)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// 求出巨大代數體 O_K 的元素 gamma，並透過同態映射 phi 映射到現實世界中
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// Y = phi(gamma) mod N
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">cpp_int&lt;/span> &lt;span class="n">Y&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 為迴避理想類群 (Ideal Class Group) 與單位群 (Unit Group) 的障礙 (Obstruction)，
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// 假設在 Phase 2 與 4 中已經加入了二次剩餘特徵 (Quadratic Characters) 序列。
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34; -&amp;gt; Homomorphism map phi applied.&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;[Phase 5] Calculating GCD(V - Y, N)...&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">cpp_int&lt;/span> &lt;span class="n">factor&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">gcd&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">V&lt;/span> &lt;span class="o">-&lt;/span> &lt;span class="n">Y&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">N&lt;/span>&lt;span class="p">);&lt;/span> &lt;span class="c1">// GCD(X-Y, N)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">factor&lt;/span> &lt;span class="o">&amp;gt;&lt;/span> &lt;span class="mi">1&lt;/span> &lt;span class="o">&amp;amp;&amp;amp;&lt;/span> &lt;span class="n">factor&lt;/span> &lt;span class="o">&amp;lt;&lt;/span> &lt;span class="n">N&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;&lt;/span>&lt;span class="se">\n&lt;/span>&lt;span class="s">================================================================&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;[SUCCESS] Non-trivial factor found: &amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">factor&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34; Other factor: &amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">N&lt;/span> &lt;span class="o">/&lt;/span> &lt;span class="n">factor&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;================================================================&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span> &lt;span class="k">else&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;[FAILURE] Trivial solution. Trying next dependency...&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// ============================================================================
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// Main Execution Pipeline
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// ============================================================================
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>&lt;span class="kt">int&lt;/span> &lt;span class="nf">main&lt;/span>&lt;span class="p">()&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;================================================================&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34; [SOTA GNFS] General Number Field Sieve Engine (Boost C++) &amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;================================================================&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// RSA-270 等，想要質因數分解的巨大合成數 N
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">cpp_int&lt;/span> &lt;span class="n">N&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="s">&amp;#34;233108530344407544527637656910680524145619812480305449042948611968495918245135782867888369318577116418213919268572658314913060672626911354027609793166341626693946596196427744273886601876896313468704059066746903123910748277606548649151920812699309766587514735456594993207&amp;#34;&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 多項式的次數 (超過 130 位數時通常選擇 5 次至 6 次)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="kt">int&lt;/span> &lt;span class="n">degree&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">6&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 管線初始化
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">PolynomialSelector&lt;/span> &lt;span class="n">poly_select&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">degree&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">LatticeSieve&lt;/span> &lt;span class="n">sieve&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="mi">10000000&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">20000000&lt;/span>&lt;span class="p">);&lt;/span> &lt;span class="c1">// 實際的邊界是數千萬至數億
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">Filter&lt;/span> &lt;span class="n">filter&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">LinearAlgebraGF2&lt;/span> &lt;span class="n">linalg&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">AlgebraicSquareRoot&lt;/span> &lt;span class="n">sqrt_step&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">auto&lt;/span> &lt;span class="n">start_time&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">chrono&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">high_resolution_clock&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">now&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 1. 多項式選擇
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">poly_select&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">select&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">N&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 2. 篩法 (Sieve) 處理
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">sieve&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">generate_factor_bases&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">Relation&lt;/span>&lt;span class="o">&amp;gt;&lt;/span> &lt;span class="n">relations&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">sieve&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">sieve&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">poly_select&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 3. 過濾 (矩陣壓縮)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">filter&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">reduce_matrix&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">relations&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 4. 線性代數 (GF(2) 上的零空間搜尋)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="kt">int&lt;/span>&lt;span class="o">&amp;gt;&amp;gt;&lt;/span> &lt;span class="n">dependencies&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">linalg&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">solve_nullspace&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">relations&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 5. 代數平方根的計算與 GCD
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="k">for&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="k">const&lt;/span> &lt;span class="k">auto&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="nl">dep&lt;/span> &lt;span class="p">:&lt;/span> &lt;span class="n">dependencies&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">sqrt_step&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">compute_and_factor&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">relations&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">dep&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">N&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">auto&lt;/span> &lt;span class="n">end_time&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">chrono&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">high_resolution_clock&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">now&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">chrono&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">duration&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="kt">double&lt;/span>&lt;span class="o">&amp;gt;&lt;/span> &lt;span class="n">elapsed&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">end_time&lt;/span> &lt;span class="o">-&lt;/span> &lt;span class="n">start_time&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;&lt;/span>&lt;span class="se">\n&lt;/span>&lt;span class="s">[System] SOTA GNFS Pipeline completed in &amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">elapsed&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">count&lt;/span>&lt;span class="p">()&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34; seconds.&amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;p>那麼，這段程式碼究竟是如何突破密碼學的高牆呢？我們將按 5 個階段，將其縝密的演算法與高等數學咀嚼並解說。&lt;/p>
&lt;hr>
&lt;h2 id="2-gnfs-的最終目的-x2-equiv-y2-pmod-n">2. GNFS 的最終目的： $X^2 \equiv Y^2 \pmod N$
&lt;/h2>&lt;p>不僅是 GNFS，現代巨大質因數分解演算法的目標，大多都是要找到滿足以下同餘式的非平凡數對 $(X, Y)$。&lt;/p>
$$X^2 \equiv Y^2 \pmod N$$
&lt;p>這個式子代表「$X^2$ 與 $Y^2$ 除以 $N$ 的餘數相等」。將其變形後可得：
$X^2 - Y^2 \equiv 0 \pmod N$
也就是說，$(X-Y)(X+Y)$ 是 $N$ 的倍數。&lt;/p>
&lt;p>如果 $X \not\equiv \pm Y \pmod N$（非平凡解），那麼在 $(X-Y)$ 與 $N$ 之間，就會存在「大於 1 且小於 $N$ 的公因數」。
此時，只要使用歐幾里得輾轉相除法計算 &lt;strong>$\gcd(X-Y, N)$&lt;/strong> ，就能輕易求出 $N$ 的質因數。&lt;/p>
&lt;p>然而，要找到這個 $X$ 與 $Y$ 猶如大海撈針。因此 GNFS 採取了天才般的策略：創造出「現實整數的世界」與「多項式代數體的世界」這 &lt;strong>兩個世界&lt;/strong> ，並將計算分散。&lt;/p>
&lt;hr>
&lt;h2 id="3-phase-1-多項式選擇polynomial-selection">3. Phase 1: 多項式選擇（Polynomial Selection）
&lt;/h2>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt"> 1
&lt;/span>&lt;span class="lnt"> 2
&lt;/span>&lt;span class="lnt"> 3
&lt;/span>&lt;span class="lnt"> 4
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&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="k">class&lt;/span> &lt;span class="nc">PolynomialSelector&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// ...
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="kt">void&lt;/span> &lt;span class="nf">select&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="k">const&lt;/span> &lt;span class="n">cpp_int&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="n">N&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// m = N^(1/d) 的計算與 base-m 展開
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// ...
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="k">for&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="kt">int&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">&amp;lt;=&lt;/span> &lt;span class="n">degree&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="o">++&lt;/span>&lt;span class="n">i&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">f&lt;/span>&lt;span class="p">[&lt;/span>&lt;span class="n">i&lt;/span>&lt;span class="p">]&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">temp&lt;/span> &lt;span class="o">%&lt;/span> &lt;span class="n">m&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">temp&lt;/span> &lt;span class="o">/=&lt;/span> &lt;span class="n">m&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">g&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="p">{&lt;/span>&lt;span class="o">-&lt;/span>&lt;span class="n">m&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">};&lt;/span> &lt;span class="c1">// g(x) = x - m
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;p>GNFS 的第一步，是建立用來橋接這兩個世界的「魔法多項式」。
對於巨大的數字 $N$，我們選擇一個整數 $m$。通常會選擇讓 $m \approx N^{1/d}$ （在程式碼中假設為 $d=6$ 次的多項式）。&lt;/p>
&lt;p>接著，將 $N$ 進行 $m$ 進位展開，並使用其係數來建構多項式 $f(x)$。
&lt;/p>
$$N = c_d m^d + c_{d-1} m^{d-1} + \dots + c_1 m + c_0$$
$$f(x) = c_d x^d + c_{d-1} x^{d-1} + \dots + c_1 x + c_0$$
&lt;p>這個多項式 $f(x)$ 有一個極為重要的性質： &lt;strong>「當變數 $x$ 代入 $m$ 時，剛好會等於 $N$（$f(m) = N$）」&lt;/strong> 。換句話說，$f(m) \equiv 0 \pmod N$。
有理側的多項式則定義為 $g(x) = x - m$。&lt;/p>
&lt;p>藉此，由 $f(x)=0$ 的根 $\alpha$ 所支配的 &lt;strong>「代數體的世界 $\mathbb{Z}[\alpha]$」&lt;/strong> ，與一般的 &lt;strong>「有理數（整數）的世界 $\mathbb{Z}$」&lt;/strong> ，將透過 $x \to m$ 這個「環同態映射（Homomorphism）」被緊密地連結起來。&lt;/p>
&lt;p>在最尖端的 CADO-NFS 等實作中，會使用 KleinJung 演算法或 LLL 晶格基底歸約演算法，花費數個月的時間來尋找「極致完美的多項式 $f(x)$」，使其係數不會過大，且在後續步驟中更容易出現質數（更容易變得平滑）。&lt;/p>
&lt;hr>
&lt;h2 id="4-phase-2-特殊-q-晶格篩法special-q-lattice-sieving">4. Phase 2: 特殊 $q$ 晶格篩法（Special-q Lattice Sieving）
&lt;/h2>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;span class="lnt">5
&lt;/span>&lt;span class="lnt">6
&lt;/span>&lt;span class="lnt">7
&lt;/span>&lt;span class="lnt">8
&lt;/span>&lt;span class="lnt">9
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="k">class&lt;/span> &lt;span class="nc">LatticeSieve&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// ...
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">Relation&lt;/span>&lt;span class="o">&amp;gt;&lt;/span> &lt;span class="n">sieve&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="k">const&lt;/span> &lt;span class="n">PolynomialSelector&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="n">poly&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// ...
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// 將 (a, b) 的數對映射到每個特殊質數 q 的晶格上，
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// 執行將快取效率提升到極限的篩法 (Sieve)。
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// ...
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;p>準備好兩個世界後，接下來進入在兩個世界中尋找「平滑數（僅由小質數構成的數）」的步驟。
產生無數個整數對 $(a, b)$，並計算以下兩個值：&lt;/p>
&lt;ol>
&lt;li>&lt;strong>有理側的值&lt;/strong> ： $a - bm$&lt;/li>
&lt;li>&lt;strong>代數側的範數 (Norm)&lt;/strong> ： $b^d f(a/b)$&lt;/li>
&lt;/ol>
&lt;p>GNFS 的目標是收集數千萬至數億個 &lt;strong>「有理側與代數側的值，兩者都能完全被小質因數分解的數對（Relation：關係）」&lt;/strong> 。&lt;/p>
&lt;p>早期的 GNFS 使用「直線篩法（Line Sieve）」，將 $(a, b)$ 排列在 $xy$ 平面上，從頭開始依序用質數去除。但這種方法會造成記憶體到處存取而頻繁發生快取未命中（Cache Miss），這是一個非常慢的弱點。&lt;/p>
&lt;p>因此，現在最尖端的程式碼中使用了 &lt;strong>「特殊 $q$ 晶格篩法（Special-q Lattice Sieve）」&lt;/strong> 。
固定一個適度大的質數 $q$，只將「代數側的值必定能被 $q$ 整除的 $(a, b)$ 數對」作為計算對象。滿足此條件的 $(a, b)$ 會在平面上形成「晶格（Lattice）」，因此計算的位址跳躍幅度會固定，完美契合 CPU 的 L1/L2 快取。
導入這個晶格篩法後，GNFS 的計算速度獲得了戲劇性的提升。&lt;/p>
&lt;hr>
&lt;h2 id="5-phase-3-過濾filtering">5. Phase 3: 過濾（Filtering）
&lt;/h2>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;span class="lnt">5
&lt;/span>&lt;span class="lnt">6
&lt;/span>&lt;span class="lnt">7
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="k">class&lt;/span> &lt;span class="nc">Filter&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">public&lt;/span>&lt;span class="o">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="kt">void&lt;/span> &lt;span class="n">reduce_matrix&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">Relation&lt;/span>&lt;span class="o">&amp;gt;&amp;amp;&lt;/span> &lt;span class="n">relations&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 1. Singleton removal (刪除只出現過一次的質數的 Relation)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// 2. Clique merging (為使稀疏矩陣變密集而合併 Relation)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;p>在 Phase 2 中，全世界的電腦花費數個月收集了數億個 Relation。然而，如果直接將這些資料丟進下一個「解聯立方程式的步驟（矩陣計算）」中，超級電腦的記憶體也會被撐爆。&lt;/p>
&lt;p>因此，會進行被稱為 &lt;strong>Filtering（過濾）&lt;/strong> 的矩陣超壓縮過程。&lt;/p>
&lt;ol>
&lt;li>
&lt;p>&lt;strong>Singleton removal（奇異點清除）&lt;/strong>
假設某個巨大的質數 $p$，在數億個 Relation 中「只出現了一次」。我們的目標是「讓所有質數的指數都變成偶數（2 的倍數）」，所以只出現一次的質數絕對不可能變成偶數。
因此，包含該質數的 Relation 會立即被視為「無用的垃圾」而刪除（清除）。這個連鎖反應發生後，原本數億行的資料就會不斷被削減。&lt;/p>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>Clique merging（派系合併）&lt;/strong>
進一步地，將共享特定質數的 Relation 互相相乘（相加），在減少行數的同時，將稀疏（空洞）的矩陣壓縮成更密集的狀態（使用類似圖論中派系搜尋的手法）。&lt;/p>
&lt;/li>
&lt;/ol>
&lt;p>透過這個最佳化，巨大的稀疏矩陣將被戲劇性地壓縮至可計算的大小。&lt;/p>
&lt;hr>
&lt;h2 id="6-phase-4-gf2-上的線性代數block-wiedemann-法">6. Phase 4: GF(2) 上的線性代數（Block Wiedemann 法）
&lt;/h2>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
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&lt;/span>&lt;span class="lnt">5
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&lt;/span>&lt;span class="lnt">7
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="k">class&lt;/span> &lt;span class="nc">LinearAlgebraGF2&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">public&lt;/span>&lt;span class="o">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="kt">int&lt;/span>&lt;span class="o">&amp;gt;&amp;gt;&lt;/span> &lt;span class="n">solve_nullspace&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="k">const&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">Relation&lt;/span>&lt;span class="o">&amp;gt;&amp;amp;&lt;/span> &lt;span class="n">relations&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 反覆進行稀疏矩陣 (Sparse Matrix) 與向量的乘法運算，
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// 找到多個滿足 M * x = 0 mod 2 的解向量 (核, Kernel)。
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;p>終於來到了謎題的核心。
將收集到的 Relation 相乘，尋找 &lt;strong>「所有質因數的指數都變成偶數的組合」&lt;/strong> 。&lt;/p>
&lt;p>這在數學上，等同於使用一個以各質數指數的「偶數・奇數（亦即 0 或 1）」為元素的巨大矩陣 $M$，以及一個表示要使用哪些 Relation 的向量 $x$，來求解滿足
&lt;strong>$M \cdot x \equiv 0 \pmod 2$&lt;/strong>
的解向量 $x$ （零空間・核，Nullspace / Kernel）。&lt;/p>
&lt;p>這需要解開數百萬行 × 數百萬列這種龐大尺寸矩陣的聯立方程式。若使用一般的基斯消去法（高斯消去法），計算複雜度將達到 $O(N^3)$，就算到宇宙毀滅也算不完。&lt;/p>
&lt;p>因此，最尖端的實作採用了 &lt;strong>「Block Wiedemann（區塊・維德曼）法」&lt;/strong> 。
這是一種克雷洛夫子空間法（Krylov Subspace Method），利用矩陣 $M$ 「非常稀疏（幾乎都是 0）」的特性，反覆進行矩陣與向量的乘法來導出解。
與舊有的 Block Lanczos 法不同，Block Wiedemann 法可以將計算過程完全分割到多個叢集中，因此在現代的分散式雲端運算或超級電腦的平行計算中，能發揮壓倒性的威力。&lt;/p>
&lt;hr>
&lt;h2 id="7-phase-5-代數平方根algebraic-square-root與密碼崩潰">7. Phase 5: 代數平方根（Algebraic Square Root）與密碼崩潰
&lt;/h2>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt"> 1
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&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="k">class&lt;/span> &lt;span class="nc">AlgebraicSquareRoot&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">public&lt;/span>&lt;span class="o">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="kt">void&lt;/span> &lt;span class="n">compute_and_factor&lt;/span>&lt;span class="p">(...)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 1. 有理側的平方根 V 的計算
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">cpp_int&lt;/span> &lt;span class="n">V&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 2. 代數側的平方根 gamma 的計算
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">cpp_int&lt;/span> &lt;span class="n">Y&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// ...
