月更 技术博客 CXX优先 Zola 2026-08-11T00:00:00+00:00 https://suchaharcan.github.io/categories/writing/atom.xml 2026-08-11T00:00:00+00:00 2026-08-11T00:00:00+00:00 Suchaharcan https://suchaharcan.github.io/01Write_blog_AlgorithmDesign/408-graph/ <h1 id="kao-yan-408-tu-he-xin-zhi-shi-dian">考研 408 · 图核心知识点</h1> <blockquote> <p>图是 408 大题最爱：<strong>存储 → 遍历 → 生成树 → 最短路 → 拓扑/关键路径</strong>。</p> </blockquote> <hr /> <h2 id="1-tu-de-cun-chu">1. 图的存储</h2> <h3 id="lin-jie-ju-zhen">邻接矩阵</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span> 1 2 3 4</span></span> <span class="giallo-l"><span>1 [ 0 1 1 0 ]</span></span> <span class="giallo-l"><span>2 [ 1 0 1 1 ]</span></span> <span class="giallo-l"><span>3 [ 1 1 0 1 ]</span></span> <span class="giallo-l"><span>4 [ 0 1 1 0 ]</span></span></code></pre> <p>无向图对称；有向图按出边填写。<strong>判断两点是否相邻 O(1)，求度方便；但空间 O(n²)</strong>。</p> <h3 id="lin-jie-biao">邻接表</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>1 → 2 → 3</span></span> <span class="giallo-l"><span>2 → 1 → 3 → 4</span></span> <span class="giallo-l"><span>3 → 1 → 2 → 4</span></span> <span class="giallo-l"><span>4 → 2 → 3</span></span></code></pre> <p><strong>空间 O(n+e)，适合稀疏图</strong>；求某点出度方便，判断相邻需扫描。</p> <table><thead><tr><th>存储</th><th>空间</th><th>判断相邻</th><th>求所有邻点</th></tr></thead><tbody> <tr><td>邻接矩阵</td><td>O(n²)</td><td>O(1)</td><td>O(n)</td></tr> <tr><td>邻接表</td><td>O(n+e)</td><td>O(degree)</td><td>O(degree)</td></tr> </tbody></table> <hr /> <h2 id="2-bian-li">2. 遍历</h2> <h3 id="dfs-shen-du-you-xian-yong-zhan-di-gui">DFS（深度优先，用栈/递归）</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>访问顶点 → 递归访问第一个未访问邻点 → 回溯</span></span></code></pre><h3 id="bfs-yan-du-you-xian-yong-dui-lie">BFS（广度优先，用队列）</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>访问顶点 → 邻点全部入队 → 逐个出队重复</span></span></code></pre> <p><strong>复杂度</strong>：邻接表 O(n+e)，邻接矩阵 O(n²)。</p> <p>BFS 还能求<strong>无权图最短路径（边数）</strong>、判断连通分量数。</p> <hr /> <h2 id="3-zui-xiao-sheng-cheng-shu-mst">3. 最小生成树 MST</h2> <h3 id="prim-jia-dian">Prim（加点）</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>从一个顶点出发，每次选择&quot;连接已选集合与未选集合的最短边&quot;加入集合，直到覆盖全部顶点。</span></span> <span class="giallo-l"><span>复杂度：邻接矩阵 O(n²)；适合稠密图。</span></span></code></pre><h3 id="kruskal-jia-bian">Kruskal（加边）</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>边按权排序，从小到大选边，用并查集避免成环，选 n−1 条为止。</span></span> <span class="giallo-l"><span>复杂度：O(e·log e)；适合稀疏图。</span></span></code></pre><h3 id="shi-li">示例</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span> 1 --2-- 2</span></span> <span class="giallo-l"><span> | \ |</span></span> <span class="giallo-l"><span> 2 4 3</span></span> <span class="giallo-l"><span> | \ |</span></span> <span class="giallo-l"><span> 3 --1-- 4</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span>按 Kruskal：先取 3-4(1)、1-2(2)、1-3(2)（跳过 2-4(3)） ⇒ MST 总权 5</span></span></code></pre> <hr /> <h2 id="4-zui-duan-lu-jing">4. 最短路径</h2> <h3 id="dijkstra-dan-yuan-fei-fu-quan">Dijkstra（单源，非负权）</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>维护 dist[]，每次取未确定顶点中 dist 最小者，松弛其邻边。</span></span> <span class="giallo-l"><span>复杂度：邻接矩阵 O(n²)；堆优化 O((n+e)log n)。</span></span> <span class="giallo-l"><span>不能处理负权边。</span></span></code></pre><h3 id="floyd-duo-yuan">Floyd（多源）</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>三重循环：d[i][j] = min(d[i][j], d[i][k] + d[k][j])</span></span> <span class="giallo-l"><span>复杂度 O(n³)；可处理负权（无负环）。</span></span></code></pre><h3 id="shi-li-dijkstra-cong-1-chu-fa">示例（Dijkstra 从 1 出发）</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span> 2</span></span> <span class="giallo-l"><span> 1 ───── 3</span></span> <span class="giallo-l"><span> | 1 1 |</span></span> <span class="giallo-l"><span> 2 ───── 4</span></span> <span class="giallo-l"><span> 3</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span>dist: 1→1=0, 1→2=1, 1→3=2, 1→4=3（经 3）</span></span></code></pre> <hr /> <h2 id="5-tuo-bu-pai-xu-aov-wang">5. 拓扑排序（AOV 网）</h2> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>无环有向图，顶点表示活动。</span></span> <span class="giallo-l"><span>反复：选入度为 0 的顶点输出，删除其出边，直到全部输出。</span></span> <span class="giallo-l"><span>若剩余顶点仍有入度 ⇒ 存在环。</span></span> <span class="giallo-l"><span>复杂度：邻接表 O(n+e)。</span></span></code></pre><h3 id="shi-li-1">示例</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>课程依赖：A→C, B→C, C→D</span></span> <span class="giallo-l"><span>拓扑序之一：A B C D（不唯一）</span></span></code></pre> <hr /> <h2 id="6-guan-jian-lu-jing-aoe-wang">6. 关键路径（AOE 网）</h2> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>顶点 = 事件，边 = 活动（带权=耗时）</span></span> <span class="giallo-l"><span>ve(最早发生) 正向取 max；vl(最迟发生) 逆向取 min</span></span> <span class="giallo-l"><span>活动最早 e = ve(弧尾)；活动最迟 l = vl(弧头) − 权</span></span> <span class="giallo-l"><span>e == l 的活动为关键活动，串联成关键路径</span></span> <span class="giallo-l"><span>关键路径长度 = 工程最短工期</span></span></code></pre><h3 id="shi-li-2">示例</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span> v1 ─2─▶ v2 ─3─▶ v4</span></span> <span class="giallo-l"><span> \ ▲</span></span> <span class="giallo-l"><span> 4 ────────▶ 3</span></span> <span class="giallo-l"><span>ve: v1=0, v2=2, v4=5, v3=4</span></span> <span class="giallo-l"><span>vl: v1=0, v2=2, v4=5, v3=2（逆向）</span></span> <span class="giallo-l"><span>关键活动：v1→v2(2), v2→v4(3)，关键路径长 5</span></span></code></pre> <hr /> <h2 id="7-chang-kao-ti-xing">7. 常考题型</h2> <ol> <li>画邻接矩阵/邻接表；</li> <li>给图写 DFS/BFS 序列；</li> <li>Prim/Kruskal 过程与总权；</li> <li>Dijkstra/Floyd 逐步表；</li> <li>拓扑排序与环检测；</li> <li>求 ve/vl/e/l 与关键路径；</li> <li>判断有向图强连通、无向图连通分量。</li> </ol> <hr /> <h2 id="8-yi-cuo-dian">8. 易错点</h2> <ul> <li>Dijkstra <strong>不适用负权</strong>，Floyd 可；</li> <li>MST 不含权值相等的唯一性讨论（可能不唯一）；</li> <li>拓扑排序不唯一；</li> <li>关键路径可能<strong>不止一条</strong>；</li> <li>BFS 求最短路只对<strong>无权</strong>图。</li> </ul> <blockquote> <p>上一篇：<a href="https://suchaharcan.github.io/01Write_blog_AlgorithmDesign/408-tree/">树</a> ｜ 下一篇：<a href="https://suchaharcan.github.io/01Write_blog_AlgorithmDesign/408-sort/">排序</a></p> </blockquote> 2026-08-11T00:00:00+00:00 2026-08-11T00:00:00+00:00 Suchaharcan https://suchaharcan.github.io/01Write_blog_AlgorithmDesign/408-sort/ <h1 id="kao-yan-408-pai-xu-he-xin-zhi-shi-dian">考研 408 · 排序核心知识点</h1> <blockquote> <p>排序是 408 高频选择题 + 偶尔大题：<strong>背总表、会手推过程、能判断稳定性</strong>。</p> </blockquote> <hr /> <h2 id="1-zong-biao-bi-bei">1. 总表（必背）</h2> <table><thead><tr><th>算法</th><th>类别</th><th>最好</th><th>平均</th><th>最坏</th><th>空间</th><th>稳定</th></tr></thead><tbody> <tr><td>直接插入</td><td>插入</td><td>O(n)</td><td>O(n²)</td><td>O(n²)</td><td>O(1)</td><td>✅</td></tr> <tr><td>希尔</td><td>插入</td><td>O(n^1.3)</td><td>—</td><td>O(n²)</td><td>O(1)</td><td>❌</td></tr> <tr><td>冒泡</td><td>交换</td><td>O(n)</td><td>O(n²)</td><td>O(n²)</td><td>O(1)</td><td>✅</td></tr> <tr><td>快速排序</td><td>交换</td><td>O(n log n)</td><td>O(n log n)</td><td><strong>O(n²)</strong></td><td>O(log n)</td><td>❌</td></tr> <tr><td>简单选择</td><td>选择</td><td>O(n²)</td><td>O(n²)</td><td>O(n²)</td><td>O(1)</td><td>❌</td></tr> <tr><td>堆排序</td><td>选择</td><td>O(n log n)</td><td>O(n log n)</td><td>O(n log n)</td><td>O(1)</td><td>❌</td></tr> <tr><td>归并排序</td><td>归并</td><td>O(n log n)</td><td>O(n log n)</td><td>O(n log n)</td><td><strong>O(n)</strong></td><td>✅</td></tr> <tr><td>基数排序</td><td>分配</td><td>O(d(n+r))</td><td>O(d(n+r))</td><td>O(d(n+r))</td><td>O(r)</td><td>✅</td></tr> </tbody></table> <p><strong>记忆点</strong>：稳定的只有 直接插入 / 冒泡 / 归并 / 基数；快排最坏 O(n²)；归并空间 O(n)。</p> <hr /> <h2 id="2-cha-ru-lei">2. 插入类</h2> <h3 id="zhi-jie-cha-ru">直接插入</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>初始: [3] 1 4 2</span></span> <span class="giallo-l"><span>第1趟: [1 3] 4 2</span></span> <span class="giallo-l"><span>第2趟: [1 3 4] 2</span></span> <span class="giallo-l"><span>第3趟: [1 2 3 4]</span></span></code></pre> <p><strong>思想</strong>：把待排元素插入已有序前缀的合适位置。</p> <h3 id="xi-er-pai-xu">希尔排序</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>按增量 d 分组做直接插入，增量逐步缩小到 1（最后一次就是直接插入）。</span></span> <span class="giallo-l"><span>例：d=2 时分成奇偶两组分别插入排序。</span></span></code></pre> <hr /> <h2 id="3-jiao-huan-lei">3. 交换类</h2> <h3 id="mou-pao">冒泡</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>第1趟: 3 1 4 2 → 1 3 2 [4]（4 冒到末尾）</span></span> <span class="giallo-l"><span>第2趟: 1 3 2 → 1 2 [3] 4</span></span> <span class="giallo-l"><span>第3趟: 1 [2] 3 4</span></span></code></pre> <p><strong>无交换可提前结束</strong>，最好 O(n)。