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">cpp_int&lt;/span> &lt;span class="n">factor&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">gcd&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">V&lt;/span> &lt;span class="o">-&lt;/span> &lt;span class="n">Y&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">N&lt;/span>&lt;span class="p">);&lt;/span> &lt;span class="c1">// GCD(X-Y, N)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;p>透過 Phase 4 的矩陣計算，我們獲得了「相乘後所有質因數皆為偶數次方的 Relation 集合 $S$」。
藉此，我們可以在有理側與代數側這兩個世界中，各自建構出「平方（2 次方）」。&lt;/p>
&lt;p>有理側只是單純的整數乘法，所以計算平方根 $V$ 非常容易。
&lt;/p>
$$V^2 = \prod_{S} (a - bm)$$
&lt;p>&lt;strong>然而，真正的地獄在「代數側」。&lt;/strong>
在代數體的世界 $\mathbb{Z}[\alpha]$ 中，質因數分解的唯一性並不成立，因此我們一直使用理想（Ideal）來進行計算。矩陣計算所保證的 &lt;strong>只有「成為理想的平方」，並不能保證成為「元素的平方（$\gamma^2$）」&lt;/strong> 。&lt;/p>
&lt;p>這裡會遇到被稱為「理想類群的障礙」與「單位群的障礙」，這是代數整數論中非常巨大的高牆。
GNFS 為了打破這面牆，使用了被稱為 &lt;strong>「二次剩餘特徵（Quadratic Characters）」&lt;/strong> 的魔法。
在 Phase 4 的矩陣中，事先偷偷加入針對幾十個特殊質理想的二次剩餘（勒讓德符號）序列。這樣一來，找到的集合 $S$ 就有極大的機率能避開障礙，順利形成「真正元素的平方 $\gamma^2$」。&lt;/p>
&lt;p>求取 $\gamma$ 的工作（代數平方根），是使用 Montgomery 法等極其複雜的演算法來計算的。&lt;/p>
&lt;p>最終，將代數側的平方根 $\gamma$，透過環同態映射 $\phi$ 瞬移回現實世界（將 $x$ 代入 $m$），得到 $Y$。
將有理側的 $V$ 直接當作 $X$，我們夢寐以求的絕對等式終於完成了。&lt;/p>
&lt;p>&lt;strong>$$X^2 \equiv Y^2 \pmod N$$&lt;/strong>&lt;/p>
&lt;p>剩下的就只有計算 $\gcd(X-Y, N)$ 而已。0.001 秒的處理一閃而過，當非平凡的因數印在螢幕上的那一刻，號稱堅不可摧的 RSA 密碼便徹底崩潰。&lt;/p>
&lt;hr>
&lt;h2 id="結語">結語
&lt;/h2>&lt;p>GNFS 不僅僅是一種程式設計的技巧。
它是用超級電腦的分散式架構與快取最佳化等「極致的工程學」，去折服抽象代數學、環論、理想類群等「純數學深淵」的人類智慧結晶。&lt;/p>
&lt;p>我們不經意傳送的聊天訊息或信用卡資訊，就是建立在這種天文數字般的數學攻防之上受到保護的。&lt;/p>
&lt;p>希望透過這個 C++ 框架，能讓各位感受到最尖端密碼破解演算法背後的「數學與計算機的浪漫」。&lt;/p></description></item><item><title>如何從 C++ 呼叫 Microsoft.Windows.AI</title><link>http://kenji.blog/zh-tw/p/%E5%A6%82%E4%BD%95%E5%BE%9Ec-%E5%91%BC%E5%8F%ABmicrosoft.windows.ai/</link><pubDate>Sat, 19 Jul 2025 10:03:51 +0900</pubDate><guid>http://kenji.blog/zh-tw/p/%E5%A6%82%E4%BD%95%E5%BE%9Ec-%E5%91%BC%E5%8F%ABmicrosoft.windows.ai/</guid><description>&lt;img src="http://kenji.blog/p/c-%E3%81%8B%E3%82%89microsoft.windows.ai%E3%82%92%E5%91%BC%E3%81%B3%E5%87%BA%E3%81%99%E6%96%B9%E6%B3%95/img.png" alt="Featured image of post 如何從 C++ 呼叫 Microsoft.Windows.AI" />&lt;h1 id="-如何從-c-呼叫-microsoftwindowsai附範例程式碼">🎯 如何從 C++ 呼叫 &lt;code>Microsoft.Windows.AI&lt;/code>【附範例程式碼】
&lt;/h1>&lt;p>自 Windows 10 起，Windows 預設內建了 &lt;strong>能夠執行 ONNX 格式 AI 模型的執行階段&lt;/strong> 。這就是 &lt;strong>Windows ML (Windows.AI.MachineLearning)&lt;/strong> 。&lt;/p>
&lt;p>這篇文章將具體解說如何從 &lt;strong>C++（基於 Win32 應用程式）&lt;/strong> 呼叫 &lt;code>Microsoft.Windows.AI.MachineLearning&lt;/code> ，並 &lt;strong>附上範例程式碼具體解說&lt;/strong> 。&lt;/p>
&lt;hr>
&lt;h2 id="-準備篇">✅ 準備篇
&lt;/h2>&lt;h3 id="-系統需求">◾ 系統需求
&lt;/h3>&lt;ul>
&lt;li>Windows 10 (1809+) 或 Windows 11&lt;/li>
&lt;li>Visual Studio 2019 或以上版本（Community 版即可）&lt;/li>
&lt;li>支援 C++/WinRT (&lt;code>Microsoft.Windows.CppWinRT&lt;/code>)&lt;/li>
&lt;li>Windows SDK 10.0.17763.0 或以上版本&lt;/li>
&lt;/ul>
&lt;hr>
&lt;h2 id="-專案結構">✅ 專案結構
&lt;/h2>&lt;p>在 Visual Studio 中建立具有以下結構的專案。&lt;/p>
&lt;ul>
&lt;li>
&lt;p>類型：C++ Windows 桌面應用程式（空白專案）&lt;/p>
&lt;/li>
&lt;li>
&lt;p>子系統：Windows (&lt;code>WinMain&lt;/code>)&lt;/p>
&lt;/li>
&lt;li>
&lt;p>透過 NuGet 新增以下套件&lt;/p>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-fallback" data-lang="fallback">&lt;span class="line">&lt;span class="cl">Microsoft.Windows.CppWinRT
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;/li>
&lt;/ul>
&lt;hr>
&lt;h2 id="-範例程式碼">✅ 範例程式碼
&lt;/h2>&lt;p>以下是使用 &lt;code>WinMain&lt;/code> 並結合 Win32 API 與 &lt;code>Windows.AI.MachineLearning&lt;/code> 的最小配置範例。&lt;/p>
&lt;blockquote>
&lt;p>※ 使用的 ONNX 模型假設為 &lt;code>model.onnx&lt;/code> ，請將其放置在與執行檔相同的資料夾中。&lt;/p>
&lt;/blockquote>
&lt;h3 id="maincpp">&lt;code>main.cpp&lt;/code>
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&lt;/span>&lt;span class="lnt">37
&lt;/span>&lt;span class="lnt">38
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;windows.h&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;winrt/Windows.AI.MachineLearning.h&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;winrt/Windows.Storage.h&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#pragma comment(lib, &amp;#34;windowsapp&amp;#34;) &lt;/span>&lt;span class="c1">// 用於 WinRT 連結
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">winrt&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">Windows&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">AI&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">MachineLearning&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">Windows&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Storage&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kt">int&lt;/span> &lt;span class="n">WINAPI&lt;/span> &lt;span class="nf">WinMain&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">HINSTANCE&lt;/span> &lt;span class="n">hInstance&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">HINSTANCE&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">LPSTR&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="kt">int&lt;/span> &lt;span class="n">nCmdShow&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// WinRT 初始化（MTA 或 STA 皆可）
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">winrt&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">init_apartment&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">try&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 讀取模型檔案
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="k">auto&lt;/span> &lt;span class="n">modelFile&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">StorageFile&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">GetFileFromPathAsync&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;model.onnx&amp;#34;&lt;/span>&lt;span class="p">).&lt;/span>&lt;span class="n">get&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">LearningModel&lt;/span> &lt;span class="n">model&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">LearningModel&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">LoadFromStorageFileAsync&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">modelFile&lt;/span>&lt;span class="p">).&lt;/span>&lt;span class="n">get&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 建立工作階段
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">LearningModelSession&lt;/span> &lt;span class="n">session&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">model&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">LearningModelBinding&lt;/span> &lt;span class="n">binding&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">session&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 模型的輸入與輸出（此處暫時為空輸入）
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="c1">// 實際上需要繫結 TensorFloat 等
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 執行推論
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="k">auto&lt;/span> &lt;span class="n">result&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">session&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">EvaluateAsync&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">binding&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;&amp;#34;&lt;/span>&lt;span class="p">).&lt;/span>&lt;span class="n">get&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">MessageBox&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="k">nullptr&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;推論已完成&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;Windows ML (C++)&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">MB_OK&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">catch&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">winrt&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">hresult_error&lt;/span> &lt;span class="k">const&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="n">ex&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">MessageBox&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="k">nullptr&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">ex&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">message&lt;/span>&lt;span class="p">().&lt;/span>&lt;span class="n">c_str&lt;/span>&lt;span class="p">(),&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;錯誤&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">MB_ICONERROR&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;hr>
&lt;h2 id="-補充如何指定輸入與輸出-tensor">✅ 補充：如何指定輸入與輸出 Tensor
&lt;/h2>&lt;p>根據模型的不同，在推論前可能需要 &lt;strong>建立並繫結 Tensor&lt;/strong> 。&lt;/p>
&lt;p>範例：&lt;/p>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;span class="lnt">5
&lt;/span>&lt;span class="lnt">6
&lt;/span>&lt;span class="lnt">7
&lt;/span>&lt;span class="lnt">8
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// 將一維 float 陣列轉換為 Tensor
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>&lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="kt">float&lt;/span>&lt;span class="o">&amp;gt;&lt;/span> &lt;span class="n">inputData&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="p">{&lt;/span>&lt;span class="mf">0.5f&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mf">0.3f&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mf">0.2f&lt;/span>&lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="kt">int64_t&lt;/span>&lt;span class="o">&amp;gt;&lt;/span> &lt;span class="n">shape&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="p">{&lt;/span>&lt;span class="mi">1&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">3&lt;/span>&lt;span class="p">};&lt;/span> &lt;span class="c1">// 形狀：[1, 3]
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">auto&lt;/span> &lt;span class="n">tensor&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">TensorFloat&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">CreateFromArray&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">shape&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">inputData&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">// 輸入繫結（需符合模型的輸入名稱）
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>&lt;span class="n">binding&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">Bind&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;input_0&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">tensor&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;p>輸出也同樣可以透過 &lt;code>result.Outputs().Lookup(L&amp;quot;output_0&amp;quot;)&lt;/code> 取得。&lt;/p>
&lt;hr>
&lt;h2 id="-偵錯時的注意事項">✅ 偵錯時的注意事項
&lt;/h2>&lt;ul>
&lt;li>若模型檔案不存在於執行資料夾中，將會拋出 &lt;code>FileNotFoundException&lt;/code> 。&lt;/li>
&lt;li>若輸入或輸出名稱不符，將會產生 &lt;code>invalid_argument&lt;/code> 錯誤。&lt;/li>
&lt;li>模型正確的 IO 規格可以使用 &lt;a class="link" href="https://netron.app" target="_blank" rel="noopener"
>Netron&lt;/a> 等工具確認。&lt;/li>
&lt;/ul>
&lt;hr>
&lt;h2 id="-總結">✅ 總結
&lt;/h2>&lt;table>
&lt;thead>
&lt;tr>
&lt;th>項目&lt;/th>
&lt;th>內容&lt;/th>
&lt;/tr>
&lt;/thead>
&lt;tbody>
&lt;tr>
&lt;td>使用 API&lt;/td>
&lt;td>Windows.AI.MachineLearning (WinRT)&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>語言&lt;/td>
&lt;td>C++（基於 Win32）&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>建議方法&lt;/td>
&lt;td>透過 C++/WinRT 標頭檔&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>優點&lt;/td>
&lt;td>原生執行 ONNX 模型，也支援 GPU&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>注意&lt;/td>
&lt;td>注意模型的輸入名稱與 Tensor 形狀&lt;/td>
&lt;/tr>
&lt;/tbody>
&lt;/table>
&lt;hr>
&lt;h2 id="-替代方案給不想使用-winrt-的人">✅ 替代方案：給不想使用 WinRT 的人
&lt;/h2>&lt;ul>
&lt;li>若使用微軟的 &lt;code>ONNX Runtime&lt;/code> ，就能 &lt;strong>完全不需要 WinRT 即可從 C++ 處理 ONNX 模型&lt;/strong> 。&lt;/li>
&lt;li>支援跨平台，在 Windows 或 Linux 上也可以使用共通的程式碼。&lt;/li>
&lt;/ul>
&lt;hr>
&lt;h2 id="-結語">📌 結語
&lt;/h2>&lt;p>Windows ML (Microsoft.Windows.AI) 是一個非常強大的人工智慧推論引擎，即使從 C++ 也能輕鬆使用。如果需要在 Windows 上進行原生推論，請務必嘗試看看。&lt;/p>
&lt;p>如果您需要建立 ONNX 模型或 Tensor 繫結的具體範例，我們將在後續文章中進行解說！&lt;/p></description></item><item><title>從 C++ 呼叫 TinyLLaMA 的步驟（使用 llama.cpp）</title><link>http://kenji.blog/zh-tw/p/%E5%BE%9E-c-%E5%91%BC%E5%8F%AB-tinyllama-%E7%9A%84%E6%AD%A5%E9%A9%9F%E4%BD%BF%E7%94%A8-llama.cpp/</link><pubDate>Sat, 19 Jul 2025 09:40:53 +0900</pubDate><guid>http://kenji.blog/zh-tw/p/%E5%BE%9E-c-%E5%91%BC%E5%8F%AB-tinyllama-%E7%9A%84%E6%AD%A5%E9%A9%9F%E4%BD%BF%E7%94%A8-llama.cpp/</guid><description>&lt;img src="http://kenji.blog/p/tinyllama-%E3%82%92-c-%E3%81%8B%E3%82%89%E5%91%BC%E3%81%B3%E5%87%BA%E3%81%9B%E3%82%8B%E3%82%88%E3%81%86%E3%81%AB%E3%81%99%E3%82%8B%E6%89%8B%E9%A0%86llama.cpp%E4%BD%BF%E7%94%A8/img.png" alt="Featured image of post 從 C++ 呼叫 TinyLLaMA 的步驟（使用 llama.cpp）" />&lt;h1 id="-tinyllama--c-設定步驟使用-llamacpp">✅ TinyLLaMA × C++ 設定步驟（使用 &lt;code>llama.cpp&lt;/code>）
&lt;/h1>&lt;hr>
&lt;h2 id="-step-1-準備-llamacpp">🔧 Step 1: 準備 llama.cpp
&lt;/h2>&lt;h3 id="1-1-必備環境最低需求">1-1. 必備環境（最低需求）
&lt;/h3>&lt;ul>
&lt;li>OS: Windows / Linux / macOS&lt;/li>
&lt;li>開發環境: g++ / clang / MSVC&lt;/li>
&lt;li>Git / CMake&lt;/li>
&lt;/ul>
&lt;h3 id="1-2-取得並建置-llamacpp">1-2. 取得並建置 llama.cpp
&lt;/h3>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;span class="lnt">5
&lt;/span>&lt;span class="lnt">6
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-bash" data-lang="bash">&lt;span class="line">&lt;span class="cl">git clone https://github.com/ggerganov/llama.cpp
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="nb">cd&lt;/span> llama.cpp
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">mkdir build
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="nb">cd&lt;/span> build
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">cmake ..