</p> <h3 id="kuai-su-pai-xu-fen-zhi">快速排序（分治）</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>选基准（通常首元素）→ 一趟划分：左小右大 → 递归两侧</span></span> <span class="giallo-l"><span>例 [4 2 5 1 3] 以 4 为基准一趟后：[1 2 3] 4 [5]</span></span></code></pre><pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">int</span><span class="z-entity z-name z-function"> partition</span><span class="z-punctuation">(</span><span class="z-storage z-type">int</span><span class="z-variable z-parameter"> a</span><span class="z-punctuation">[</span><span class="z-punctuation">]</span><span class="z-punctuation">,</span><span class="z-storage z-type"> int</span><span class="z-variable z-parameter"> low</span><span class="z-punctuation">,</span><span class="z-storage z-type"> int</span><span class="z-variable z-parameter"> high</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type"> int</span><span class="z-source"> pivot </span><span class="z-keyword z-operator">=</span><span class="z-variable z-other"> a</span><span class="z-punctuation">[</span><span class="z-source">low</span><span class="z-punctuation">]</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> while</span><span class="z-punctuation"> (</span><span class="z-source">low </span><span class="z-keyword z-operator">&lt;</span><span class="z-source"> high</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-keyword z-control"> while</span><span class="z-punctuation"> (</span><span class="z-source">low </span><span class="z-keyword z-operator">&lt;</span><span class="z-source"> high </span><span class="z-keyword z-operator">&amp;&amp;</span><span class="z-variable z-other"> a</span><span class="z-punctuation">[</span><span class="z-source">high</span><span class="z-punctuation">]</span><span class="z-keyword z-operator"> &gt;=</span><span class="z-source"> pivot</span><span class="z-punctuation">)</span><span class="z-source"> high</span><span class="z-keyword z-operator">--</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-variable z-other"> a</span><span class="z-punctuation">[</span><span class="z-source">low</span><span class="z-punctuation">]</span><span class="z-keyword z-operator"> =</span><span class="z-variable z-other"> a</span><span class="z-punctuation">[</span><span class="z-source">high</span><span class="z-punctuation">]</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> while</span><span class="z-punctuation"> (</span><span class="z-source">low </span><span class="z-keyword z-operator">&lt;</span><span class="z-source"> high </span><span class="z-keyword z-operator">&amp;&amp;</span><span class="z-variable z-other"> a</span><span class="z-punctuation">[</span><span class="z-source">low</span><span class="z-punctuation">]</span><span class="z-keyword z-operator"> &lt;=</span><span class="z-source"> pivot</span><span class="z-punctuation">)</span><span class="z-source"> low</span><span class="z-keyword z-operator">++</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-variable z-other"> a</span><span class="z-punctuation">[</span><span class="z-source">high</span><span class="z-punctuation">]</span><span class="z-keyword z-operator"> =</span><span class="z-variable z-other"> a</span><span class="z-punctuation">[</span><span class="z-source">low</span><span class="z-punctuation">]</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-variable z-other"> a</span><span class="z-punctuation">[</span><span class="z-source">low</span><span class="z-punctuation">]</span><span class="z-keyword z-operator"> =</span><span class="z-source"> pivot</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> return</span><span class="z-source"> low</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <p><strong>快排平均 O(n log n)；若每次划分极不平衡（已有序）最坏 O(n²)。</strong></p> <hr /> <h2 id="4-xuan-ze-lei">4. 选择类</h2> <h3 id="jian-dan-xuan-ze">简单选择</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>每趟选剩余最小元素与当前位置交换：</span></span> <span class="giallo-l"><span>[1] 3 4 2 → 1 [2] 4 3 → 1 2 [3] 4</span></span></code></pre> <p>比较次数固定 n(n−1)/2，与初始状态无关。</p> <h3 id="dui-pai-xu">堆排序</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>建大根堆 → 堆顶与末尾交换 → 下沉调整</span></span> <span class="giallo-l"><span>[4 3 2 1] 交换 1： [1 3 2] 4 → 下沉 → [3 1 2] 4 → 交换 → [2 1] 3 4 → ...</span></span></code></pre><pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>大根堆：parent ≥ children；调整（sift down）O(log n)</span></span> <span class="giallo-l"><span>建堆 O(n)；排序 O(n log n)</span></span></code></pre> <hr /> <h2 id="5-gui-bing-pai-xu-er-lu">5. 归并排序（二路）</h2> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>分：数组二分到底；治：两两有序合并</span></span> <span class="giallo-l"><span>[4 2 5 1] → [4 2][5 1] → [2 4][1 5] → [1 2 4 5]</span></span></code></pre><pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">void</span><span class="z-entity z-name z-function"> merge</span><span class="z-punctuation">(</span><span class="z-storage z-type">int</span><span class="z-variable z-parameter"> a</span><span class="z-punctuation">[</span><span class="z-punctuation">]</span><span class="z-punctuation">,</span><span class="z-storage z-type"> int</span><span class="z-variable z-parameter"> low</span><span class="z-punctuation">,</span><span class="z-storage z-type"> int</span><span class="z-variable z-parameter"> mid</span><span class="z-punctuation">,</span><span class="z-storage z-type"> int</span><span class="z-variable z-parameter"> high</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 复制到临时数组，双指针比较归并</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"><span class="z-storage z-type">void</span><span class="z-entity z-name z-function"> mergeSort</span><span class="z-punctuation">(</span><span class="z-storage z-type">int</span><span class="z-variable z-parameter"> a</span><span class="z-punctuation">[</span><span class="z-punctuation">]</span><span class="z-punctuation">,</span><span class="z-storage z-type"> int</span><span class="z-variable z-parameter"> low</span><span class="z-punctuation">,</span><span class="z-storage z-type"> int</span><span class="z-variable z-parameter"> high</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-keyword z-control"> if</span><span class="z-punctuation"> (</span><span class="z-source">low </span><span class="z-keyword z-operator">&lt;</span><span class="z-source"> high</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type"> int</span><span class="z-source"> mid </span><span class="z-keyword z-operator">=</span><span class="z-punctuation"> (</span><span class="z-source">low </span><span class="z-keyword z-operator">+</span><span class="z-source"> high</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> /</span><span class="z-constant z-numeric"> 2</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> mergeSort</span><span class="z-punctuation">(</span><span class="z-source">a</span><span class="z-punctuation">,</span><span class="z-source"> low</span><span class="z-punctuation">,</span><span class="z-source"> mid</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> mergeSort</span><span class="z-punctuation">(</span><span class="z-source">a</span><span class="z-punctuation">,</span><span class="z-source"> mid </span><span class="z-keyword z-operator">+</span><span class="z-constant z-numeric"> 1</span><span class="z-punctuation">,</span><span class="z-source"> high</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> merge</span><span class="z-punctuation">(</span><span class="z-source">a</span><span class="z-punctuation">,</span><span class="z-source"> low</span><span class="z-punctuation">,</span><span class="z-source"> mid</span><span class="z-punctuation">,</span><span class="z-source"> high</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <p><strong>稳定、O(n log n)、空间 O(n)</strong>；适合外部排序基础。</p> <hr /> <h2 id="6-ji-shu-pai-xu">6. 基数排序</h2> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>按&quot;位&quot;分配-收集：个位 → 十位 → 百位…</span></span> <span class="giallo-l"><span>例 [12, 3, 45]：</span></span> <span class="giallo-l"><span> 个位收集：3(03) 12 45 → 十位收集：3 12 45</span></span> <span class="giallo-l"><span>复杂度 O(d(n+r))，d 位数、r 基数（十进制 10）</span></span></code></pre> <hr /> <h2 id="7-408-gao-pin-jie-lun">7. 408 高频结论</h2> <table><thead><tr><th>考点</th><th>结论</th></tr></thead><tbody> <tr><td>快排最坏</td><td>基本有序时退化 O(n²)</td></tr> <tr><td>稳定性判断</td><td>相邻交换类（冒泡/插入）稳定；跳跃交换不稳定</td></tr> <tr><td>比较次数与初始无关</td><td>简单选择、折半插入、基数</td></tr> <tr><td>一趟排序后能确定位置</td><td>快排基准、选择类每趟定一个</td></tr> <tr><td>与初始状态有关</td><td>插入/冒泡/快排（趟数）；选择/归并/基数无关</td></tr> <tr><td>n 较小 / 基本有序</td><td>直接插入最佳</td></tr> </tbody></table> <hr /> <h2 id="8-wai-bu-pai-xu-liao-jie">8. 外部排序（了解）</h2> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>归并段（run）→ 败者树多路归并 → 置换选择排序生成更长段</span></span> <span class="giallo-l"><span>总代价 ≈ 内部归并 + I/O 次数；I/O 次数 = 2×趟数×块数</span></span> <span class="giallo-l"><span>增加归并路数、减少初始段数可减少 I/O</span></span></code></pre> <hr /> <h2 id="9-li-ti-su-lan">9. 例题速览</h2> <p><strong>例 1</strong>：<code>[1, 3, 2, 5, 4]</code> 用直接插入排序第 2 趟结果。</p> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>第1趟: [1 3] 2 5 4</span></span> <span class="giallo-l"><span>第2趟: [1 2 3] 5 4</span></span></code></pre> <p><strong>例 2</strong>：下列哪个排序是稳定的？直接插入 / 快排 / 堆排 / 希尔。</p> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>答案：直接插入</span></span></code></pre> <hr /> <blockquote> <p>上一篇：<a href="https://suchaharcan.github.io/01Write_blog_AlgorithmDesign/408-graph/">图</a></p> </blockquote> 2026-08-11T00:00:00+00:00 2026-08-11T00:00:00+00:00 Suchaharcan https://suchaharcan.github.io/01Write_blog_AlgorithmDesign/408-string/ <h1 id="kao-yan-408-zi-fu-chuan-he-xin-zhi-shi-dian">考研 408 · 字符串核心知识点</h1> <blockquote> <p>408 中字符串以 <strong>模式匹配（朴素 / KMP）</strong> 为绝对重点，配合字符串存储与基本操作。</p> </blockquote> <hr /> <h2 id="1-zi-fu-chuan-de-cun-chu">1. 字符串的存储</h2> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>顺序存储：char s[MAXLEN]，用 &#39;\0&#39; 或 length 记录长度</span></span> <span class="giallo-l"><span>堆分配：char* s，长度动态管理</span></span> <span class="giallo-l"><span>块链存储：链表每个结点存多个字符（块），省指针空间</span></span></code></pre> <p><strong>408 约定</strong>：字符数组下标常从 1 开始（<code>s[1..n]</code>），便于 next 数组推导；下标 0 存长度或不用。</p> <hr /> <h2 id="2-po-su-mo-shi-pi-pei-bf">2. 朴素模式匹配（BF）</h2> <p>主串 <code>s</code>（长 n）、模式串 <code>p</code>（长 m）：</p> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>从主串每个位置 i 起，与 p 逐位比较；</span></span> <span class="giallo-l"><span>失配则 i 回退到 i+1，j 回到 1，继续。</span></span></code></pre> <p><strong>时间复杂度</strong>：最坏 O(n·m)；平均 O(n+m)。</p> <h3 id="tu-shi">图示</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>主串: a b a b c a b</span></span> <span class="giallo-l"><span>模式: a b c</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span>第 1 趟: a b a 失配于 c vs a → 主串从第 2 位再来</span></span> <span class="giallo-l"><span>第 2 趟: a b a</span></span> <span class="giallo-l"><span>第 3 趟: a b c ✓ 匹配成功，位置 3</span></span></code></pre> <hr /> <h2 id="3-kmp-suan-fa">3. KMP 算法</h2> <h3 id="he-xin-si-xiang">核心思想</h3> <p><strong>失配时主串不回溯，模式串沿 next 数组滑动</strong>，把已匹配前缀的信息利用起来。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">int</span><span class="z-entity z-name z-function"> KMP</span><span class="z-punctuation">(</span><span class="z-storage z-modifier">const</span><span class="z-storage z-type"> char</span><span class="z-variable z-parameter"> s</span><span class="z-punctuation">[</span><span class="z-punctuation">]</span><span class="z-punctuation">,</span><span class="z-storage z-modifier"> const</span><span class="z-storage z-type"> char</span><span class="z-variable z-parameter"> p</span><span class="z-punctuation">[</span><span class="z-punctuation">]</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type"> int</span><span class="z-source"> i </span><span class="z-keyword z-operator">=</span><span class="z-constant z-numeric"> 1</span><span class="z-punctuation">,</span><span class="z-source"> j </span><span class="z-keyword z-operator">=</span><span class="z-constant z-numeric"> 1</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> while</span><span class="z-punctuation"> (</span><span class="z-source">i </span><span class="z-keyword z-operator">&lt;=</span><span class="z-variable z-other"> s</span><span class="z-punctuation">[</span><span class="z-constant z-numeric">0</span><span class="z-punctuation">]</span><span class="z-keyword z-operator"> &amp;&amp;</span><span class="z-source"> j </span><span class="z-keyword z-operator">&lt;=</span><span class="z-variable z-other"> p</span><span class="z-punctuation">[</span><span class="z-constant z-numeric">0</span><span class="z-punctuation">]</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-keyword z-control"> if</span><span class="z-punctuation"> (</span><span class="z-source">j </span><span class="z-keyword z-operator">==</span><span class="z-constant z-numeric"> 0</span><span class="z-keyword z-operator"> ||</span><span class="z-variable z-other"> s</span><span class="z-punctuation">[</span><span class="z-source">i</span><span class="z-punctuation">]</span><span class="z-keyword z-operator"> ==</span><span class="z-variable z-other"> p</span><span class="z-punctuation">[</span><span class="z-source">j</span><span class="z-punctuation">]</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-source"> i</span><span class="z-keyword z-operator">++</span><span class="z-punctuation z-terminator">;</span><span class="z-source"> j</span><span class="z-keyword z-operator">++</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-keyword z-control"> else</span><span class="z-source"> j </span><span class="z-keyword z-operator">=</span><span class="z-variable z-other"> next</span><span class="z-punctuation">[</span><span class="z-source">j</span><span class="z-punctuation">]</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-keyword z-control"> if</span><span class="z-punctuation"> (</span><span class="z-source">j </span><span class="z-keyword z-operator">&gt;</span><span class="z-variable z-other"> p</span><span class="z-punctuation">[</span><span class="z-constant z-numeric">0</span><span class="z-punctuation">]</span><span class="z-punctuation">)</span><span class="z-keyword z-control"> return</span><span class="z-source"> i </span><span class="z-keyword z-operator">-</span><span class="z-variable z-other"> p</span><span class="z-punctuation">[</span><span class="z-constant z-numeric">0</span><span class="z-punctuation">]</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 匹配位置</span></span> <span class="giallo-l"><span class="z-keyword z-control"> return</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre><h3 id="next-shu-zu-ding-yi-next-1-0">next 数组定义（next[1] = 0）</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>next[j] = 模式串 p[1..j-1] 中&quot;最长相等前后缀长度 + 1&quot;</span></span> <span class="giallo-l"><span>失配时 j = next[j] 再比。</span></span></code></pre><h3 id="qiu-jie-next-di-tui">求解 next（递推）</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">void</span><span class="z-entity z-name z-function"> getNext</span><span class="z-punctuation">(</span><span class="z-storage z-modifier">const</span><span class="z-storage z-type"> char</span><span class="z-variable z-parameter"> p</span><span class="z-punctuation">[</span><span class="z-punctuation">]</span><span class="z-punctuation">,</span><span class="z-storage z-type"> int</span><span class="z-variable z-parameter"> next</span><span class="z-punctuation">[</span><span class="z-punctuation">]</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type"> int</span><span class="z-source"> j </span><span class="z-keyword z-operator">=</span><span class="z-constant z-numeric"> 1</span><span class="z-punctuation">,</span><span class="z-source"> k </span><span class="z-keyword z-operator">=</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-variable z-other"> next</span><span class="z-punctuation">[</span><span class="z-constant z-numeric">1</span><span class="z-punctuation">]</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> while</span><span class="z-punctuation"> (</span><span class="z-source">j </span><span class="z-keyword z-operator">&lt;</span><span class="z-variable z-other"> p</span><span class="z-punctuation">[</span><span class="z-constant z-numeric">0</span><span class="z-punctuation">]</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-keyword z-control"> if</span><span class="z-punctuation"> (</span><span class="z-source">k </span><span class="z-keyword z-operator">==</span><span class="z-constant z-numeric"> 0</span><span class="z-keyword z-operator"> ||</span><span class="z-variable z-other"> p</span><span class="z-punctuation">[</span><span class="z-source">j</span><span class="z-punctuation">]</span><span class="z-keyword z-operator"> ==</span><span class="z-variable z-other"> p</span><span class="z-punctuation">[</span><span class="z-source">k</span><span class="z-punctuation">]</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-source"> j</span><span class="z-keyword z-operator">++</span><span class="z-punctuation z-terminator">;</span><span class="z-source"> k</span><span class="z-keyword z-operator">++</span><span class="z-punctuation z-terminator">;</span><span class="z-variable z-other"> next</span><span class="z-punctuation">[</span><span class="z-source">j</span><span class="z-punctuation">]</span><span class="z-keyword z-operator"> =</span><span class="z-source"> k</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span><span class="z-keyword z-control"> else</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-source"> k </span><span class="z-keyword z-operator">=</span><span class="z-variable z-other"> next</span><span class="z-punctuation">[</span><span class="z-source">k</span><span class="z-punctuation">]</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre><h3 id="tu-shi-p-a-b-a-b-a-a">图示（p = a b a b a a）</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>j : 1 2 3 4 5 6 7</span></span> <span class="giallo-l"><span>p : a b a b a a -</span></span> <span class="giallo-l"><span>next: 0 1 1 2 3 4 2</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span>例：j=5 时 p[1..4] = a b a b，最长相等前后缀 &quot;ab&quot; 长 2 ⇒ next[5] = 3</span></span></code></pre><h3 id="nextval-you-hua-next">nextval（优化 next）</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>若 p[j] == p[next[j]]，则 nextval[j] = nextval[next[j]]，进一步跳过相同字符比较。</span></span></code></pre> <p><strong>时间复杂度</strong>：O(n+m)；空间 O(m)。</p> <hr /> <h2 id="4-chang-yong-ti-xing">4. 常用题型</h2> <table><thead><tr><th>题型</th><th>解法要点</th></tr></thead><tbody> <tr><td>求 next / nextval 数组</td><td>手算“最长相等前后缀“</td></tr> <tr><td>主串定位</td><td>KMP 主循环 + next</td></tr> <tr><td>循环节问题</td><td>周期 = m − next[m]（若整除）</td></tr> <tr><td>字符串相等判断</td><td>长度 + 逐位比较</td></tr> <tr><td>模式串滑动次数</td><td>每趟失配后 j=next[j] 计数</td></tr> </tbody></table> <hr /> <h2 id="5-li-ti-su-lan">5. 