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">cmake --build . --config Release
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;blockquote>
&lt;p>Windows 使用者可以在 &lt;code>Visual Studio Developer Command Prompt&lt;/code> 中執行 &lt;code>cmake --build . --config Release&lt;/code> 會比較方便。&lt;/p>
&lt;/blockquote>
&lt;hr>
&lt;h2 id="-step-2-下載-tinyllama-模型並轉換">📦 Step 2: 下載 TinyLLaMA 模型並轉換
&lt;/h2>&lt;h3 id="2-1-從-huggingface-取得原始模型">2-1. 從 HuggingFace 取得原始模型
&lt;/h3>&lt;p>範例: &lt;a class="link" href="https://huggingface.co/openaccess-ai-collective/TinyLlama-1.1B-Chat-v1.0" target="_blank" rel="noopener"
>TinyLLaMA-1.1B&lt;/a>&lt;/p>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;span class="lnt">5
&lt;/span>&lt;span class="lnt">6
&lt;/span>&lt;span class="lnt">7
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-bash" data-lang="bash">&lt;span class="line">&lt;span class="cl">&lt;span class="c1"># 如有需要，使用 transformers 進行下載&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">pip install transformers huggingface_hub
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">python3 -m transformers.models.llama.convert_llama_weights_to_hf &lt;span class="se">\
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="se">&lt;/span> --input_dir ./TinyLlama-1.1B-Chat &lt;span class="se">\
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="se">&lt;/span> --model_size 1B &lt;span class="se">\
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="se">&lt;/span> --output_dir ./hf_model
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;blockquote>
&lt;p>這是轉換為 Hugging Face 格式的步驟。&lt;/p>
&lt;/blockquote>
&lt;hr>
&lt;h3 id="2-2-轉換為-gguf-格式供-llamacpp-使用">2-2. 轉換為 GGUF 格式（供 &lt;code>llama.cpp&lt;/code> 使用）
&lt;/h3>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-bash" data-lang="bash">&lt;span class="line">&lt;span class="cl">&lt;span class="nb">cd&lt;/span> llama.cpp
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">python3 convert.py ./hf_model --outfile tinyllama.gguf
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;h3 id="2-3-模型量化縮減大小">2-3. 模型量化（縮減大小）
&lt;/h3>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-bash" data-lang="bash">&lt;span class="line">&lt;span class="cl">./quantize ./tinyllama.gguf ./tinyllama-q4.gguf q4_0
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;blockquote>
&lt;p>&lt;code>q4_0&lt;/code> 為 4bit 量化。模型大小大約會縮減至 ** 350MB前後 ** 。&lt;/p>
&lt;/blockquote>
&lt;hr>
&lt;h2 id="-step-3-從-c-呼叫模型程式碼範例">🧪 Step 3: 從 C++ 呼叫模型（程式碼範例）
&lt;/h2>&lt;h3 id="3-1-簡易-c-程式碼推論">3-1. 簡易 C++ 程式碼（推論）
&lt;/h3>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
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&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;#34;llama.h&amp;#34;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;iostream&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kt">int&lt;/span> &lt;span class="nf">main&lt;/span>&lt;span class="p">()&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">llama_model_params&lt;/span> &lt;span class="n">model_params&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">llama_model_default_params&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">llama_context_params&lt;/span> &lt;span class="n">ctx_params&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">llama_context_default_params&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">llama_model&lt;/span> &lt;span class="o">*&lt;/span>&lt;span class="n">model&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">llama_load_model_from_file&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="s">&amp;#34;tinyllama-q4.gguf&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">model_params&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">llama_context&lt;/span> &lt;span class="o">*&lt;/span>&lt;span class="n">ctx&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">llama_new_context_with_model&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">model&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">ctx_params&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">string&lt;/span> &lt;span class="n">prompt&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="s">&amp;#34;使用者說想要讀取 Excel 資料、進行篩選並儲存。節點架構為何？&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">llama_batch&lt;/span> &lt;span class="n">batch&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">llama_batch_init&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="mi">512&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">llama_token&lt;/span> &lt;span class="n">BOS&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">llama_token_bos&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">model&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">batch&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">token&lt;/span>&lt;span class="p">[&lt;/span>&lt;span class="mi">0&lt;/span>&lt;span class="p">]&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">BOS&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 進行 Tokenize
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">vector&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">llama_token&lt;/span>&lt;span class="o">&amp;gt;&lt;/span> &lt;span class="n">tokens&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">prompt&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">size&lt;/span>&lt;span class="p">()&lt;/span> &lt;span class="o">+&lt;/span> &lt;span class="mi">8&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="kt">int&lt;/span> &lt;span class="n">n&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">llama_tokenize&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">model&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">prompt&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">c_str&lt;/span>&lt;span class="p">(),&lt;/span> &lt;span class="n">tokens&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">data&lt;/span>&lt;span class="p">(),&lt;/span> &lt;span class="n">tokens&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">size&lt;/span>&lt;span class="p">(),&lt;/span> &lt;span class="nb">true&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">tokens&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">resize&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">n&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">for&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">size_t&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">&amp;lt;&lt;/span> &lt;span class="n">tokens&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">size&lt;/span>&lt;span class="p">();&lt;/span> &lt;span class="o">++&lt;/span>&lt;span class="n">i&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">batch&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">token&lt;/span>&lt;span class="p">[&lt;/span>&lt;span class="n">i&lt;/span> &lt;span class="o">+&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">]&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">tokens&lt;/span>&lt;span class="p">[&lt;/span>&lt;span class="n">i&lt;/span>&lt;span class="p">];&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">batch&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">n_tokens&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">tokens&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">size&lt;/span>&lt;span class="p">()&lt;/span> &lt;span class="o">+&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">llama_decode&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">ctx&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">batch&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 取得推論結果
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="k">for&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="kt">int&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="n">i&lt;/span> &lt;span class="o">&amp;lt;&lt;/span> &lt;span class="mi">50&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="o">++&lt;/span>&lt;span class="n">i&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">llama_token&lt;/span> &lt;span class="n">next&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">llama_sample_token&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">ctx&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="k">nullptr&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">llama_token_to_str&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">model&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">next&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">llama_batch&lt;/span> &lt;span class="n">next_batch&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">llama_batch_init&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="mi">1&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">next_batch&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">token&lt;/span>&lt;span class="p">[&lt;/span>&lt;span class="mi">0&lt;/span>&lt;span class="p">]&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">next&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">next_batch&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">n_tokens&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">1&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">llama_decode&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">ctx&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">next_batch&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">llama_free&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">ctx&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">llama_free_model&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">model&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;hr>
&lt;h2 id="-step-4-編譯方法範例">🧱 Step 4: 編譯方法（範例）
&lt;/h2>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-bash" data-lang="bash">&lt;span class="line">&lt;span class="cl">g++ -I./llama.cpp main.cpp ./llama.cpp/build/libllama.a -o tiny_infer -pthread -std&lt;span class="o">=&lt;/span>c++11
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;blockquote>
&lt;p>&lt;code>libllama.a&lt;/code> 會在建置後的 &lt;code>build/&lt;/code> 目錄中產生。&lt;/p>
&lt;/blockquote>
&lt;hr>
&lt;h2 id="-成果物結構範例整理">✅ 成果物結構範例（整理）
&lt;/h2>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;span class="lnt">5
&lt;/span>&lt;span class="lnt">6
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-fallback" data-lang="fallback">&lt;span class="line">&lt;span class="cl">my_app/
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">├── tinyllama-q4.gguf # 已量化模型 (~350MB)
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">├── main.cpp # 上述 C++ 程式碼
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">├── llama.cpp/ # llama.cpp 本體
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">└── build/
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> └── libllama.a # 已編譯函式庫
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;hr>
&lt;h2 id="-應用於使用案例的補充說明">🧠 應用於使用案例的補充說明
&lt;/h2>&lt;ul>
&lt;li>在 C++ 內保有接受輸出並 &lt;code>比對/選擇節點範本&lt;/code> 的程式碼&lt;/li>
&lt;li>範例：若包含「Excel」「篩選」「儲存」→ 產生對應的節點群組&lt;/li>
&lt;li>此部分採用 &lt;code>if 判斷式 + 讀取 JSON 範本&lt;/code> 的簡單架構即可&lt;/li>
&lt;/ul>
&lt;hr>
&lt;h2 id="-總結">📌 總結
&lt;/h2>&lt;table>
&lt;thead>
&lt;tr>
&lt;th>項目&lt;/th>
&lt;th>內容&lt;/th>
&lt;/tr>
&lt;/thead>
&lt;tbody>
&lt;tr>
&lt;td>推薦模型&lt;/td>
&lt;td>TinyLLaMA-1.1B-Chat v1.0（GGUF + 量化）&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>大小&lt;/td>
&lt;td>~350〜450MB（4bit量化）&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>C++整合&lt;/td>
&lt;td>可透過 &lt;code>llama.cpp&lt;/code> 達成，幾乎無外部依賴&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>處理能力&lt;/td>
&lt;td>足以應付簡單的意圖理解與輸出句子生成（自然語言→架構）&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>擴充性&lt;/td>
&lt;td>結合插槽填寫與範本呼叫，即可成為節點生成 AI&lt;/td>
&lt;/tr>
&lt;/tbody>
&lt;/table></description></item><item><title>如何使用 Slack App + OAuth2 發送訊息到 Slack</title><link>http://kenji.blog/zh-tw/p/slack-app--oauth2-%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6-slack-%E3%81%AB%E3%83%A1%E3%83%83%E3%82%BB%E3%83%BC%E3%82%B8%E3%82%92%E6%8A%95%E7%A8%BF%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/</link><pubDate>Wed, 16 Jul 2025 23:36:27 +0900</pubDate><guid>http://kenji.blog/zh-tw/p/slack-app--oauth2-%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6-slack-%E3%81%AB%E3%83%A1%E3%83%83%E3%82%BB%E3%83%BC%E3%82%B8%E3%82%92%E6%8A%95%E7%A8%BF%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/</guid><description>&lt;img src="http://kenji.blog/p/slack-app--oauth2-%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6-slack-%E3%81%AB%E3%83%A1%E3%83%83%E3%82%BB%E3%83%BC%E3%82%B8%E3%82%92%E6%8A%95%E7%A8%BF%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/img.png" alt="Featured image of post 如何使用 Slack App + OAuth2 發送訊息到 Slack" />&lt;h2 id="-使用存取權杖的發文方法slack-web-api">✅ 使用存取權杖的發文方法（Slack Web API）
&lt;/h2>&lt;p>Slack 的「OAuth Token（例如 xoxb-&amp;hellip; 等）」是用來透過 Slack 的 &lt;a class="link" href="https://api.slack.com/methods/chat.postMessage" target="_blank" rel="noopener"
>Web API&lt;/a> 發文的密鑰。
在這種情況下，與 Webhook 不同，你需要向 &lt;strong>Slack API 端點&lt;/strong> 進行帶有 &lt;code>Authorization: Bearer&lt;/code> 標頭的 &lt;code>POST&lt;/code> 請求。&lt;/p>
&lt;hr>
&lt;h2 id="-必要前提">🔑 必要前提
&lt;/h2>&lt;p>你必須在 Slack 應用程式的 &lt;strong>OAuth 範圍內包含 &lt;code>chat:write&lt;/code>&lt;/strong> ：&lt;/p>
&lt;h3 id="設定步驟">設定步驟
&lt;/h3>&lt;ol>
&lt;li>前往 &lt;a class="link" href="https://api.slack.com/apps" target="_blank" rel="noopener"
>https://api.slack.com/apps&lt;/a>&lt;/li>
&lt;li>建立應用程式或選擇現有應用程式&lt;/li>
&lt;li>在「OAuth &amp;amp; Permissions」 &amp;gt; &lt;code>Scopes&lt;/code> 中
→ 新增 &lt;code>chat:write&lt;/code>&lt;/li>
&lt;li>點擊「Install to Workspace」或「Reinstall」以獲取 &lt;code>Access Token&lt;/code>（例如：&lt;code>xoxb-xxxxxxxxxx&lt;/code>）&lt;/li>
&lt;/ol>
&lt;hr>
&lt;h2 id="-c-程式碼使用-winhttp-向-slack-api-發送請求">💻 C++ 程式碼（使用 WinHTTP 向 Slack API 發送請求）
&lt;/h2>&lt;div class="highlight">&lt;div class="chroma">