例题速览</h2> <p><strong>例 1</strong>：主串 <code>ababcabcacbab</code>，模式 <code>abcac</code>，求 next 数组并用 KMP 找首次匹配。</p> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>p : a b c a c</span></span> <span class="giallo-l"><span>next: 0 1 1 1 2</span></span> <span class="giallo-l"><span>比较过程：</span></span> <span class="giallo-l"><span> a b a b c a b c a c a b</span></span> <span class="giallo-l"><span> a b c 失配(c vs a) → j = next[3] = 1</span></span> <span class="giallo-l"><span> a b c a c 匹配成功，位置 6</span></span></code></pre> <p><strong>例 2</strong>：<code>next[7]</code> 语义 = 当第 7 位失配时，模式串从第 <code>next[7]</code> 位继续比较。</p> <hr /> <h2 id="6-yi-cuo-dian">6. 易错点</h2> <ul> <li>next 数组下标从 1 开始、<code>next[1]=0</code>；</li> <li>前缀/后缀都是真子串（不含自身）；</li> <li>KMP 主串指针<strong>只增不减</strong>；</li> <li>朴素匹配最坏情况如 <code>s=aaaaab, p=aaab</code>。</li> </ul> <blockquote> <p>下一篇：<a href="https://suchaharcan.github.io/01Write_blog_AlgorithmDesign/408-tree/">树</a></p> </blockquote> 2026-08-11T00:00:00+00:00 2026-08-11T00:00:00+00:00 Suchaharcan https://suchaharcan.github.io/01Write_blog_AlgorithmDesign/408-tree/ <h1 id="kao-yan-408-shu-he-xin-zhi-shi-dian">考研 408 · 树核心知识点</h1> <blockquote> <p>树是 408 数据结构大题高发区：<strong>性质 → 遍历 → BST/AVL → 哈夫曼 → 并查集</strong>。</p> </blockquote> <hr /> <h2 id="1-er-cha-shu-ji-ben-xing-zhi">1. 二叉树基本性质</h2> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>① 第 i 层至多 2^(i−1) 个结点</span></span> <span class="giallo-l"><span>② 深度为 k 的二叉树至多 2^k − 1 个结点</span></span> <span class="giallo-l"><span>③ 叶子数 n₀ = 度为 2 结点数 n₂ + 1</span></span> <span class="giallo-l"><span>④ 完全二叉树 n 个结点：深度 = ⌊log₂n⌋ + 1</span></span> <span class="giallo-l"><span>⑤ 顺序存储（完全二叉树）：i 的左孩子 2i、右孩子 2i+1、父 ⌊i/2⌋</span></span></code></pre><h3 id="er-cha-shu-de-xing-tai-shu">二叉树的形态数</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>n 个结点的不同二叉树形态数 = 卡特兰数 C(n) = C(2n,n)/(n+1)</span></span></code></pre> <hr /> <h2 id="2-bian-li">2. 遍历</h2> <h3 id="di-gui-xu-xian-zhong-hou">递归序（先/中/后）</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>先序：根 → 左 → 右 DLR</span></span> <span class="giallo-l"><span>中序：左 → 根 → 右 LDR</span></span> <span class="giallo-l"><span>后序：左 → 右 → 根 LRD</span></span> <span class="giallo-l"><span>层序：逐层从左到右</span></span></code></pre><h3 id="tu-shi">图示</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span> 1</span></span> <span class="giallo-l"><span> / \</span></span> <span class="giallo-l"><span> 2 3</span></span> <span class="giallo-l"><span> / \ \</span></span> <span class="giallo-l"><span> 4 5 6</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span>先序: 1 2 4 5 3 6</span></span> <span class="giallo-l"><span>中序: 4 2 5 1 3 6</span></span> <span class="giallo-l"><span>后序: 4 5 2 6 3 1</span></span> <span class="giallo-l"><span>层序: 1 2 3 4 5 6</span></span></code></pre><h3 id="you-bian-li-xu-lie-que-ding-er-cha-shu">由遍历序列确定二叉树</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>必须知道中序 + （先序 或 后序 之一）</span></span> <span class="giallo-l"><span>先序/后序确定根，中序划分左右子树</span></span> <span class="giallo-l"><span>层序 + 中序亦可</span></span></code></pre><h3 id="fei-di-gui-bian-li-yao-dian">非递归遍历要点</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-punctuation z-definition z-comment">//</span><span class="z-comment"> 先序非递归：栈</span></span> <span class="giallo-l"><span class="z-entity z-name z-function">push</span><span class="z-punctuation">(</span><span class="z-source">root</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control">while</span><span class="z-punctuation"> (</span><span class="z-keyword z-operator">!</span><span class="z-variable z-other">stack</span><span class="z-punctuation">.</span><span class="z-entity z-name z-function">empty</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-source"> node </span><span class="z-keyword z-operator">=</span><span class="z-entity z-name z-function"> pop</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-entity z-name z-function"> visit</span><span class="z-punctuation">(</span><span class="z-source">node</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> if</span><span class="z-punctuation"> (</span><span class="z-variable z-other">node</span><span class="z-punctuation">-&gt;</span><span class="z-variable z-other z-property">right</span><span class="z-punctuation">)</span><span class="z-entity z-name z-function"> push</span><span class="z-punctuation">(</span><span class="z-variable z-other">node</span><span class="z-punctuation">-&gt;</span><span class="z-variable z-other z-property">right</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> if</span><span class="z-punctuation"> (</span><span class="z-variable z-other">node</span><span class="z-punctuation">-&gt;</span><span class="z-variable z-other z-property">left</span><span class="z-punctuation">)</span><span class="z-entity z-name z-function"> push</span><span class="z-punctuation">(</span><span class="z-variable z-other">node</span><span class="z-punctuation">-&gt;</span><span class="z-variable z-other z-property">left</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"><span class="z-punctuation z-definition z-comment">//</span><span class="z-comment"> 层序：队列</span></span> <span class="giallo-l"><span class="z-entity z-name z-function">enqueue</span><span class="z-punctuation">(</span><span class="z-source">root</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control">while</span><span class="z-punctuation"> (</span><span class="z-keyword z-operator">!</span><span class="z-variable z-other">queue</span><span class="z-punctuation">.</span><span class="z-entity z-name z-function">empty</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-source"> node </span><span class="z-keyword z-operator">=</span><span class="z-entity z-name z-function"> dequeue</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-entity z-name z-function"> visit</span><span class="z-punctuation">(</span><span class="z-source">node</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> if</span><span class="z-punctuation"> (</span><span class="z-variable z-other">node</span><span class="z-punctuation">-&gt;</span><span class="z-variable z-other z-property">left</span><span class="z-punctuation">)</span><span class="z-entity z-name z-function"> enqueue</span><span class="z-punctuation">(</span><span class="z-variable z-other">node</span><span class="z-punctuation">-&gt;</span><span class="z-variable z-other z-property">left</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> if</span><span class="z-punctuation"> (</span><span class="z-variable z-other">node</span><span class="z-punctuation">-&gt;</span><span class="z-variable z-other z-property">right</span><span class="z-punctuation">)</span><span class="z-entity z-name z-function"> enqueue</span><span class="z-punctuation">(</span><span class="z-variable z-other">node</span><span class="z-punctuation">-&gt;</span><span class="z-variable z-other z-property">right</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <hr /> <h2 id="3-xian-suo-er-cha-shu">3. 线索二叉树</h2> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>利用空指针域：</span></span> <span class="giallo-l"><span>ltag = 0 左孩子 / 1 前驱；rtag = 0 右孩子 / 1 后继</span></span></code></pre> <p>中序线索化后，可快速找某结点的<strong>中序前驱/后继</strong>，遍历不需要栈。</p> <hr /> <h2 id="4-er-cha-pai-xu-shu-bst">4. 二叉排序树 BST</h2> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>左子树 &lt; 根 &lt; 右子树</span></span></code></pre><table><thead><tr><th>操作</th><th>平均复杂度</th></tr></thead><tbody> <tr><td>查找 / 插入 / 删除</td><td>O(log n)（树高）</td></tr> <tr><td>最坏（退化为链）</td><td>O(n)</td></tr> </tbody></table> <p>删除三种情况：叶子直接删；单孩子提升；双孩子用<strong>前驱或后继</strong>替换。</p> <hr /> <h2 id="5-ping-heng-er-cha-shu-avl">5. 平衡二叉树 AVL</h2> <p><strong>平衡因子</strong> = 左子树高 − 右子树高，绝对值 ≤ 1。</p> <p>插入后失衡四种调整：</p> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>LL：右旋 RR：左旋</span></span> <span class="giallo-l"><span>LR：先左旋再右旋 RL：先右旋再左旋</span></span></code></pre><h3 id="tu-shi-ll-you-xuan">图示（LL 右旋）</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span> 3 2</span></span> <span class="giallo-l"><span> / 右旋 / \</span></span> <span class="giallo-l"><span> 2 ─────▶ 1 3</span></span> <span class="giallo-l"><span> /</span></span> <span class="giallo-l"><span> 1</span></span></code></pre> <p><strong>最小失衡子树调整后，整棵树恢复平衡；AVL 查找/插入/删除均 O(log n)。</strong></p> <hr /> <h2 id="6-hong-hei-shu-408-yao-qiu-zhang-wo-xing-zhi-yu-cha-ru-guo-cheng">6. 红黑树（408 要求掌握性质与插入过程）</h2> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>① 结点非红即黑</span></span> <span class="giallo-l"><span>② 根是黑色</span></span> <span class="giallo-l"><span>③ 叶子（外部空结点）黑色</span></span> <span class="giallo-l"><span>④ 红结点的两个孩子必为黑（无连续红）</span></span> <span class="giallo-l"><span>⑤ 任一结点到其所有后代叶子的路径含相同数目的黑结点（黑高相等）</span></span></code></pre> <p>插入调整：先染红新结点，再按叔结点颜色分情况 <strong>变色 / 旋转</strong>；根始终染黑。</p> <p><strong>红黑树高度 ≤ 2·log₂(n+1)，保证 O(log n) 平衡查找。</strong></p> <hr /> <h2 id="7-ha-fu-man-shu-yu-bian-ma">7. 哈夫曼树与编码</h2> <h3 id="gou-zao">构造</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>每次取权值最小的两棵树合并，新根权 = 两者之和，重复至一棵树。</span></span></code></pre><h3 id="xing-zhi">性质</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>WPL = Σ(叶权 × 路径长度) 最小</span></span> <span class="giallo-l"><span>只有度为 0 和 2 的结点：n 个叶子 ⇒ 2n−1 个结点</span></span></code></pre><h3 id="shi-li-quan-7-5-2-4">示例（权 7 5 2 4）</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span> 18</span></span> <span class="giallo-l"><span> / \</span></span> <span class="giallo-l"><span> 7 11</span></span> <span class="giallo-l"><span> / \</span></span> <span class="giallo-l"><span> 5 6</span></span> <span class="giallo-l"><span> / \</span></span> <span class="giallo-l"><span> 2 4</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span>编码（左 0 右 1）：</span></span> <span class="giallo-l"><span>7 → 0 5 → 10</span></span> <span class="giallo-l"><span>2 → 110 4 → 111</span></span> <span class="giallo-l"><span>WPL = 7×1 + 5×2 + 2×3 + 4×3 = 35</span></span></code></pre> <p><strong>哈夫曼编码是最优前缀编码</strong>（任一编码不是另一编码的前缀）。</p> <hr /> <h2 id="8-shu-sen-lin-er-cha-shu">8. 树 / 森林 ↔ 二叉树</h2> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>孩子兄弟表示法：</span></span> <span class="giallo-l"><span>左孩子指针 = 第一个孩子；右孩子指针 = 下一个兄弟</span></span> <span class="giallo-l"><span>森林转二叉树：各树根依次作为右子树连接</span></span></code></pre> <p><strong>树的先序 = 对应二叉树的先序；树的后序 = 对应二叉树的中序。</strong></p> <hr /> <h2 id="9-bing-cha-ji">9. 并查集</h2> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">int</span><span class="z-entity z-name z-function"> find</span><span class="z-punctuation">(</span><span class="z-storage z-type">int</span><span class="z-variable z-parameter"> x</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-keyword z-control"> while</span><span class="z-punctuation"> (</span><span class="z-variable z-other">parent</span><span class="z-punctuation">[</span><span class="z-source">x</span><span class="z-punctuation">]</span><span class="z-keyword z-operator"> !=</span><span class="z-source"> x</span><span class="z-punctuation">)</span><span class="z-source"> x </span><span class="z-keyword z-operator">=</span><span class="z-variable z-other"> parent</span><span class="z-punctuation">[</span><span class="z-source">x</span><span class="z-punctuation">]</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> return</span><span class="z-source"> x</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"><span class="z-storage z-type">void</span><span class="z-entity z-name z-function"> unionSet</span><span class="z-punctuation">(</span><span class="z-storage z-type">int</span><span class="z-variable z-parameter"> a</span><span class="z-punctuation">,</span><span class="z-storage z-type"> int</span><span class="z-variable z-parameter"> b</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type"> int</span><span class="z-source"> ra </span><span class="z-keyword z-operator">=</span><span class="z-entity z-name z-function"> find</span><span class="z-punctuation">(</span><span class="z-source">a</span><span class="z-punctuation">)</span><span class="z-punctuation">,</span><span class="z-source"> rb </span><span class="z-keyword z-operator">=</span><span class="z-entity z-name z-function"> find</span><span class="z-punctuation">(</span><span class="z-source">b</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> if</span><span class="z-punctuation"> (</span><span class="z-source">ra </span><span class="z-keyword z-operator">!=</span><span class="z-source"> rb</span><span class="z-punctuation">)</span><span class="z-variable z-other"> parent</span><span class="z-punctuation">[</span><span class="z-source">ra</span><span class="z-punctuation">]</span><span class="z-keyword z-operator"> =</span><span class="z-source"> rb</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 可加按秩合并</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <p>用途：判断连通分量、Kruskal 判环、集合合并。路径压缩 + 按秩合并后近似 O(α(n))。</p> <hr /> <h2 id="10-dui">10. 堆</h2> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>大根堆：parent ≥ children；小根堆：parent ≤ children</span></span> <span class="giallo-l"><span>存储：完全二叉树顺序存储，下标 1 开始</span></span></code></pre><table><thead><tr><th>操作</th><th>复杂度</th></tr></thead><tbody> <tr><td>建堆</td><td>O(n)</td></tr> <tr><td>插入 / 删除堆顶</td><td>O(log n)</td></tr> <tr><td>堆排序</td><td>O(n log n)</td></tr> </tbody></table> <hr /> <h2 id="11-chang-kao-ti-xing">11. 常考题型</h2> <ol> <li>由先序+中序还原二叉树并求后序；</li> <li>完全二叉树结点编号与父子关系；</li> <li>AVL 插入旋转过程；</li> <li>哈夫曼树构造与 WPL、编码；</li> <li>树转二叉树后的遍历关系；</li> <li>并查集查找次数与路径压缩；</li> <li>判断是否为 BST / AVL / 堆。</li> </ol> <blockquote> <p>上一篇：<a href="https://suchaharcan.github.io/01Write_blog_AlgorithmDesign/408-string/">字符串</a> ｜ 下一篇：<a href="https://suchaharcan.github.io/01Write_blog_AlgorithmDesign/408-graph/">图</a></p> </blockquote> 2026-08-11T00:00:00+00:00 2026-08-11T00:00:00+00:00 Suchaharcan https://suchaharcan.github.io/01Write_blog_Jai/jai-syntax-intro/ <h1 id="jai-ru-men-yu-fa-xiang-jie">Jai 入门 · 语法详解</h1> <blockquote> <p>Jai 是 Jonathan Blow（《Braid》《The Witness》作者）设计的<strong>面向性能与数据导向</strong>的静态强类型语言，目标之一是做“C 的现代替代品“。本文语料主要来自 GitHub 上的 JaiPrimer 与 The Way to Jai 社区教程。</p> </blockquote> <hr /> <h2 id="1-jai-de-she-ji-zhe-xue">1. Jai 的设计哲学</h2> <p>Jai 关注三件事：</p> <ol> <li><strong>写更快的代码</strong>：无 GC、无异常、无类继承包袱，程序员直接控制内存与性能特征；</li> <li><strong>减少摩擦</strong>：语法一致、重构成本低、编译快速；</li> <li><strong>数据导向（Data-Oriented Design）</strong>：程序本质是“填充内存的数据 + 高效算法“。</li> </ol> <table><thead><tr><th>与 C/C++ 对比</th><th>C / C++</th><th>Jai</th></tr></thead><tbody> <tr><td>内存管理</td><td>malloc/free 或 RAII</td><td><code>new</code> / <code>delete</code>，指针所有权 <code>!</code> 标记，无 GC</td></tr> <tr><td>多态</td><td>虚函数 / 模板</td><td>函数级多态 <code>$T</code> + 编译期代码</td></tr> <tr><td>构建</td><td>Make/CMake</td><td>构建过程由 Jai 源码本身指定</td></tr> <tr><td>数据组织</td><td>AoS 为主</td><td><code>struct SOA</code> 一键切换 SoA/AoS</td></tr> <tr><td>反射</td><td>无原生支持</td><td>全类型信息运行时可查</td></tr> </tbody></table> <hr /> <h2 id="2-cheng-xu-ru-kou-yu-ji-ben-jie-gou">2. 程序入口与基本结构</h2> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-variable z-other">#import</span><span class="z-punctuation"> &quot;</span><span class="z-string">Basic</span><span class="z-punctuation">&quot;</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-entity z-name">main</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">Hello, Jai!</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <p>要点：</p> <ul> <li><code>main :: ()</code> 是入口过程；</li> <li><code>#import</code> 导入标准/自定义模块；</li> <li><code>print</code> 支持 <code>%</code> 占位符：<code>print("x = %\n", x)</code>。</li> </ul> <hr /> <h2 id="3-bian-liang-yu-lei-xing">3. 变量与类型</h2> <h3 id="sheng-ming-yu-fa-ming-zi-lei-xing-zhi">声明语法：<code>名字 : 类型 = 值;</code></h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-source">counter :</span><span class="z-storage z-type"> int</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-source">name : string </span><span class="z-keyword z-operator">=</span><span class="z-punctuation"> &quot;</span><span class="z-string">Jon</span><span class="z-punctuation">&quot;</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-source">average :</span><span class="z-storage z-type"> float</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-constant z-numeric">.</span><span class="z-constant z-numeric">5</span><span class="z-keyword z-operator"> *</span><span class="z-punctuation"> (</span><span class="z-source">x </span><span class="z-keyword z-operator">+</span><span class="z-source"> y</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span></code></pre><h3 id="lei-xing-sheng-lue-bian-yi-qi-tui-duan-ming-zi-zhi">类型省略（编译器推断）：<code>名字 ::= 值;</code></h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-source">counter :</span><span class="z-keyword z-operator">=</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> int</span></span> <span class="giallo-l"><span class="z-source">name :</span><span class="z-keyword z-operator">=</span><span class="z-punctuation"> &quot;</span><span class="z-string">Jon</span><span class="z-punctuation">&quot;</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> string</span></span> <span class="giallo-l"><span class="z-source">average :</span><span class="z-keyword z-operator">=</span><span class="z-constant z-numeric"> 0</span><span class="z-constant z-numeric">.</span><span class="z-constant z-numeric">5</span><span class="z-keyword z-operator"> *</span><span class="z-punctuation"> (</span><span class="z-source">x</span><span class="z-keyword z-operator">+</span><span class="z-source">y</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> float</span></span></code></pre><h3 id="zhi-sheng-ming-bu-chu-shi-hua">只声明不初始化</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-source">counter :</span><span class="z-storage z-type"> int</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-source">flag :</span><span class="z-storage z-type"> bool</span><span class="z-punctuation z-terminator">;</span></span></code></pre><h3 id="ji-ben-lei-xing">基本类型</h3> <p><code>bool</code>、<code>int</code>、<code>int8/16/32/64</code>、<code>uint</code>、<code>float</code>、<code>float32/64</code>、<code>string</code>、<code>rawptr</code> 等。