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&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;windows.h&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;winhttp.h&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;iostream&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#pragma comment(lib, &amp;#34;winhttp.lib&amp;#34;)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kt">bool&lt;/span> &lt;span class="nf">PostSlackMessage&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="k">const&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="n">accessToken&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="k">const&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">string&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="n">channel&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="k">const&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">string&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="n">text&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">const&lt;/span> &lt;span class="kt">wchar_t&lt;/span>&lt;span class="o">*&lt;/span> &lt;span class="n">host&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;slack.com&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">const&lt;/span> &lt;span class="kt">wchar_t&lt;/span>&lt;span class="o">*&lt;/span> &lt;span class="n">path&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;/api/chat.postMessage&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">HINTERNET&lt;/span> &lt;span class="n">hSession&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">WinHttpOpen&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;SlackPoster/1.0&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_ACCESS_TYPE_DEFAULT_PROXY&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_NO_PROXY_NAME&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_NO_PROXY_BYPASS&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="o">!&lt;/span>&lt;span class="n">hSession&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="k">return&lt;/span> &lt;span class="nb">false&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">HINTERNET&lt;/span> &lt;span class="n">hConnect&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">WinHttpConnect&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hSession&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">host&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">INTERNET_DEFAULT_HTTPS_PORT&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="o">!&lt;/span>&lt;span class="n">hConnect&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="k">return&lt;/span> &lt;span class="nb">false&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">HINTERNET&lt;/span> &lt;span class="n">hRequest&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">WinHttpOpenRequest&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hConnect&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;POST&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">path&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nb">NULL&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">WINHTTP_NO_REFERER&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_DEFAULT_ACCEPT_TYPES&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_FLAG_SECURE&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// Authorization 標頭與 Content-Type
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span> &lt;span class="n">headers&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;Content-Type: application/json&lt;/span>&lt;span class="se">\r\n&lt;/span>&lt;span class="s">&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">headers&lt;/span> &lt;span class="o">+=&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;Authorization: Bearer &amp;#34;&lt;/span> &lt;span class="o">+&lt;/span> &lt;span class="n">accessToken&lt;/span> &lt;span class="o">+&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;&lt;/span>&lt;span class="se">\r\n&lt;/span>&lt;span class="s">&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// JSON 內容
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">string&lt;/span> &lt;span class="n">body&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">R&lt;/span>&lt;span class="s">&amp;#34;({&amp;#34;&lt;/span>&lt;span class="n">channel&lt;/span>&lt;span class="s">&amp;#34;:&amp;#34;&lt;/span>&lt;span class="p">)&lt;/span>&lt;span class="s">&amp;#34; + channel + R&amp;#34;&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="s">&amp;#34;,&amp;#34;&lt;/span>&lt;span class="n">text&lt;/span>&lt;span class="s">&amp;#34;:&amp;#34;&lt;/span>&lt;span class="p">)&lt;/span>&lt;span class="s">&amp;#34; + text + R&amp;#34;&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="s">&amp;#34;})&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">BOOL&lt;/span> &lt;span class="n">result&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">WinHttpSendRequest&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hRequest&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">headers&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">c_str&lt;/span>&lt;span class="p">(),&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">(&lt;/span>&lt;span class="n">DWORD&lt;/span>&lt;span class="p">)&lt;/span>&lt;span class="o">-&lt;/span>&lt;span class="mi">1&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">(&lt;/span>&lt;span class="n">LPVOID&lt;/span>&lt;span class="p">)&lt;/span>&lt;span class="n">body&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">c_str&lt;/span>&lt;span class="p">(),&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">body&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">length&lt;/span>&lt;span class="p">(),&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">body&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">length&lt;/span>&lt;span class="p">(),&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="mi">0&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="o">!&lt;/span>&lt;span class="n">result&lt;/span> &lt;span class="o">||&lt;/span> &lt;span class="o">!&lt;/span>&lt;span class="n">WinHttpReceiveResponse&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hRequest&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="nb">NULL&lt;/span>&lt;span class="p">))&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cerr&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;發送錯誤&lt;/span>&lt;span class="se">\n&lt;/span>&lt;span class="s">&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="nb">false&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 確認狀態碼
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">DWORD&lt;/span> &lt;span class="n">statusCode&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">DWORD&lt;/span> &lt;span class="n">size&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="k">sizeof&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">statusCode&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WinHttpQueryHeaders&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hRequest&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_QUERY_STATUS_CODE&lt;/span> &lt;span class="o">|&lt;/span> &lt;span class="n">WINHTTP_QUERY_FLAG_NUMBER&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_HEADER_NAME_BY_INDEX&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="o">&amp;amp;&lt;/span>&lt;span class="n">statusCode&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="o">&amp;amp;&lt;/span>&lt;span class="n">size&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">WINHTTP_NO_HEADER_INDEX&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WinHttpCloseHandle&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hRequest&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WinHttpCloseHandle&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hConnect&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WinHttpCloseHandle&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hSession&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">statusCode&lt;/span> &lt;span class="o">==&lt;/span> &lt;span class="mi">200&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kt">int&lt;/span> &lt;span class="nf">main&lt;/span>&lt;span class="p">()&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span> &lt;span class="n">token&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;xoxb-你的存取權杖&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="c1">// 存取權杖
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">string&lt;/span> &lt;span class="n">channel&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="s">&amp;#34;頻道ID或者#general&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="c1">// 範例: &amp;#34;#general&amp;#34; 或 &amp;#34;C0123456789&amp;#34;
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">string&lt;/span> &lt;span class="n">message&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="s">&amp;#34;嘗試從 C++ 發送訊息到 Slack！&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">PostSlackMessage&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">token&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">channel&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">message&lt;/span>&lt;span class="p">))&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;發文成功！&lt;/span>&lt;span class="se">\n&lt;/span>&lt;span class="s">&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span> &lt;span class="k">else&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cerr&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;發文失敗。&lt;/span>&lt;span class="se">\n&lt;/span>&lt;span class="s">&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;hr>
&lt;h2 id="-如何獲取頻道-id">📌 如何獲取頻道 ID
&lt;/h2>&lt;p>僅使用頻道名稱（例如：&lt;code>#general&lt;/code>）可能會導致錯誤。
最可靠的方法是使用 Slack 頻道頁面 URL 中的 ID。&lt;/p>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-fallback" data-lang="fallback">&lt;span class="line">&lt;span class="cl">https://app.slack.com/client/Txxxxx/C0123456789
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> ↑這部分就是頻道 ID
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;hr>
&lt;h2 id="-關於權杖類型補充">✅ 關於權杖類型（補充）
&lt;/h2>&lt;table>
&lt;thead>
&lt;tr>
&lt;th>權杖格式&lt;/th>
&lt;th>用途&lt;/th>
&lt;th>範例&lt;/th>
&lt;/tr>
&lt;/thead>
&lt;tbody>
&lt;tr>
&lt;td>&lt;code>xoxb-...&lt;/code>&lt;/td>
&lt;td>Bot Token（推薦）&lt;/td>
&lt;td>發文、編輯、刪除&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>&lt;code>xoxp-...&lt;/code>&lt;/td>
&lt;td>User Token（不推薦）&lt;/td>
&lt;td>非 Bot 相關操作&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>Refresh Token&lt;/td>
&lt;td>用於長期權杖更新&lt;/td>
&lt;td>通常不使用&lt;/td>
&lt;/tr>
&lt;/tbody>
&lt;/table>
&lt;hr>
&lt;h2 id="-總結">📝 總結
&lt;/h2>&lt;ul>
&lt;li>要從 C++ 發文到 Slack，使用 Slack Web API + Bearer Token 方式最為可靠&lt;/li>
&lt;li>使用 HTTPS POST 發送至 &lt;code>chat.postMessage&lt;/code> 端點&lt;/li>
&lt;li>必須透過 Bearer 標頭發送權杖&lt;/li>
&lt;li>確保 &lt;strong>指定頻道 ID&lt;/strong> 以確保準確性&lt;/li>
&lt;/ul></description></item><item><title>使用 C++（Win32 API + WinHTTP）發送訊息至 Slack 的方法【支援 Webhook】</title><link>http://kenji.blog/zh-tw/p/%E4%BD%BF%E7%94%A8-c-win32-api--winhttp%E7%99%BC%E9%80%81%E8%A8%8A%E6%81%AF%E8%87%B3-slack-%E7%9A%84%E6%96%B9%E6%B3%95%E6%94%AF%E6%8F%B4-webhook/</link><pubDate>Wed, 16 Jul 2025 19:42:56 +0900</pubDate><guid>http://kenji.blog/zh-tw/p/%E4%BD%BF%E7%94%A8-c-win32-api--winhttp%E7%99%BC%E9%80%81%E8%A8%8A%E6%81%AF%E8%87%B3-slack-%E7%9A%84%E6%96%B9%E6%B3%95%E6%94%AF%E6%8F%B4-webhook/</guid><description>&lt;img src="http://kenji.blog/p/c-win32-api--winhttp%E3%81%A7slack%E3%81%AB%E3%83%A1%E3%83%83%E3%82%BB%E3%83%BC%E3%82%B8%E3%82%92%E6%8A%95%E7%A8%BF%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95webhook%E5%AF%BE%E5%BF%9C/img.png" alt="Featured image of post 使用 C++（Win32 API + WinHTTP）發送訊息至 Slack 的方法【支援 Webhook】" />&lt;h1 id="使用-cwin32-api--winhttp發送訊息至-slack-的方法支援-webhook">使用 C++（Win32 API + WinHTTP）發送訊息至 Slack 的方法【支援 Webhook】
&lt;/h1>&lt;p>想要從 C++ 發送訊息到 Slack。
在 Node.js 或 Python 中這很常見，但使用「C++ × Win32 API × WinHTTP」來做的情況應該很少見吧。&lt;/p>
&lt;p>這篇文章將以循序漸進的方式，淺顯易懂地解說 &lt;strong>如何使用 Webhook URL 從 C++ 發送訊息到 Slack&lt;/strong> 。&lt;/p>
&lt;hr>
&lt;h2 id="-整體流程">✅ 整體流程
&lt;/h2>&lt;p>要發布到 Slack，需要遵循以下步驟。&lt;/p>
&lt;ol>
&lt;li>取得 Slack 的 Webhook URL（API 金鑰）&lt;/li>
&lt;li>使用 WinHTTP 發送 &lt;code>POST&lt;/code> 請求&lt;/li>
&lt;li>以 JSON 格式建立訊息主體&lt;/li>
&lt;li>檢查結果即可完成！&lt;/li>
&lt;/ol>
&lt;hr>
&lt;h2 id="-step1取得-slack-webhook-url-的方法">🔑 Step1：取得 Slack Webhook URL 的方法
&lt;/h2>&lt;p>在 Slack 中，可以使用 Incoming Webhooks 的功能，輕鬆地從外部服務發送訊息。&lt;/p>
&lt;h3 id="取得步驟">取得步驟
&lt;/h3>&lt;ol>
&lt;li>進入 &lt;a class="link" href="https://api.slack.com/apps" target="_blank" rel="noopener"
>https://api.slack.com/apps&lt;/a>&lt;/li>
&lt;li>點擊 &lt;code>Create New App&lt;/code>&lt;/li>
&lt;li>選擇 &lt;code>From scratch&lt;/code> 並選擇應用程式名稱與發布目標工作區&lt;/li>
&lt;li>從左側選單選擇 &lt;strong>「Incoming Webhooks」&lt;/strong> 並啟用&lt;/li>
&lt;li>點擊 &lt;strong>「Add New Webhook to Workspace」&lt;/strong> ，然後選擇頻道&lt;/li>
&lt;li>複製發行的 URL（例如: &lt;code>https://hooks.slack.com/services/xxx/yyy/zzz&lt;/code>）&lt;/li>
&lt;/ol>
&lt;p>這個 URL 將如同 API 金鑰般發揮作用。&lt;/p>
&lt;hr>
&lt;h2 id="-step2使用-c-程式碼發送訊息至-slack">💻 Step2：使用 C++ 程式碼發送訊息至 Slack
&lt;/h2>&lt;h3 id="使用技術">使用技術
&lt;/h3>&lt;ul>
&lt;li>Win32 API&lt;/li>
&lt;li>WinHTTP（標準函式庫）&lt;/li>
&lt;li>JSON 格式訊息&lt;/li>
&lt;/ul>
&lt;h3 id="範例程式碼發佈至-slack">範例程式碼（發佈至 Slack）
&lt;/h3>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
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&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;windows.h&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;winhttp.h&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;iostream&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#pragma comment(lib, &amp;#34;winhttp.lib&amp;#34;)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kt">bool&lt;/span> &lt;span class="nf">PostToSlack&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="k">const&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="n">webhookUrl&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="k">const&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">string&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="n">messageJson&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 解析 URL
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">URL_COMPONENTS&lt;/span> &lt;span class="n">urlComp&lt;/span>&lt;span class="p">{};&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="kt">wchar_t&lt;/span> &lt;span class="n">hostName&lt;/span>&lt;span class="p">[&lt;/span>&lt;span class="mi">256&lt;/span>&lt;span class="p">];&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="kt">wchar_t&lt;/span> &lt;span class="n">urlPath&lt;/span>&lt;span class="p">[&lt;/span>&lt;span class="mi">1024&lt;/span>&lt;span class="p">];&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">urlComp&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">dwStructSize&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="k">sizeof&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">urlComp&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">urlComp&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">lpszHostName&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">hostName&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">urlComp&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">dwHostNameLength&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">_countof&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hostName&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">urlComp&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">lpszUrlPath&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">urlPath&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">urlComp&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">dwUrlPathLength&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">_countof&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">urlPath&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="o">!&lt;/span>&lt;span class="n">WinHttpCrackUrl&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">webhookUrl&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">c_str&lt;/span>&lt;span class="p">(),&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="o">&amp;amp;&lt;/span>&lt;span class="n">urlComp&lt;/span>&lt;span class="p">))&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wcerr&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;URL 解析失敗&lt;/span>&lt;span class="se">\n&lt;/span>&lt;span class="s">&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="nb">false&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// HTTP 階段與連線
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">HINTERNET&lt;/span> &lt;span class="n">hSession&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">WinHttpOpen&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;SlackPoster/1.0&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_ACCESS_TYPE_DEFAULT_PROXY&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_NO_PROXY_NAME&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_NO_PROXY_BYPASS&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">HINTERNET&lt;/span> &lt;span class="n">hConnect&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">WinHttpConnect&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hSession&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">hostName&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">urlComp&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">nPort&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">HINTERNET&lt;/span> &lt;span class="n">hRequest&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">WinHttpOpenRequest&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hConnect&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;POST&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">urlPath&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nb">NULL&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">WINHTTP_NO_REFERER&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_DEFAULT_ACCEPT_TYPES&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_FLAG_SECURE&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span> &lt;span class="n">headers&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;Content-Type: application/json&lt;/span>&lt;span class="se">\r\n&lt;/span>&lt;span class="s">&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">BOOL&lt;/span> &lt;span class="n">result&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">WinHttpSendRequest&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hRequest&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">headers&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">c_str&lt;/span>&lt;span class="p">(),&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="o">-&lt;/span>&lt;span class="mi">1&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">(&lt;/span>&lt;span class="n">LPVOID&lt;/span>&lt;span class="p">)&lt;/span>&lt;span class="n">messageJson&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">c_str&lt;/span>&lt;span class="p">(),&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">messageJson&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">length&lt;/span>&lt;span class="p">(),&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">messageJson&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">length&lt;/span>&lt;span class="p">(),&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="mi">0&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="o">!&lt;/span>&lt;span class="n">result&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cerr&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;發送請求失敗&lt;/span>&lt;span class="se">\n&lt;/span>&lt;span class="s">&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="nb">false&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WinHttpReceiveResponse&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hRequest&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="nb">NULL&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">DWORD&lt;/span> &lt;span class="n">statusCode&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">DWORD&lt;/span> &lt;span class="n">size&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="k">sizeof&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">statusCode&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WinHttpQueryHeaders&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hRequest&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_QUERY_STATUS_CODE&lt;/span> &lt;span class="o">|&lt;/span> &lt;span class="n">WINHTTP_QUERY_FLAG_NUMBER&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_HEADER_NAME_BY_INDEX&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="o">&amp;amp;&lt;/span>&lt;span class="n">statusCode&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="o">&amp;amp;&lt;/span>&lt;span class="n">size&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">WINHTTP_NO_HEADER_INDEX&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="c1">// 釋放資源
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span> &lt;span class="n">WinHttpCloseHandle&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hRequest&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WinHttpCloseHandle&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hConnect&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WinHttpCloseHandle&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hSession&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">statusCode&lt;/span> &lt;span class="o">==&lt;/span> &lt;span class="mi">200&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kt">int&lt;/span> &lt;span class="nf">main&lt;/span>&lt;span class="p">()&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span> &lt;span class="n">webhookUrl&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;https://hooks.slack.com/services/xxx/yyy/zzz&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span> &lt;span class="c1">// 請替換成自己的 Webhook
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="c1">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">string&lt;/span> &lt;span class="n">message&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">R&lt;/span>&lt;span class="s">&amp;#34;({&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="s">&amp;#34;text&amp;#34;&lt;/span>&lt;span class="o">:&lt;/span> &lt;span class="s">&amp;#34;Hello from C++ :rocket:&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="s">&amp;#34;username&amp;#34;&lt;/span>&lt;span class="o">:&lt;/span> &lt;span class="s">&amp;#34;C++ Bot&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="s">&amp;#34;icon_emoji&amp;#34;&lt;/span>&lt;span class="o">:&lt;/span> &lt;span class="s">&amp;#34;:robot_face:&amp;#34;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">})&lt;/span>&lt;span class="s">&amp;#34;;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">PostToSlack&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">webhookUrl&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">message&lt;/span>&lt;span class="p">))&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;發布成功！&lt;/span>&lt;span class="se">\n&lt;/span>&lt;span class="s">&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span> &lt;span class="k">else&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">cerr&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="s">&amp;#34;發布失敗。&lt;/span>&lt;span class="se">\n&lt;/span>&lt;span class="s">&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;hr>
&lt;h2 id="-自訂-json-訊息">🧪 自訂 JSON 訊息
&lt;/h2>&lt;p>在 Slack 的 Webhook 中，可以包含以下參數：&lt;/p>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;span class="lnt">5
&lt;/span>&lt;span class="lnt">6
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-json" data-lang="json">&lt;span class="line">&lt;span class="cl">&lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nt">&amp;#34;text&amp;#34;&lt;/span>&lt;span class="p">:&lt;/span> &lt;span class="s2">&amp;#34;通知內容&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nt">&amp;#34;username&amp;#34;&lt;/span>&lt;span class="p">:&lt;/span> &lt;span class="s2">&amp;#34;Bot 名稱&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nt">&amp;#34;icon_emoji&amp;#34;&lt;/span>&lt;span class="p">:&lt;/span> &lt;span class="s2">&amp;#34;:rocket:&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nt">&amp;#34;channel&amp;#34;&lt;/span>&lt;span class="p">:&lt;/span> &lt;span class="s2">&amp;#34;#任意頻道名稱&amp;#34;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;hr>
&lt;h2 id="-補充事項">📌 補充事項
&lt;/h2>&lt;ul>
&lt;li>&lt;code>Content-Type&lt;/code> 必須指定為 &lt;code>&amp;quot;application/json&amp;quot;&lt;/code>&lt;/li>
&lt;li>Webhook URL 直接以 &lt;code>wstring&lt;/code> 傳遞即可（無需 URL 編碼）&lt;/li>
&lt;li>因為是 HTTPS 通訊，請別忘了加上 &lt;code>WINHTTP_FLAG_SECURE&lt;/code>&lt;/li>
&lt;/ul>
&lt;hr>
&lt;h2 id="-附錄slack-中的發布確認範例">🎉 附錄：Slack 中的發布確認範例
&lt;/h2>&lt;p>在 Slack 中會這樣顯示：&lt;/p>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-fallback" data-lang="fallback">&lt;span class="line">&lt;span class="cl">[C++ Bot]
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">Hello from C++ :rocket:
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;hr>
&lt;h2 id="-總結">✍️ 總結
&lt;/h2>&lt;table>
&lt;thead>
&lt;tr>
&lt;th>項目&lt;/th>
&lt;th>內容&lt;/th>
&lt;/tr>
&lt;/thead>
&lt;tbody>
&lt;tr>
&lt;td>發布方式&lt;/td>
&lt;td>Webhook (Incoming Webhooks)&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>通訊函式庫&lt;/td>
&lt;td>WinHTTP&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>資料格式&lt;/td>
&lt;td>JSON&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>可用參數&lt;/td>
&lt;td>text, username, icon_emoji, channel 等&lt;/td>
&lt;/tr>
&lt;/tbody>
&lt;/table>
&lt;p>還在想著怎麼用 C++ 整合 Slack 嗎？你也可以從今天開始加入通知 Bot！&lt;/p>
&lt;hr>
&lt;h2 id="-下集預告">🚀 下集預告？
&lt;/h2>&lt;p>如果您有興趣，下次我們可以：&lt;/p>
&lt;ul>
&lt;li>&lt;strong>檔案附件&lt;/strong>&lt;/li>
&lt;li>&lt;strong>帶按鈕的 UI&lt;/strong>&lt;/li>
&lt;li>&lt;strong>使用 Slack App + OAuth2 進行靈活的 API 操作&lt;/strong>&lt;/li>
&lt;/ul>
&lt;p>等，為您介紹更進一步的 Slack 整合！&lt;/p></description></item><item><title>如何從 C++ 向 Microsoft Teams 發佈訊息（WinHTTP + Graph API）</title><link>http://kenji.blog/zh-tw/p/%E5%A6%82%E4%BD%95%E5%BE%9E-c-%E5%90%91-microsoft-teams-%E7%99%BC%E4%BD%88%E8%A8%8A%E6%81%AFwinhttp--graph-api/</link><pubDate>Mon, 14 Jul 2025 23:40:15 +0900</pubDate><guid>http://kenji.blog/zh-tw/p/%E5%A6%82%E4%BD%95%E5%BE%9E-c-%E5%90%91-microsoft-teams-%E7%99%BC%E4%BD%88%E8%A8%8A%E6%81%AFwinhttp--graph-api/</guid><description>&lt;img src="http://kenji.blog/p/c-%E3%81%8B%E3%82%89-microsoft-teams-%E3%81%AB%E3%83%A1%E3%83%83%E3%82%BB%E3%83%BC%E3%82%B8%E3%82%92%E6%8A%95%E7%A8%BF%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95winhttp--graph-api/img.png" alt="Featured image of post 如何從 C++ 向 Microsoft Teams 發佈訊息（WinHTTP + Graph API）" />&lt;h1 id="如何從-c-向-microsoft-teams-發佈訊息winhttp--graph-api">如何從 C++ 向 Microsoft Teams 發佈訊息（WinHTTP + Graph API）
&lt;/h1>&lt;p>想自動發佈訊息到 Microsoft Teams 聊天室中嗎？&lt;br>
這時候可以使用的就是 &lt;strong>Microsoft Graph API&lt;/strong> 。&lt;br>
在本文中，我們將透過步驟介紹 &lt;strong>使用 WinHTTP 的 C++ 程式碼範例&lt;/strong> 以及 &lt;strong>必要的 API 認證步驟&lt;/strong> 。&lt;/p>
&lt;hr>
&lt;h2 id="-必要的準備microsoft-graph-api-認證設定">🔧 必要的準備（Microsoft Graph API 認證設定）
&lt;/h2>&lt;h3 id="1-在-azure-入口網站註冊應用程式">1. 在 Azure 入口網站註冊應用程式
&lt;/h3>&lt;p>首先，要使用 Microsoft Graph API，必須在 Azure 註冊應用程式。&lt;/p>
&lt;ol>
&lt;li>前往 &lt;a class="link" href="https://portal.azure.com" target="_blank" rel="noopener"
>Azure Portal&lt;/a>&lt;/li>
&lt;li>&lt;strong>「Microsoft Entra ID」&lt;/strong> &amp;gt; &lt;strong>「＋新增」&lt;/strong> &amp;gt; &lt;strong>「應用程式註冊」&lt;/strong> &amp;gt; &lt;strong>「新增註冊」&lt;/strong>&lt;/li>
&lt;li>輸入任意應用程式名稱後點擊「註冊」&lt;/li>
&lt;/ol>
&lt;h3 id="2-新增-api-權限">2. 新增 API 權限
&lt;/h3>&lt;ol>
&lt;li>前往左側選單的「API 權限」&lt;/li>
&lt;li>在 &lt;strong>「Microsoft Graph」&lt;/strong> &amp;gt; &lt;strong>「新增權限」&lt;/strong> 中搜尋以下範圍，然後點擊 &lt;strong>「更新權限」&lt;/strong>&lt;/li>
&lt;/ol>
&lt;ul>
&lt;li>Chat.ReadWrite&lt;/li>
&lt;li>User.Read&lt;/li>
&lt;/ul>
&lt;blockquote>
&lt;p>※ 若想要發佈到頻道，則還需要 &lt;code>ChannelMessage.Send&lt;/code>&lt;/p>
&lt;/blockquote>
&lt;h3 id="3-記下用戶端識別碼與租用戶識別碼">3. 記下用戶端識別碼與租用戶識別碼
&lt;/h3>&lt;p>記下顯示在「概觀」索引標籤中的以下兩項：&lt;/p>
&lt;ul>
&lt;li>應用程式 (用戶端) 識別碼&lt;/li>
&lt;li>目錄 (租用戶) 識別碼&lt;/li>
&lt;/ul>
&lt;h3 id="4-建立用戶端密碼">4. 建立用戶端密碼
&lt;/h3>&lt;ol>
&lt;li>前往「憑證與密碼」索引標籤&lt;/li>
&lt;li>點擊「新增用戶端密碼」 &amp;gt; 設定到期日後，點擊「新增」&lt;/li>
&lt;li>顯示的值（密碼）請 &lt;strong>務必當下立刻記下&lt;/strong>&lt;/li>
&lt;/ol>
&lt;hr>
&lt;h2 id="-取得存取權杖oauth2">🔐 取得存取權杖（OAuth2）
&lt;/h2>&lt;p>取得時我們使用 &lt;code>client_credentials&lt;/code> 流程。&lt;br>
使用 curl 執行以下命令，以取得存取權杖。&lt;/p>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
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&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-bash" data-lang="bash">&lt;span class="line">&lt;span class="cl">curl -X POST ^
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> https://login.microsoftonline.com/&lt;span class="o">{&lt;/span>租用戶識別碼&lt;span class="o">}&lt;/span>/oauth2/v2.0/token ^
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> -H &lt;span class="s2">&amp;#34;Content-Type: application/x-www-form-urlencoded&amp;#34;&lt;/span> ^
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> -d &lt;span class="s2">&amp;#34;client_id={用戶端識別碼}&amp;#34;&lt;/span> ^
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> -d &lt;span class="s2">&amp;#34;scope=https%3A%2F%2Fgraph.microsoft.com%2F.default&amp;#34;&lt;/span> ^
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> -d &lt;span class="s2">&amp;#34;client_secret={用戶端密碼}&amp;#34;&lt;/span> ^
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> -d &lt;span class="s2">&amp;#34;grant_type=client_credentials&amp;#34;&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;h3 id="回應範例">回應範例
&lt;/h3>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
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&lt;/span>&lt;span class="lnt">5
&lt;/span>&lt;span class="lnt">6