整数和浮点不隐式混用，需显式转换（<code>cast</code>）。</p> <hr /> <h2 id="4-han-shu-guo-cheng">4. 函数（过程）</h2> <p>语法统一：<strong>局部函数、匿名函数、全局函数写法完全一致</strong>，这是 Jai 重构友好的核心设计。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">sum</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-source">x</span><span class="z-punctuation">:</span><span class="z-storage z-type"> float</span><span class="z-punctuation">,</span><span class="z-source"> y</span><span class="z-punctuation">:</span><span class="z-storage z-type"> float</span><span class="z-punctuation">,</span><span class="z-source"> z</span><span class="z-punctuation">:</span><span class="z-storage z-type"> float</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> -</span><span class="z-keyword z-operator">&gt;</span><span class="z-storage z-type"> float</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-keyword z-control"> return</span><span class="z-source"> x </span><span class="z-keyword z-operator">+</span><span class="z-source"> y </span><span class="z-keyword z-operator">+</span><span class="z-source"> z</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-entity z-name">main</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">Sum: %</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">,</span><span class="z-entity z-name z-function"> sum</span><span class="z-punctuation">(</span><span class="z-constant z-numeric">1</span><span class="z-punctuation">,</span><span class="z-constant z-numeric"> 2</span><span class="z-punctuation">,</span><span class="z-constant z-numeric"> 3</span><span class="z-punctuation">)</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <p>匿名函数：</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-source">add_one :</span><span class="z-keyword z-operator">=</span><span class="z-punctuation"> (</span><span class="z-source">x</span><span class="z-punctuation">:</span><span class="z-storage z-type"> int</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> -</span><span class="z-keyword z-operator">&gt;</span><span class="z-storage z-type"> int</span><span class="z-punctuation"> {</span><span class="z-keyword z-control"> return</span><span class="z-source"> x </span><span class="z-keyword z-operator">+</span><span class="z-constant z-numeric"> 1</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span></code></pre> <p><code>::</code> 表示“绑定一个常量名字到右侧值“；过程、结构体、枚举、常量都用它声明。</p> <hr /> <h2 id="5-jie-gou-ti-mei-ju-lian-he">5. 结构体 / 枚举 / 联合</h2> <h3 id="struct">struct</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">Vector3</span><span class="z-punctuation"> ::</span><span class="z-storage z-type"> struct</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-source"> x:</span><span class="z-storage z-type"> float</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 1</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-source"> y:</span><span class="z-storage z-type"> float</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 4</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-source"> z:</span><span class="z-storage z-type"> float</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 9</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-source">v : Vector3</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-variable z-other">v</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">x</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 2</span><span class="z-punctuation z-terminator">;</span></span></code></pre> <p>成员可以带默认值。<strong>没有构造函数/析构函数</strong>（Jai 刻意去掉 RAII）。</p> <h3 id="enum">enum</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">Color</span><span class="z-punctuation"> ::</span><span class="z-storage z-type"> enum</span><span class="z-entity z-name z-type"> u16</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-variable z-other z-enummember"> RED</span><span class="z-punctuation">,</span></span> <span class="giallo-l"><span class="z-variable z-other z-enummember"> GREEN</span><span class="z-punctuation">,</span></span> <span class="giallo-l"><span class="z-variable z-other z-enummember"> BLUE</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 80</span><span class="z-punctuation">,</span></span> <span class="giallo-l"><span class="z-variable z-other z-enummember"> ALPHA</span><span class="z-punctuation">,</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre><h3 id="union">union</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">Value</span><span class="z-punctuation"> ::</span><span class="z-storage z-type"> union</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-source"> i:</span><span class="z-storage z-type"> int</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-source"> f:</span><span class="z-storage z-type"> float</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <hr /> <h2 id="6-shu-zu-yu-qie-pian">6. 数组与切片</h2> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-source">a : </span><span class="z-punctuation">[</span><span class="z-constant z-numeric">50</span><span class="z-punctuation">]</span><span class="z-storage z-type"> int</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 定长数组</span></span> <span class="giallo-l"><span class="z-source">b :</span><span class="z-punctuation"> [</span><span class="z-source">..</span><span class="z-punctuation">]</span><span class="z-source"> int;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 动态数组</span></span> <span class="giallo-l"><span class="z-source">c :</span><span class="z-punctuation"> [</span><span class="z-punctuation">]</span><span class="z-source"> int;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 切片（宽指针，携带长度）</span></span></code></pre> <p>数组<strong>不会退化为指针</strong>，自带长度信息 <code>count</code>：</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">print_int_array</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-source">a</span><span class="z-punctuation">:</span><span class="z-punctuation"> [</span><span class="z-punctuation">]</span><span class="z-source"> int) </span><span class="z-punctuation">{</span></span> <span class="giallo-l"><span class="z-source"> n :</span><span class="z-keyword z-operator">=</span><span class="z-variable z-other"> a</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">count</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> for</span><span class="z-source"> i : </span><span class="z-invalid">0..n</span><span class="z-keyword z-operator">-</span><span class="z-constant z-numeric">1</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">array[%] = %</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">,</span><span class="z-source"> i</span><span class="z-punctuation">,</span><span class="z-variable z-other"> a</span><span class="z-punctuation">[</span><span class="z-source">i</span><span class="z-punctuation">]</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <hr /> <h2 id="7-kong-zhi-liu">7. 控制流</h2> <h3 id="if-else">if / else</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-keyword z-control">if</span><span class="z-source"> a </span><span class="z-keyword z-operator">==</span><span class="z-source"> b </span><span class="z-punctuation">{</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">equal</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-keyword z-control"> else</span><span class="z-keyword z-control"> if</span><span class="z-source"> a </span><span class="z-keyword z-operator">&gt;</span><span class="z-source"> b </span><span class="z-punctuation">{</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">greater</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-keyword z-control"> else</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">less</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre><h3 id="if-case-dui-zhi-lie-biao-pi-pei">if-case（对值列表匹配）</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-keyword z-control">if</span><span class="z-source"> x </span><span class="z-punctuation">{</span></span> <span class="giallo-l"><span class="z-constant z-numeric"> 1</span><span class="z-punctuation">,</span><span class="z-constant z-numeric"> 2</span><span class="z-punctuation">,</span><span class="z-constant z-numeric"> 3</span><span class="z-keyword z-operator"> =</span><span class="z-keyword z-operator">&gt;</span><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">small</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> else</span><span class="z-keyword z-operator"> =</span><span class="z-keyword z-operator">&gt;</span><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">other</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre><h3 id="for">for</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-keyword z-control">for</span><span class="z-source"> i : </span><span class="z-invalid">0..9</span><span class="z-punctuation"> {</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 范围</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">%</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">,</span><span class="z-source"> i</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-keyword z-control">for</span><span class="z-source"> item : items </span><span class="z-punctuation">{</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 遍历集合</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">%</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">,</span><span class="z-source"> item</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre><h3 id="while">while</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-keyword z-control">while</span><span class="z-source"> count </span><span class="z-keyword z-operator">&lt;</span><span class="z-constant z-numeric"> 10</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-source"> count </span><span class="z-keyword z-operator">+=</span><span class="z-constant z-numeric"> 1</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre><h3 id="defer-zuo-yong-yu-tui-chu-shi-zhi-xing">defer（作用域退出时执行）</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-punctuation">{</span></span> <span class="giallo-l"><span class="z-entity z-name z-label"> ptr</span><span class="z-punctuation"> :</span><span class="z-keyword z-operator">=</span><span class="z-keyword z-operator z-new"> new</span><span class="z-storage z-type"> int</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-source"> defer</span><span class="z-keyword z-operator"> delete</span><span class="z-punctuation">(</span><span class="z-source">ptr</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 离开作用域时自动释放</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <hr /> <h2 id="8-zhi-zhen-yu-nei-cun">8. 指针与内存</h2> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-source">p : </span><span class="z-keyword z-operator">*</span><span class="z-storage z-type">int</span><span class="z-keyword z-operator"> =</span><span class="z-keyword z-operator z-new"> new</span><span class="z-storage z-type"> int</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 分配</span></span> <span class="giallo-l"><span class="z-source">p.</span><span class="z-keyword z-operator">*</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 42</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 解引用（后缀 .*）</span></span> <span class="giallo-l"><span class="z-keyword z-operator">delete</span><span class="z-source"> p</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 释放</span></span></code></pre> <p>结构体指针所有权：成员类型前加 <code>!</code> 表示“该指针由本结构体拥有，删除结构体时一并删除“：</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">node</span><span class="z-punctuation"> ::</span><span class="z-storage z-type"> struct</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-source"> owned_a : </span><span class="z-keyword z-operator">!</span><span class="z-keyword z-operator">*</span><span class="z-source">node </span><span class="z-keyword z-operator">=</span><span class="z-source"> null</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-source">example :</span><span class="z-keyword z-operator">=</span><span class="z-keyword z-operator z-new"> new</span><span class="z-source"> node</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-variable z-other">example</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">owned_a</span><span class="z-keyword z-operator"> =</span><span class="z-keyword z-operator z-new"> new</span><span class="z-source"> node</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-operator">delete</span><span class="z-source"> example</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> owned_a 也会被释放</span></span></code></pre> <p>Jai <strong>没有 GC 与自动内存管理</strong>，但用所有权标注 + <code>defer</code> 让手动管理可控。</p> <hr /> <h2 id="9-han-shu-ji-duo-tai-t">9. 函数级多态（<code>$T</code>）</h2> <p>Jai 的多态在<strong>函数级</strong>，参数前加 <code>$</code> 声明类型变量：</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">sum</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-source">a</span><span class="z-punctuation">:</span><span class="z-source"> $T</span><span class="z-punctuation">,</span><span class="z-source"> b</span><span class="z-punctuation">:</span><span class="z-source"> T</span><span class="z-punctuation">)</span><span class="z-punctuation"> -&gt;</span><span class="z-variable z-other z-property"> T</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-keyword z-control"> return</span><span class="z-source"> a </span><span class="z-keyword z-operator">+</span><span class="z-source"> b</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-source">f3 :</span><span class="z-keyword z-operator">=</span><span class="z-entity z-name z-function"> sum</span><span class="z-punctuation">(</span><span class="z-constant z-numeric">1</span><span class="z-constant z-numeric">.</span><span class="z-constant z-numeric">0</span><span class="z-punctuation">,</span><span class="z-constant z-numeric"> 2</span><span class="z-constant z-numeric">.</span><span class="z-constant z-numeric">0</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> float + float</span></span> <span class="giallo-l"><span class="z-source">i3 :</span><span class="z-keyword z-operator">=</span><span class="z-entity z-name z-function"> sum</span><span class="z-punctuation">(</span><span class="z-constant z-numeric">1</span><span class="z-punctuation">,</span><span class="z-constant z-numeric"> 2</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> int + int</span></span></code></pre> <p>类型由 <code>$</code> 标记的参数推断，并可以做类型特化（<code>#if</code> 按类型分支）。</p> <h3 id="any-lei-xing">Any 类型</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">print_any</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-source">a</span><span class="z-punctuation">:</span><span class="z-source"> Any</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-keyword z-control"> if</span><span class="z-variable z-other"> a</span><span class="z-punctuation">.</span><span class="z-variable z-other">type</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">type</span><span class="z-keyword z-operator"> ==</span><span class="z-variable z-other"> Type_Info_Tag</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">FLOAT</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">a is float</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <p><code>Any</code> 携带类型信息，适合需要“任意类型“参数的场景。</p> <h3 id="jin-jie-1-lei-xing-yue-shu-t-foo-yu-t-interface">进阶 1：类型约束（<code>$T/Foo</code> 与 <code>$T/interface</code>）</h3> <p><code>$T</code> 不限制类型；要约束“必须拥有某组字段/成员“，用 <code>/</code> 写法（类似 trait / interface）：</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">Vec3</span><span class="z-punctuation"> ::</span><span class="z-storage z-type"> struct</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-source"> x</span><span class="z-punctuation">,</span><span class="z-source"> y</span><span class="z-punctuation">,</span><span class="z-source"> z:</span><span class="z-storage z-type"> float</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-entity z-name">dot_product</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-source">a</span><span class="z-punctuation">:</span><span class="z-source"> $T</span><span class="z-keyword z-operator">/</span><span class="z-source">interface Vec3</span><span class="z-punctuation">,</span><span class="z-source"> b</span><span class="z-punctuation">:</span><span class="z-source"> T</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> -</span><span class="z-keyword z-operator">&gt;</span><span class="z-storage z-type"> float</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-keyword z-control"> return</span><span class="z-variable z-other"> a</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">x</span><span class="z-keyword z-operator"> *</span><span class="z-variable z-other"> b</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">x</span><span class="z-keyword z-operator"> +</span><span class="z-variable z-other"> a</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">y</span><span class="z-keyword z-operator"> *</span><span class="z-variable z-other"> b</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">y</span><span class="z-keyword z-operator"> +</span><span class="z-variable z-other"> a</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">z</span><span class="z-keyword z-operator"> *</span><span class="z-variable z-other"> b</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">z</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-punctuation z-definition z-comment">//</span><span class="z-comment"> 任何&quot;拥有 x/y/z float 字段&quot;的结构体都能传入，不必继承 Vec3</span></span></code></pre> <p>区别：</p> <table><thead><tr><th>写法</th><th>含义</th></tr></thead><tbody> <tr><td><code>a: $T</code></td><td>任意编译期已知类型</td></tr> <tr><td><code>a: Foo($T)</code></td><td>必须是 <code>Foo</code> 的某种特化，内层 <code>$T</code> 