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-json" data-lang="json">&lt;span class="line">&lt;span class="cl">&lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nt">&amp;#34;token_type&amp;#34;&lt;/span>&lt;span class="p">:&lt;/span>&lt;span class="s2">&amp;#34;Bearer&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nt">&amp;#34;expires_in&amp;#34;&lt;/span>&lt;span class="p">:&lt;/span>&lt;span class="mi">3599&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nt">&amp;#34;ext_expires_in&amp;#34;&lt;/span>&lt;span class="p">:&lt;/span>&lt;span class="mi">3599&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nt">&amp;#34;access_token&amp;#34;&lt;/span>&lt;span class="p">:&lt;/span> &lt;span class="s2">&amp;#34;eyJ0eXAiOiJKV1QiLCJub...（省略）&amp;#34;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;p>使用此 access_token 來呼叫 Microsoft Graph API。&lt;/p>
&lt;h2 id="-投稿到-teams-聊天室的-c-範例">💬 投稿到 Teams 聊天室的 C++ 範例
&lt;/h2>&lt;p>這裡示範使用 WinHTTP 向聊天室發佈訊息的 C++ 範例。&lt;/p>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
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&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;windows.h&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;winhttp.h&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;iostream&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;string&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#pragma comment(lib, &amp;#34;winhttp.lib&amp;#34;)
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kt">void&lt;/span> &lt;span class="nf">PostToTeamsChat&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="k">const&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="n">accessToken&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="k">const&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="n">chatId&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="k">const&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span>&lt;span class="o">&amp;amp;&lt;/span> &lt;span class="n">message&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">HINTERNET&lt;/span> &lt;span class="n">hSession&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">WinHttpOpen&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;TeamsPoster/1.0&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">WINHTTP_ACCESS_TYPE_DEFAULT_PROXY&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_NO_PROXY_NAME&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">WINHTTP_NO_PROXY_BYPASS&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">HINTERNET&lt;/span> &lt;span class="n">hConnect&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">WinHttpConnect&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hSession&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;graph.microsoft.com&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">INTERNET_DEFAULT_HTTPS_PORT&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span> &lt;span class="n">endpoint&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;/v1.0/chats/&amp;#34;&lt;/span> &lt;span class="o">+&lt;/span> &lt;span class="n">chatId&lt;/span> &lt;span class="o">+&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;/messages&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">HINTERNET&lt;/span> &lt;span class="n">hRequest&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">WinHttpOpenRequest&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hConnect&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;POST&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">endpoint&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">c_str&lt;/span>&lt;span class="p">(),&lt;/span> &lt;span class="nb">NULL&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WINHTTP_NO_REFERER&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">WINHTTP_DEFAULT_ACCEPT_TYPES&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">WINHTTP_FLAG_SECURE&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span> &lt;span class="n">jsonBody&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;{&lt;/span>&lt;span class="se">\&amp;#34;&lt;/span>&lt;span class="s">body&lt;/span>&lt;span class="se">\&amp;#34;&lt;/span>&lt;span class="s">: {&lt;/span>&lt;span class="se">\&amp;#34;&lt;/span>&lt;span class="s">content&lt;/span>&lt;span class="se">\&amp;#34;&lt;/span>&lt;span class="s">: &lt;/span>&lt;span class="se">\&amp;#34;&lt;/span>&lt;span class="s">&amp;#34;&lt;/span> &lt;span class="o">+&lt;/span> &lt;span class="n">message&lt;/span> &lt;span class="o">+&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;&lt;/span>&lt;span class="se">\&amp;#34;&lt;/span>&lt;span class="s">}}&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span> &lt;span class="n">headers&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;Authorization: Bearer &amp;#34;&lt;/span> &lt;span class="o">+&lt;/span> &lt;span class="n">accessToken&lt;/span> &lt;span class="o">+&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;&lt;/span>&lt;span class="se">\r\n&lt;/span>&lt;span class="s">Content-Type: application/json&lt;/span>&lt;span class="se">\r\n&lt;/span>&lt;span class="s">&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">BOOL&lt;/span> &lt;span class="n">bResult&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">WinHttpSendRequest&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hRequest&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">headers&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">c_str&lt;/span>&lt;span class="p">(),&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">DWORD&lt;/span>&lt;span class="p">)&lt;/span>&lt;span class="o">-&lt;/span>&lt;span class="mi">1L&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">(&lt;/span>&lt;span class="n">LPVOID&lt;/span>&lt;span class="p">)&lt;/span>&lt;span class="n">jsonBody&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">c_str&lt;/span>&lt;span class="p">(),&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">DWORD&lt;/span>&lt;span class="p">)(&lt;/span>&lt;span class="n">jsonBody&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">length&lt;/span>&lt;span class="p">()&lt;/span> &lt;span class="o">*&lt;/span> &lt;span class="k">sizeof&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="kt">wchar_t&lt;/span>&lt;span class="p">)),&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">(&lt;/span>&lt;span class="n">DWORD&lt;/span>&lt;span class="p">)(&lt;/span>&lt;span class="n">jsonBody&lt;/span>&lt;span class="p">.&lt;/span>&lt;span class="n">length&lt;/span>&lt;span class="p">()&lt;/span> &lt;span class="o">*&lt;/span> &lt;span class="k">sizeof&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="kt">wchar_t&lt;/span>&lt;span class="p">)),&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">bResult&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WinHttpReceiveResponse&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hRequest&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="nb">NULL&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">DWORD&lt;/span> &lt;span class="n">dwSize&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WinHttpQueryDataAvailable&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hRequest&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="o">&amp;amp;&lt;/span>&lt;span class="n">dwSize&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">if&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">dwSize&lt;/span> &lt;span class="o">&amp;gt;&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">)&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span> &lt;span class="n">response&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">dwSize&lt;/span> &lt;span class="o">/&lt;/span> &lt;span class="k">sizeof&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="kt">wchar_t&lt;/span>&lt;span class="p">),&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">DWORD&lt;/span> &lt;span class="n">dwDownloaded&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WinHttpReadData&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hRequest&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="o">&amp;amp;&lt;/span>&lt;span class="n">response&lt;/span>&lt;span class="p">[&lt;/span>&lt;span class="mi">0&lt;/span>&lt;span class="p">],&lt;/span> &lt;span class="n">dwSize&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="o">&amp;amp;&lt;/span>&lt;span class="n">dwDownloaded&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wcout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;Response: &amp;#34;&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">response&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">endl&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WinHttpCloseHandle&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hRequest&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WinHttpCloseHandle&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hConnect&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">WinHttpCloseHandle&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">hSession&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kt">int&lt;/span> &lt;span class="nf">main&lt;/span>&lt;span class="p">()&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span> &lt;span class="n">access&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span> &lt;span class="n">chatId&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;19:&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wstring&lt;/span> &lt;span class="n">message&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;Hello from C++!&amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wcout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;Enter your access token: &amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">getline&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wcin&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">access&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wcout&lt;/span> &lt;span class="o">&amp;lt;&amp;lt;&lt;/span> &lt;span class="sa">L&lt;/span>&lt;span class="s">&amp;#34;Enter chat ID: &amp;#34;&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">getline&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">wcin&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">chatId&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">PostToTeamsChat&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">access&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">chatId&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">message&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;h2 id="-取得聊天室識別碼的方法">🔍 取得聊天室識別碼的方法
&lt;/h2>&lt;p>聊天室識別碼可以透過 GET /v1.0/me/chats 來確認。&lt;/p>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-fallback" data-lang="fallback">&lt;span class="line">&lt;span class="cl">curl -X GET ^
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> https://graph.microsoft.com/v1.0/me/chats ^
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> -H &amp;#34;Authorization: Bearer {access_token}&amp;#34; ^
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> -H &amp;#34;Content-Type: application/json&amp;#34;
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;h3 id="回應範例-1">回應範例
&lt;/h3>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;span class="lnt">5
&lt;/span>&lt;span class="lnt">6
&lt;/span>&lt;span class="lnt">7
&lt;/span>&lt;span class="lnt">8
&lt;/span>&lt;span class="lnt">9
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-json" data-lang="json">&lt;span class="line">&lt;span class="cl">&lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nt">&amp;#34;value&amp;#34;&lt;/span>&lt;span class="p">:&lt;/span> &lt;span class="p">[&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nt">&amp;#34;id&amp;#34;&lt;/span>&lt;span class="p">:&lt;/span> &lt;span class="s2">&amp;#34;19:abc123xyz@thread.v2&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nt">&amp;#34;topic&amp;#34;&lt;/span>&lt;span class="p">:&lt;/span> &lt;span class="kc">null&lt;/span>&lt;span class="p">,&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="nt">&amp;#34;chatType&amp;#34;&lt;/span>&lt;span class="p">:&lt;/span> &lt;span class="s2">&amp;#34;oneOnOne&amp;#34;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">]&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;h2 id="-注意事項">📌 注意事項
&lt;/h2>&lt;ul>
&lt;li>此範例為最基本實作。在實際運用中：
&lt;ul>
&lt;li>權杖過期處理&lt;/li>
&lt;li>HTTPS 憑證驗證&lt;/li>
&lt;li>錯誤處理的強化&lt;/li>
&lt;/ul>
&lt;/li>
&lt;li>頻道發佈請使用 teams/{team-id}/channels/{channel-id}/messages 。&lt;/li>
&lt;li>傳送附件檔案需要多部分處理 (multipart) 或 Graph Drive API。&lt;/li>
&lt;/ul>
&lt;h2 id="總結">總結
&lt;/h2>&lt;h2 id="-總結">📎 總結
&lt;/h2>&lt;table>
&lt;thead>
&lt;tr>
&lt;th>功能&lt;/th>
&lt;th>概要&lt;/th>
&lt;/tr>
&lt;/thead>
&lt;tbody>
&lt;tr>
&lt;td>Graph API&lt;/td>
&lt;td>與 Teams 互動的官方 API&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>應用程式註冊&lt;/td>
&lt;td>Azure 上必要的認證手續&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>存取權杖&lt;/td>
&lt;td>透過 OAuth2 取得，並用於請求中&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>C++ 實作&lt;/td>
&lt;td>使用 WinHTTP 呼叫 Graph API&lt;/td>
&lt;/tr>
&lt;/tbody>
&lt;/table>
&lt;h2 id="-下一步">🚀 下一步
&lt;/h2>&lt;p>作為更進階的範例，以下也是可行的：&lt;/p>
&lt;ul>
&lt;li>團隊頻道發佈 (&lt;code>/teams/{team-id}/channels/...&lt;/code>)&lt;/li>
&lt;li>帶有附件檔案的發佈&lt;/li>
&lt;li>機器人帳號或使用者帳號的切換&lt;/li>
&lt;li>包含取得權杖在內的完整 C++ 實作&lt;/li>
&lt;/ul>
&lt;p>如有任何需求，歡迎隨時留言！&lt;/p></description></item><item><title>使用 Win32API + C++ 開發程式的優缺點</title><link>http://kenji.blog/zh-tw/p/win32api-c-%E3%81%A7%E3%83%97%E3%83%AD%E3%82%B0%E3%83%A9%E3%83%A0%E3%82%92%E4%BD%9C%E3%82%8B%E3%83%A1%E3%83%AA%E3%83%83%E3%83%88%E3%81%A8%E3%83%87%E3%83%A1%E3%83%AA%E3%83%83%E3%83%88/</link><pubDate>Sat, 12 Jul 2025 12:30:35 +0900</pubDate><guid>http://kenji.blog/zh-tw/p/win32api-c-%E3%81%A7%E3%83%97%E3%83%AD%E3%82%B0%E3%83%A9%E3%83%A0%E3%82%92%E4%BD%9C%E3%82%8B%E3%83%A1%E3%83%AA%E3%83%83%E3%83%88%E3%81%A8%E3%83%87%E3%83%A1%E3%83%AA%E3%83%83%E3%83%88/</guid><description>&lt;img src="http://kenji.blog/p/win32api-c-%E3%81%A7%E3%83%97%E3%83%AD%E3%82%B0%E3%83%A9%E3%83%A0%E3%82%92%E4%BD%9C%E3%82%8B%E3%83%A1%E3%83%AA%E3%83%83%E3%83%88%E3%81%A8%E3%83%87%E3%83%A1%E3%83%AA%E3%83%83%E3%83%88/img_1.png" alt="Featured image of post 使用 Win32API + C++ 開發程式的優缺點" />&lt;h1 id="win32api--c-開發的魅力與挑戰">Win32API + C++ 開發的魅力與挑戰
&lt;/h1>&lt;p>對於想要精通 Windows 應用程式開發的人來說， &lt;strong>Win32API + C++&lt;/strong> 仍然是一個強大的選擇。
這種允許與作業系統進行最密切互動的組合，兼具了速度與靈活性。&lt;/p>
&lt;p>另一方面，要掌握它需要決心，因為它與現代開發風格有很大的不同。&lt;/p>
&lt;p>在本頁中，我們將從 &lt;strong>現役 Windows 應用程式開發人員的視角&lt;/strong> 清晰地解釋其優點和缺點。&lt;/p>
&lt;hr>
&lt;h2 id="優點">優點
&lt;/h2>&lt;h3 id="超高速的原生執行">超高速的原生執行
&lt;/h3>&lt;p>由於 C++ 和 Win32API 在最接近作業系統的層級上運作，因此幾乎沒有不必要的開銷。
CPU 和記憶體的使用效率極高，擁有 &lt;strong>壓倒性的執行速度&lt;/strong> 。&lt;/p>
&lt;h3 id="高靈活性和自由度">高靈活性和自由度
&lt;/h3>&lt;p>您可以 &lt;strong>自行精細地控制&lt;/strong> 應用程式的所有行為，例如視窗控制、非同步處理、COM 整合和行程管理。
也可以建立專門的工具和自己的原創框架。&lt;/p>
&lt;h3 id="易於分發無需執行環境">易於分發，無需執行環境
&lt;/h3>&lt;p>由於不需要像 .NET 或 Java 這樣的外部執行環境，因此它 &lt;strong>可以作為單一的執行檔進行分發&lt;/strong> 。
在重新分發期間較少發生問題，且無需安裝程式即可輕鬆執行。&lt;/p>
&lt;h3 id="可以建立輕量級應用程式">可以建立輕量級應用程式
&lt;/h3>&lt;p>由於它只需要最少必要的配置，其特點是 &lt;strong>記憶體佔用非常小&lt;/strong> 。
即使在低規格 PC 或虛擬機器環境中也能舒適地運作。&lt;/p>
&lt;h3 id="能夠實現作業系統級別的進階控制">能夠實現作業系統級別的進階控制
&lt;/h3>&lt;p>您還可以實現 &lt;strong>使用一般語言和函式庫難以達成的控制&lt;/strong> ，例如全域滑鼠和鍵盤鉤子（Hook）、視窗樣式的微調以及系統選單操作。&lt;/p>
&lt;hr>
&lt;h2 id="缺點">缺點
&lt;/h2>&lt;h3 id="開發效率低">開發效率低
&lt;/h3>&lt;p>即使是 GUI 的建構也必須完全在程式碼中完成，有時 &lt;strong>僅僅為了建立一個按鈕就需要幾十行程式碼&lt;/strong> 。
修改設計也很繁瑣，且與使用 UI 框架的開發相比，生產力較低。&lt;/p>
&lt;h3 id="易於降低可維護性">易於降低可維護性
&lt;/h3>&lt;p>有許多 &lt;strong>具有特殊結構的程式碼&lt;/strong> ，例如訊息迴圈和視窗程序，這阻礙了可讀性和可重複使用性。
它還有不適合團隊開發和長期維護的方面。&lt;/p>
&lt;h3 id="難以支援現代-ui">難以支援現代 UI
&lt;/h3>&lt;p>很 &lt;strong>難支援近年來要求的 UX&lt;/strong> ，例如高 DPI 支援、觸控介面、無障礙功能和深色模式。
您必須手動處理每一項，這需要花費大量的精力。&lt;/p>
&lt;h3 id="不支援跨平台">不支援跨平台
&lt;/h3>&lt;p>由於它是一個完全 Windows 專用的 API，因此 &lt;strong>無法移植到 macOS 或 Linux&lt;/strong> 。
如果您計劃跨平台部署，則需要選擇其他技術。&lt;/p>
&lt;h3 id="學習成本極高">學習成本極高
&lt;/h3>&lt;p>您必須了解 &lt;strong>如今已很少使用的概念和機制&lt;/strong> ，例如 Handles (控制代碼)、GDI、COM 和 OLE。
許多文件都很舊，需要時間和耐心來學習。&lt;/p>
&lt;hr>
&lt;h2 id="適合的用途">適合的用途
&lt;/h2>&lt;ul>
&lt;li>&lt;strong>輕量級工具&lt;/strong> ，如檔案啟動器和快捷鍵輔助工具&lt;/li>
&lt;li>&lt;strong>系統實用程式&lt;/strong> ，如剪貼簿操作和 IME 控制&lt;/li>
&lt;li>&lt;strong>基於原生控制的應用程式&lt;/strong> ，如全域鉤子和視窗擷取&lt;/li>
&lt;li>與硬體緊密連結的 &lt;strong>驅動程式支援工具&lt;/strong>&lt;/li>
&lt;/ul>
&lt;hr>
&lt;h2 id="不適合的用途">不適合的用途
&lt;/h2>&lt;ul>
&lt;li>現代 UI / UX 重要的 &lt;strong>一般消費者應用程式&lt;/strong>&lt;/li>
&lt;li>考慮到速度而建立的 &lt;strong>原型設計和 MVP 開發&lt;/strong>&lt;/li>
&lt;li>基於長期運作和團隊開發的 &lt;strong>大型專案&lt;/strong>&lt;/li>
&lt;li>需要支援多個作業系統的 &lt;strong>跨平台產品&lt;/strong>&lt;/li>
&lt;/ul>
&lt;hr>
&lt;h2 id="評估總結">評估總結
&lt;/h2>&lt;table>
&lt;thead>
&lt;tr>
&lt;th>觀點&lt;/th>
&lt;th>評估&lt;/th>
&lt;/tr>
&lt;/thead>
&lt;tbody>
&lt;tr>
&lt;td>執行速度&lt;/td>
&lt;td>◎ 非常快&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>記憶體效率&lt;/td>
&lt;td>◎ 優秀&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>開發速度&lt;/td>
&lt;td>× 慢&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>可維護性&lt;/td>
&lt;td>× 低&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>跨平台支援&lt;/td>
&lt;td>× 不支援&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>現代 UI 支援&lt;/td>
&lt;td>× 弱&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>作業系統控制自由度&lt;/td>
&lt;td>◎ 壓倒性地高&lt;/td>
&lt;/tr>
&lt;/tbody>
&lt;/table>
&lt;hr>
&lt;h2 id="結論">結論
&lt;/h2>&lt;p>&lt;strong>Win32API + C++ 是為那些「想要親自處理作業系統中所有事情」的開發人員準備的工具。&lt;/strong>
雖然其力量巨大，但學習和操作需要相應的決心。&lt;/p>
&lt;blockquote>
&lt;p>是否值得「大膽選擇」取決於您目標應用程式的性質。&lt;/p>
&lt;/blockquote>
&lt;hr>
&lt;p>潛入 &lt;code>#include &amp;lt;windows.h&amp;gt;&lt;/code> 的世界而不依賴 GUI 框架或現代語言 ――
這個選擇在今天仍然有意義。&lt;/p></description></item><item><title>【初學者指南】使用 vcpkg 在 Visual Studio 中安裝 libcurl（支援 OpenSSL）的步驟</title><link>http://kenji.blog/zh-tw/p/vcpkg-%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6-visual-studio-%E3%81%AB-curl-%E3%82%92%E3%82%A4%E3%83%B3%E3%82%B9%E3%83%88%E3%83%BC%E3%83%AB/</link><pubDate>Mon, 07 Jul 2025 21:46:08 +0900</pubDate><guid>http://kenji.blog/zh-tw/p/vcpkg-%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6-visual-studio-%E3%81%AB-curl-%E3%82%92%E3%82%A4%E3%83%B3%E3%82%B9%E3%83%88%E3%83%BC%E3%83%AB/</guid><description>&lt;img src="http://kenji.blog/p/vcpkg-%E3%82%92%E4%BD%BF%E3%81%A3%E3%81%A6-visual-studio-%E3%81%AB-curl-%E3%82%92%E3%82%A4%E3%83%B3%E3%82%B9%E3%83%88%E3%83%BC%E3%83%AB/img.png" alt="Featured image of post 【初學者指南】使用 vcpkg 在 Visual Studio 中安裝 libcurl（支援 OpenSSL）的步驟" />&lt;h2 id="如果您要在-visual-studio-中使用-libcurl支援-openssl強烈推薦引入-vcpkg非常簡單">如果您要在 Visual Studio 中使用 libcurl（支援 OpenSSL），強烈推薦引入 vcpkg，非常簡單
&lt;/h2>&lt;p>在 C++ 中處理 HTTP 通訊時，經常會使用 libcurl。但是，編譯和調整相依性卻意外地麻煩，對吧？&lt;/p>
&lt;p>這時候能派上用場的就是微軟開發的 C++ 函式庫管理工具 ** 「vcpkg」 ** 。
這次我們將介紹如何使用 cpkg 來引入 libcurl（支援 OpenSSL），並讓它在 Visual Studio 中能順暢使用的步驟。&lt;/p>
&lt;hr>
&lt;h3 id="vcpkg-的安裝僅限尚未安裝者">vcpkg 的安裝（僅限尚未安裝者）
&lt;/h3>&lt;p>首先，我們來安裝 cpkg. 請在 PowerShell 中執行以下步驟。&lt;/p>
&lt;p>&lt;code>powershell git clone https://github.com/microsoft/vcpkg cd vcpkg .ootstrap-vcpkg.bat &lt;/code>&lt;/p>
&lt;p>※如果您還沒安裝 Git，請到 &lt;a class="link" href="https://git-scm.com/" target="_blank" rel="noopener"
>Git 官方網站&lt;/a> 進行安裝。&lt;/p>
&lt;hr>
&lt;h3 id="libcurl支援-openssl的安裝">libcurl（支援 OpenSSL）的安裝
&lt;/h3>&lt;p>接著，使用 vcpkg 來安裝 libcurl. 為了指定支援 OpenSSL 的 64 位元版本，請執行以下命令。&lt;/p>
&lt;p>&lt;code>powershell vcpkg install curl[ssl] --triplet x64-windows &lt;/code>&lt;/p>
&lt;p>執行此命令後，必要的相依性（如 OpenSSL）也會被自動設定好。&lt;/p>
&lt;hr>
&lt;h3 id="與-visual-studio-的整合設定">與 Visual Studio 的整合設定
&lt;/h3>&lt;p>為了讓在 vcpkg 引入的函式庫能從 Visual Studio 專案中輕鬆使用，請使用下列命令進行整合設定。&lt;/p>
&lt;p>&lt;code>powershell vcpkg integrate install &lt;/code>&lt;/p>
&lt;p>設定好之後，在 Visual Studio 的專案中就能自動使用 #include &amp;lt;curl/curl.h&amp;gt;，不再需要手動設定函式庫的路徑或連結器。&lt;/p>
&lt;hr>
&lt;h2 id="結語">結語
&lt;/h2>&lt;p>至此，在 Visual Studio 中引入 libcurl（支援 OpenSSL）的準備工作就完成了。&lt;/p>
&lt;ul>
&lt;li>只要使用 vcpkg，就能一次管理所有麻煩的相依性&lt;/li>
&lt;li>使用 cpkg install curl[ssl] &amp;ndash;triplet x64-windows 輕鬆引入 libcurl&lt;/li>
&lt;li>使用 cpkg integrate install 即可與 Visual Studio 進行自動整合&lt;/li>
&lt;/ul>
&lt;p>接下來，只要在專案中包含標頭檔，並使用 libcurl 的 API 就能開始開發了。
請善用方便的 vcpkg，一口氣提升您的開發效率吧。&lt;/p></description></item><item><title>從 C++ 透過 C++/CLI DLL 執行 PowerShell 的步驟</title><link>http://kenji.blog/zh-tw/p/c-%E3%81%8B%E3%82%89-powershell-%E3%82%92-c-cli-dll-%E7%B5%8C%E7%94%B1%E3%81%A7%E5%AE%9F%E8%A1%8C%E3%81%99%E3%82%8B%E6%89%8B%E9%A0%86/</link><pubDate>Wed, 16 Apr 2025 01:58:03 +0900</pubDate><guid>http://kenji.blog/zh-tw/p/c-%E3%81%8B%E3%82%89-powershell-%E3%82%92-c-cli-dll-%E7%B5%8C%E7%94%B1%E3%81%A7%E5%AE%9F%E8%A1%8C%E3%81%99%E3%82%8B%E6%89%8B%E9%A0%86/</guid><description>&lt;img src="http://kenji.blog/p/c-%E3%81%8B%E3%82%89-powershell-%E3%82%92-c-cli-dll-%E7%B5%8C%E7%94%B1%E3%81%A7%E5%AE%9F%E8%A1%8C%E3%81%99%E3%82%8B%E6%89%8B%E9%A0%86/img.png" alt="Featured image of post 從 C++ 透過 C++/CLI DLL 執行 PowerShell 的步驟" />&lt;h1 id="-從-c-透過-ccli-dll-執行-powershell-的步驟visual-studio-2022--c">🎯 從 C++ 透過 C++/CLI DLL 執行 PowerShell 的步驟（Visual Studio 2022 / C++）
&lt;/h1>&lt;h2 id="-整體架構">✅ 整體架構
&lt;/h2>&lt;h3 id="--cli-封裝-dllccli">🔹 ① CLI 封裝 DLL（C++/CLI）
&lt;/h3>&lt;p>提供執行 PowerShell 腳本的功能。&lt;/p>
&lt;h3 id="--原生-c-呼叫端">🔹 ② 原生 C++ 呼叫端
&lt;/h3>&lt;p>呼叫 CLI DLL 以執行 PowerShell 腳本。&lt;/p>
&lt;hr>
&lt;h2 id="-步驟-1建立-cli-封裝-dll-專案">🔧 步驟 1：建立 CLI 封裝 DLL 專案
&lt;/h2>&lt;h3 id="1-建立專案">1. 建立專案
&lt;/h3>&lt;ul>
&lt;li>[建立新專案] → [C++] → &lt;strong>CLR 類別庫 (.NET Framework)&lt;/strong>&lt;/li>
&lt;li>名稱：&lt;code>PowerShellWrapper&lt;/code>&lt;/li>
&lt;/ul>
&lt;blockquote>
&lt;p>💡 如果未顯示此範本，請安裝「.NET 桌面開發」工作負載。&lt;/p>
&lt;/blockquote>
&lt;hr>
&lt;h3 id="2-新增-nuget-套件">2. 新增 NuGet 套件
&lt;/h3>&lt;ol>
&lt;li>在專案上按一下右鍵 → [管理 NuGet 套件]&lt;/li>
&lt;li>搜尋並安裝 &lt;code>System.Management.Automation&lt;/code>&lt;br>
（版本 5.x 或 7.x）&lt;/li>
&lt;/ol>
&lt;hr>
&lt;h3 id="3-cli-端程式碼實作">3. CLI 端程式碼實作
&lt;/h3>&lt;h4 id="powershellwrapperh">PowerShellWrapper.h
&lt;/h4>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
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&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#pragma once
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">System&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">namespace&lt;/span> &lt;span class="n">PowerShellWrapper&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">public&lt;/span> &lt;span class="n">ref&lt;/span> &lt;span class="k">class&lt;/span> &lt;span class="nc">PowerShellExecutor&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">public&lt;/span>&lt;span class="o">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">String&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">Execute&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">String&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">script&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;h4 id="powershellwrappercpp">PowerShellWrapper.cpp
&lt;/h4>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
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&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;#34;PowerShellWrapper.h&amp;#34;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">System&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">System&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Management&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Automation&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">System&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Collections&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">ObjectModel&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="n">String&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">PowerShellWrapper&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">PowerShellExecutor&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Execute&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">String&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">script&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">PowerShell&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">ps&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">PowerShell&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Create&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">ps&lt;/span>&lt;span class="o">-&amp;gt;&lt;/span>&lt;span class="n">AddScript&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">script&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">Collection&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">PSObject&lt;/span>&lt;span class="o">^&amp;gt;^&lt;/span> &lt;span class="n">results&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">ps&lt;/span>&lt;span class="o">-&amp;gt;&lt;/span>&lt;span class="n">Invoke&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">System&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Text&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">StringBuilder&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">sb&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">gcnew&lt;/span> &lt;span class="n">System&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Text&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">StringBuilder&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">for&lt;/span> &lt;span class="nf">each&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">PSObject&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">result&lt;/span> &lt;span class="n">in&lt;/span> &lt;span class="n">results&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">sb&lt;/span>&lt;span class="o">-&amp;gt;&lt;/span>&lt;span class="n">AppendLine&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">result&lt;/span>&lt;span class="o">-&amp;gt;&lt;/span>&lt;span class="n">ToString&lt;/span>&lt;span class="p">());&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="n">sb&lt;/span>&lt;span class="o">-&amp;gt;&lt;/span>&lt;span class="n">ToString&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;hr>
&lt;h2 id="-步驟-2從原生-c-端呼叫">🔧 步驟 2：從原生 C++ 端呼叫
&lt;/h2>&lt;h3 id="1-建立-c-主控台應用程式專案">1. 建立 C++ 主控台應用程式專案
&lt;/h3>&lt;ul>
&lt;li>名稱：&lt;code>NativeApp&lt;/code>&lt;/li>
&lt;/ul>
&lt;h3 id="2-參考設定">2. 參考設定
&lt;/h3>&lt;ul>
&lt;li>在專案上按一下右鍵 → [加入] → [參考] → [專案] → 新增 &lt;code>PowerShellWrapper&lt;/code>&lt;/li>
&lt;li>[組態屬性] → [C/C++] → [Common Language Runtime 支援] → 變更為 &lt;strong>/clr&lt;/strong>&lt;/li>
&lt;/ul>
&lt;hr>
&lt;h3 id="3-執行程式碼maincpp">3. 執行程式碼（main.cpp）
&lt;/h3>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt"> 1
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&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#using &amp;lt;System.dll&amp;gt;
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#using &amp;#34;..\\PowerShellWrapper\\Debug\\PowerShellWrapper.dll&amp;#34;
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">System&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">PowerShellWrapper&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kt">int&lt;/span> &lt;span class="nf">main&lt;/span>&lt;span class="p">()&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">PowerShellExecutor&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">executor&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">gcnew&lt;/span> &lt;span class="n">PowerShellExecutor&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">String&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">result&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">executor&lt;/span>&lt;span class="o">-&amp;gt;&lt;/span>&lt;span class="n">Execute&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="s">&amp;#34;Get-Process | Select-Object -First 1&amp;#34;&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">Console&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">WriteLine&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">result&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;hr>
&lt;h2 id="-補充說明idl--tlb--com-註冊">💡 補充說明（IDL / TLB / COM 註冊）
&lt;/h2>&lt;ul>
&lt;li>此架構是直接參考 .NET DLL 而不是 COM，因此 &lt;strong>不需要 IDL、TLB 或是 COM 註冊&lt;/strong> 。&lt;/li>
&lt;/ul>
&lt;hr>
&lt;h2 id="-最終架構">✅ 最終架構
&lt;/h2>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
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&lt;/span>&lt;span class="lnt">5
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-fallback" data-lang="fallback">&lt;span class="line">&lt;span class="cl">Solution
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">├── PowerShellWrapper (C++/CLI DLL)
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">│ └── PowerShellExecutor
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">├── NativeApp (C++ EXE)
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> └── main.cpp → 呼叫 DLL
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;hr></description></item><item><title>從 C++ 透過 C++/CLI DLL 執行 PowerShell 的步驟</title><link>http://kenji.blog/zh-tw/p/c-%E3%81%8B%E3%82%89-powershell-%E3%82%92-c-cli-dll-%E7%B5%8C%E7%94%B1%E3%81%A7%E5%AE%9F%E8%A1%8C%E3%81%99%E3%82%8B%E6%89%8B%E9%A0%86/</link><pubDate>Wed, 16 Apr 2025 01:58:03 +0900</pubDate><guid>http://kenji.blog/zh-tw/p/c-%E3%81%8B%E3%82%89-powershell-%E3%82%92-c-cli-dll-%E7%B5%8C%E7%94%B1%E3%81%A7%E5%AE%9F%E8%A1%8C%E3%81%99%E3%82%8B%E6%89%8B%E9%A0%86/</guid><description>&lt;img src="http://kenji.blog/p/c-%E3%81%8B%E3%82%89-powershell-%E3%82%92-c-cli-dll-%E7%B5%8C%E7%94%B1%E3%81%A7%E5%AE%9F%E8%A1%8C%E3%81%99%E3%82%8B%E6%89%8B%E9%A0%86/img.png" alt="Featured image of post 從 C++ 透過 C++/CLI DLL 執行 PowerShell 的步驟" />&lt;h1 id="-從-c-透過-ccli-dll-執行-powershell-的步驟visual-studio-2022--c">🎯 從 C++ 透過 C++/CLI DLL 執行 PowerShell 的步驟（Visual Studio 2022 / C++）
&lt;/h1>&lt;h2 id="-整體架構">✅ 整體架構
&lt;/h2>&lt;h3 id="--cli-封裝-dllccli">🔹 ① CLI 封裝 DLL（C++/CLI）
&lt;/h3>&lt;p>提供執行 PowerShell 腳本的功能。&lt;/p>
&lt;h3 id="--原生-c-呼叫端">🔹 ② 原生 C++ 呼叫端
&lt;/h3>&lt;p>呼叫 CLI DLL 以執行 PowerShell 腳本。&lt;/p>
&lt;hr>
&lt;h2 id="-步驟-1建立-cli-封裝-dll-專案">🔧 步驟 1：建立 CLI 封裝 DLL 專案
&lt;/h2>&lt;h3 id="1-建立專案">1. 建立專案
&lt;/h3>&lt;ul>
&lt;li>[建立新專案] → [C++] → &lt;strong>CLR 類別庫 (.NET Framework)&lt;/strong>&lt;/li>
&lt;li>名稱：&lt;code>PowerShellWrapper&lt;/code>&lt;/li>
&lt;/ul>
&lt;blockquote>
&lt;p>💡 如果未顯示此範本，請安裝「.NET 桌面開發」工作負載。&lt;/p>
&lt;/blockquote>
&lt;hr>
&lt;h3 id="2-新增-nuget-套件">2. 新增 NuGet 套件
&lt;/h3>&lt;ol>
&lt;li>在專案上按一下右鍵 → [管理 NuGet 套件]&lt;/li>
&lt;li>搜尋並安裝 &lt;code>System.Management.Automation&lt;/code>&lt;br>
（版本 5.x 或 7.x）&lt;/li>
&lt;/ol>
&lt;hr>
&lt;h3 id="3-cli-端程式碼實作">3. CLI 端程式碼實作
&lt;/h3>&lt;h4 id="powershellwrapperh">PowerShellWrapper.h
&lt;/h4>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
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&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#pragma once
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">System&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">namespace&lt;/span> &lt;span class="n">PowerShellWrapper&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">public&lt;/span> &lt;span class="n">ref&lt;/span> &lt;span class="k">class&lt;/span> &lt;span class="nc">PowerShellExecutor&lt;/span> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">public&lt;/span>&lt;span class="o">:&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">String&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">Execute&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">String&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">script&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">};&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;h4 id="powershellwrappercpp">PowerShellWrapper.cpp
&lt;/h4>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt"> 1
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&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;#34;PowerShellWrapper.h&amp;#34;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">System&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">System&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Management&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Automation&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">System&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Collections&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">ObjectModel&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="n">String&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">PowerShellWrapper&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">PowerShellExecutor&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Execute&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">String&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">script&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">PowerShell&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">ps&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">PowerShell&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Create&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">ps&lt;/span>&lt;span class="o">-&amp;gt;&lt;/span>&lt;span class="n">AddScript&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">script&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">Collection&lt;/span>&lt;span class="o">&amp;lt;&lt;/span>&lt;span class="n">PSObject&lt;/span>&lt;span class="o">^&amp;gt;^&lt;/span> &lt;span class="n">results&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">ps&lt;/span>&lt;span class="o">-&amp;gt;&lt;/span>&lt;span class="n">Invoke&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">System&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Text&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">StringBuilder&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">sb&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">gcnew&lt;/span> &lt;span class="n">System&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">Text&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">StringBuilder&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">for&lt;/span> &lt;span class="nf">each&lt;/span> &lt;span class="p">(&lt;/span>&lt;span class="n">PSObject&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">result&lt;/span> &lt;span class="n">in&lt;/span> &lt;span class="n">results&lt;/span>&lt;span class="p">)&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">sb&lt;/span>&lt;span class="o">-&amp;gt;&lt;/span>&lt;span class="n">AppendLine&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">result&lt;/span>&lt;span class="o">-&amp;gt;&lt;/span>&lt;span class="n">ToString&lt;/span>&lt;span class="p">());&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="n">sb&lt;/span>&lt;span class="o">-&amp;gt;&lt;/span>&lt;span class="n">ToString&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;hr>
&lt;h2 id="-步驟-2從原生-c-端呼叫">🔧 步驟 2：從原生 C++ 端呼叫
&lt;/h2>&lt;h3 id="1-建立-c-主控台應用程式專案">1. 建立 C++ 主控台應用程式專案
&lt;/h3>&lt;ul>
&lt;li>名稱：&lt;code>NativeApp&lt;/code>&lt;/li>
&lt;/ul>
&lt;h3 id="2-參考設定">2. 參考設定
&lt;/h3>&lt;ul>
&lt;li>在專案上按一下右鍵 → [加入] → [參考] → [專案] → 新增 &lt;code>PowerShellWrapper&lt;/code>&lt;/li>
&lt;li>[組態屬性] → [C/C++] → [Common Language Runtime 支援] → 變更為 &lt;strong>/clr&lt;/strong>&lt;/li>
&lt;/ul>
&lt;hr>
&lt;h3 id="3-執行程式碼maincpp">3. 執行程式碼（main.cpp）
&lt;/h3>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt"> 1
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&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-cpp" data-lang="cpp">&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#using &amp;lt;System.dll&amp;gt;
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#using &amp;#34;..\\PowerShellWrapper\\Debug\\PowerShellWrapper.dll&amp;#34;
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">System&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="k">using&lt;/span> &lt;span class="k">namespace&lt;/span> &lt;span class="n">PowerShellWrapper&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="kt">int&lt;/span> &lt;span class="nf">main&lt;/span>&lt;span class="p">()&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">{&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">PowerShellExecutor&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">executor&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">gcnew&lt;/span> &lt;span class="n">PowerShellExecutor&lt;/span>&lt;span class="p">();&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">String&lt;/span>&lt;span class="o">^&lt;/span> &lt;span class="n">result&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">executor&lt;/span>&lt;span class="o">-&amp;gt;&lt;/span>&lt;span class="n">Execute&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="s">&amp;#34;Get-Process | Select-Object -First 1&amp;#34;&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="n">Console&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">WriteLine&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="n">result&lt;/span>&lt;span class="p">);&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> &lt;span class="k">return&lt;/span> &lt;span class="mi">0&lt;/span>&lt;span class="p">;&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="p">}&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;hr>
&lt;h2 id="-補充說明idl--tlb--com-註冊">💡 補充說明（IDL / TLB / COM 註冊）
&lt;/h2>&lt;ul>
&lt;li>此架構是直接參考 .NET DLL 而不是 COM，因此 &lt;strong>不需要 IDL、TLB 或是 COM 註冊&lt;/strong> 。&lt;/li>
&lt;/ul>
&lt;hr>
&lt;h2 id="-最終架構">✅ 最終架構
&lt;/h2>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;span class="lnt">5
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-fallback" data-lang="fallback">&lt;span class="line">&lt;span class="cl">Solution
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">├── PowerShellWrapper (C++/CLI DLL)
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">│ └── PowerShellExecutor
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">├── NativeApp (C++ EXE)
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl"> └── main.cpp → 呼叫 DLL
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;hr></description></item><item><title>如何在 C++ 中以 ISO 8601 格式輸出當前時間</title><link>http://kenji.blog/zh-tw/p/c-%E3%81%A7%E7%8F%BE%E5%9C%A8%E6%99%82%E5%88%BB%E3%82%92iso8601%E3%83%95%E3%82%A9%E3%83%BC%E3%83%9E%E3%83%83%E3%83%88%E3%81%A7%E5%87%BA%E5%8A%9B%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/</link><pubDate>Sat, 15 Apr 2023 19:35:27 +0900</pubDate><guid>http://kenji.blog/zh-tw/p/c-%E3%81%A7%E7%8F%BE%E5%9C%A8%E6%99%82%E5%88%BB%E3%82%92iso8601%E3%83%95%E3%82%A9%E3%83%BC%E3%83%9E%E3%83%83%E3%83%88%E3%81%A7%E5%87%BA%E5%8A%9B%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/</guid><description>&lt;img src="http://kenji.blog/p/c-%E3%81%A7%E7%8F%BE%E5%9C%A8%E6%99%82%E5%88%BB%E3%82%92iso8601%E3%83%95%E3%82%A9%E3%83%BC%E3%83%9E%E3%83%83%E3%83%88%E3%81%A7%E5%87%BA%E5%8A%9B%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/img.png" alt="Featured image of post 如何在 C++ 中以 ISO 8601 格式輸出當前時間" />&lt;h3 id="先決條件">先決條件
&lt;/h3>&lt;ul>
&lt;li>ISO C++ 20 標準 (/std:c++20)&lt;/li>
&lt;/ul>
&lt;h3 id="程式碼">程式碼
&lt;/h3>&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;span class="lnt">2
&lt;/span>&lt;span class="lnt">3
&lt;/span>&lt;span class="lnt">4
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-c++" data-lang="c++">&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;chrono&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">#include&lt;/span> &lt;span class="cpf">&amp;lt;format&amp;gt;&lt;/span>&lt;span class="cp">
&lt;/span>&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="cp">&lt;/span>
&lt;/span>&lt;/span>&lt;span class="line">&lt;span class="cl">&lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">string&lt;/span> &lt;span class="n">datetime&lt;/span> &lt;span class="o">=&lt;/span> &lt;span class="n">std&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">format&lt;/span>&lt;span class="p">(&lt;/span>&lt;span class="s">&amp;#34;{:%FT%TZ}&amp;#34;&lt;/span>&lt;span class="p">,&lt;/span> &lt;span class="n">system_clock&lt;/span>&lt;span class="o">::&lt;/span>&lt;span class="n">now&lt;/span>&lt;span class="p">());&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;p>以上就是在 C++ 中以 ISO 8601 格式輸出當前時間的方法。&lt;/p>
&lt;h3 id="參考資料">參考資料
&lt;/h3>&lt;ul>
&lt;li>&lt;a class="link" href="https://eel.is/c&amp;#43;&amp;#43;draft/time.format" target="_blank" rel="noopener"
>std::format&lt;/a>&lt;/li>
&lt;/ul></description></item><item><title>如何在 Windows 上編譯 OpenSSL</title><link>http://kenji.blog/zh-tw/p/windows-%E3%81%A7-openssl-%E3%82%92%E3%83%93%E3%83%AB%E3%83%89%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/</link><pubDate>Fri, 07 Apr 2023 21:06:32 +0900</pubDate><guid>http://kenji.blog/zh-tw/p/windows-%E3%81%A7-openssl-%E3%82%92%E3%83%93%E3%83%AB%E3%83%89%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/</guid><description>&lt;img src="http://kenji.blog/p/windows-%E3%81%A7-openssl-%E3%82%92%E3%83%93%E3%83%AB%E3%83%89%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95/img.png" alt="Featured image of post 如何在 Windows 上編譯 OpenSSL" />&lt;h1 id="什麼是-openssl">什麼是 OpenSSL？
&lt;/h1>&lt;p>它是一個開源函式庫，提供了執行加密通訊所需的處理功能。&lt;/p>
&lt;p>為了在程式中使用它，由於其 C 語言原始碼是公開的，您需要對其進行編譯以建立函式庫。&lt;/p>
&lt;p>下面，我們將介紹編譯步驟。&lt;/p>
&lt;h1 id="準備編譯環境">準備編譯環境
&lt;/h1>&lt;ul>
&lt;li>
&lt;p>&lt;strong>Perl&lt;/strong>&lt;/p>
&lt;p>從 &lt;a class="link" href="https://strawberryperl.com/" target="_blank" rel="noopener"
>https://strawberryperl.com/&lt;/a> 下載 &lt;code>strawberry-perl-5.32.1.1-64bit.msi&lt;/code>。最新版本應該就可以。&lt;/p>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>NASM&lt;/strong>&lt;/p>
&lt;p>從 &lt;a class="link" href="https://www.nasm.us/" target="_blank" rel="noopener"
>https://www.nasm.us/&lt;/a> 的 &lt;code>Download&lt;/code> 中下載 &lt;code>2.16.01/nasm-2.16.01-win64.zip&lt;/code>。非 RC 的最新版本應該就可以。
安裝後，您需要將安裝 NASM 的資料夾登錄到環境變數 PATH 中。&lt;/p>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>Visual Studio 2022&lt;/strong> 或 &lt;strong>Build Tools for Visual Studio 2022&lt;/strong>&lt;/p>
&lt;p>從 &lt;a class="link" href="https://visualstudio.microsoft.com/ja/downloads/" target="_blank" rel="noopener"
>https://visualstudio.microsoft.com/ja/downloads/&lt;/a> 安裝 &lt;code>Visual Studio 2022 Community&lt;/code> 或 &lt;code>Build Tools for Visual Studio 2022&lt;/code>。&lt;/p>
&lt;/li>
&lt;/ul>
&lt;h1 id="windows-上的-openssl-編譯步驟">Windows 上的 OpenSSL 編譯步驟
&lt;/h1>&lt;ol>
&lt;li>從 &lt;a class="link" href="https://www.openssl.org/source/" target="_blank" rel="noopener"
>https://www.openssl.org/source/&lt;/a> 下載 &lt;code>openssl-3.1.0.tar.gz&lt;/code> 並解壓縮。如果無法解壓縮，請在命令提示字元中執行 &lt;code>tar -xzf openssl-3.1.0.tar.gz&lt;/code>。&lt;/li>
&lt;li>&lt;strong>以系統管理員權限&lt;/strong> 啟動命令提示字元。&lt;/li>
&lt;li>開啟解壓縮後的資料夾。&lt;/li>
&lt;li>執行以下命令。 ※ 請根據您安裝的 Visual Studio 版本更改 &lt;code>Community&lt;/code> 部分。&lt;/li>
&lt;/ol>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-gdscript3" data-lang="gdscript3">&lt;span class="line">&lt;span class="cl">&lt;span class="s2">&amp;#34;C:\Program Files\Microsoft Visual Studio&lt;/span>&lt;span class="se">\202&lt;/span>&lt;span class="s2">2\Community\VC\Auxiliary\Build&lt;/span>&lt;span class="se">\v&lt;/span>&lt;span class="s2">cvarsall.bat&amp;#34;&lt;/span> &lt;span class="n">x64&lt;/span>
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;ol start="5">
&lt;li>執行以下命令：&lt;/li>
&lt;/ol>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-fallback" data-lang="fallback">&lt;span class="line">&lt;span class="cl">perl Configure VC-WIN64A
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;ol start="6">
&lt;li>執行以下命令（會花費相當長的時間）：&lt;/li>
&lt;/ol>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-fallback" data-lang="fallback">&lt;span class="line">&lt;span class="cl">nmake
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;ol start="7">
&lt;li>執行以下命令（會花費相當長的時間）：&lt;/li>
&lt;/ol>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-fallback" data-lang="fallback">&lt;span class="line">&lt;span class="cl">nmake test
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;ol start="8">
&lt;li>執行以下命令：&lt;/li>
&lt;/ol>
&lt;div class="highlight">&lt;div class="chroma">
&lt;table class="lntable">&lt;tr>&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code>&lt;span class="lnt">1
&lt;/span>&lt;/code>&lt;/pre>&lt;/td>
&lt;td class="lntd">
&lt;pre tabindex="0" class="chroma">&lt;code class="language-fallback" data-lang="fallback">&lt;span class="line">&lt;span class="cl">nmake install
&lt;/span>&lt;/span>&lt;/code>&lt;/pre>&lt;/td>&lt;/tr>&lt;/table>
&lt;/div>
&lt;/div>&lt;p>如果成功，OpenSSL 將會安裝在 &lt;code>C:\Program Files\OpenSSL&lt;/code>。&lt;/p>
&lt;p>以上。&lt;/p>
&lt;h1 id="參考資料">參考資料
&lt;/h1>&lt;p>&lt;a class="link" href="https://ja.wikipedia.org/wiki/OpenSSL" target="_blank" rel="noopener"
>https://ja.wikipedia.org/wiki/OpenSSL&lt;/a>&lt;/p></description></item></channel></rss>