任意</td></tr> <tr><td><code>a: $T/Foo</code></td><td>只要结构体内 <strong>using 了 Foo</strong> 即可（组件式组合）</td></tr> <tr><td><code>a: $T/interface Foo</code></td><td>只要拥有 Foo 的全部字段即可（结构鸭子类型）</td></tr> </tbody></table> <h3 id="jin-jie-2-duo-tai-jie-gou-ti-bian-yi-qi-can-shu-hua">进阶 2：多态结构体（编译期参数化）</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">Foo</span><span class="z-punctuation"> ::</span><span class="z-storage z-type"> struct</span><span class="z-source">(T:</span><span class="z-entity z-name z-type"> Type</span><span class="z-source">) </span><span class="z-punctuation">{</span></span> <span class="giallo-l"><span class="z-source"> some_data : T</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 运行时成员，随 T 变化</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-source">f :</span><span class="z-entity z-name z-function"> Foo</span><span class="z-punctuation">(</span><span class="z-storage z-type">int</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-entity z-name z-function">print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">%</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">,</span><span class="z-variable z-other"> f</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">T</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> =&gt; int</span></span></code></pre> <p>编译期参数不止类型，还可以是常量值，甚至函数：</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">Foo</span><span class="z-punctuation"> ::</span><span class="z-storage z-type"> struct</span><span class="z-source">(</span></span> <span class="giallo-l"><span class="z-source"> T:</span><span class="z-entity z-name z-type"> Type</span><span class="z-punctuation">,</span></span> <span class="giallo-l"><span class="z-source"> fun: (T) -&gt; T</span><span class="z-punctuation">,</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 编译期烘焙，不占运行时内存</span></span> <span class="giallo-l"><span class="z-source">) </span><span class="z-punctuation">{</span></span> <span class="giallo-l"><span class="z-source"> value: T</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 运行时数据</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <p>多态结构体的“模式匹配“写法——三种等价风格：</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">Hash_Table</span><span class="z-punctuation"> ::</span><span class="z-storage z-type"> struct</span><span class="z-source"> (K:</span><span class="z-entity z-name z-type"> Type</span><span class="z-punctuation">,</span><span class="z-source"> V:</span><span class="z-entity z-name z-type"> Type</span><span class="z-punctuation">,</span><span class="z-source"> N:</span><span class="z-storage z-type"> int</span><span class="z-source">) </span><span class="z-punctuation">{</span></span> <span class="giallo-l"><span class="z-source"> keys:</span><span class="z-punctuation"> [</span><span class="z-variable z-parameter">N</span><span class="z-punctuation">]</span><span class="z-source"> K;</span></span> <span class="giallo-l"><span class="z-source"> values:</span><span class="z-punctuation"> [</span><span class="z-variable z-parameter">N</span><span class="z-punctuation">]</span><span class="z-source"> V;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-punctuation z-definition z-comment">//</span><span class="z-comment"> 1) 显式模式匹配</span></span> <span class="giallo-l"><span class="z-entity z-name">f1</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-source">t</span><span class="z-punctuation">:</span><span class="z-entity z-name z-function"> Hash_Table</span><span class="z-punctuation">(</span><span class="z-source">$K</span><span class="z-punctuation">,</span><span class="z-source"> $V</span><span class="z-punctuation">,</span><span class="z-source"> $N</span><span class="z-punctuation">)</span><span class="z-punctuation">,</span><span class="z-source"> k</span><span class="z-punctuation">:</span><span class="z-source"> K</span><span class="z-punctuation">,</span><span class="z-source"> v</span><span class="z-punctuation">:</span><span class="z-source"> V</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-punctuation z-definition z-comment">//</span><span class="z-comment"> 2) $T/类型 + T.K 访问参数</span></span> <span class="giallo-l"><span class="z-entity z-name">f2</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-source">t</span><span class="z-punctuation">:</span><span class="z-source"> $T</span><span class="z-keyword z-operator">/</span><span class="z-source">Hash_Table</span><span class="z-punctuation">,</span><span class="z-source"> k</span><span class="z-punctuation">:</span><span class="z-variable z-other"> T</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">K</span><span class="z-punctuation">,</span><span class="z-source"> v</span><span class="z-punctuation">:</span><span class="z-variable z-other"> T</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">V</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-punctuation z-definition z-comment">//</span><span class="z-comment"> 3) 隐式多态：直接用具体类型访问其编译期参数</span></span> <span class="giallo-l"><span class="z-entity z-name">f4</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-source">t</span><span class="z-punctuation">:</span><span class="z-source"> Hash_Table</span><span class="z-punctuation">,</span><span class="z-source"> k</span><span class="z-punctuation">:</span><span class="z-variable z-other"> t</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">K</span><span class="z-punctuation">,</span><span class="z-source"> v</span><span class="z-punctuation">:</span><span class="z-variable z-other"> t</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">V</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-punctuation"> }</span></span></code></pre><h3 id="jin-jie-3-duo-tai-shu-zu-chang-du-yu-yuan-su-lei-xing-du-shi-lei-xing-de-yi-bu-fen">进阶 3：多态数组（长度与元素类型都是类型的一部分）</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">foo</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-source">x</span><span class="z-punctuation">:</span><span class="z-punctuation"> [</span><span class="z-source">$</span><span class="z-variable z-parameter">N</span><span class="z-punctuation">]</span><span class="z-source">$T) </span><span class="z-punctuation">{</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">%: %, %</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">,</span><span class="z-entity z-name z-function"> type_of</span><span class="z-punctuation">(</span><span class="z-source">N</span><span class="z-punctuation">)</span><span class="z-punctuation">,</span><span class="z-source"> N</span><span class="z-punctuation">,</span><span class="z-source"> T</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-source">x </span><span class="z-punctuation">:</span><span class="z-keyword z-operator">=</span><span class="z-storage z-type"> int</span><span class="z-source">.</span><span class="z-punctuation">[</span><span class="z-constant z-numeric">1</span><span class="z-punctuation">,</span><span class="z-constant z-numeric"> 2</span><span class="z-punctuation">,</span><span class="z-constant z-numeric"> 3</span><span class="z-punctuation">,</span><span class="z-constant z-numeric"> 4</span><span class="z-punctuation">]</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-entity z-name z-function">foo</span><span class="z-punctuation">(</span><span class="z-source">x</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> =&gt; s64: 4, s64（N 本身是编译期 int）</span></span></code></pre> <p>注意：<code>[4] int</code> 与 <code>[5] int</code> 是<strong>不同类型</strong>，不能互相赋值。</p> <h3 id="jin-jie-4-you-can-shu-tui-dao-fan-hui-lei-xing-helper-jie-gou-ti-run">进阶 4：由参数推导返回类型（Helper 结构体 + <code>#run</code>）</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">Helper</span><span class="z-punctuation"> ::</span><span class="z-storage z-type"> struct</span><span class="z-source">(A:</span><span class="z-entity z-name z-type"> Type</span><span class="z-punctuation">,</span><span class="z-source"> B:</span><span class="z-entity z-name z-type"> Type</span><span class="z-source">) </span><span class="z-punctuation">{</span></span> <span class="giallo-l"><span class="z-entity z-name"> T</span><span class="z-punctuation"> ::</span><span class="z-variable z-other"> #run</span><span class="z-entity z-name z-function"> helper</span><span class="z-punctuation">(</span><span class="z-source">A</span><span class="z-punctuation">,</span><span class="z-source"> B</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 编译期计算返回类型</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-entity z-name">helper</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-source">$A</span><span class="z-punctuation">:</span><span class="z-source"> Type</span><span class="z-punctuation">,</span><span class="z-source"> $B</span><span class="z-punctuation">:</span><span class="z-source"> Type</span><span class="z-punctuation">)</span><span class="z-punctuation"> -&gt;</span><span class="z-variable z-other z-property"> Type</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-entity z-name z-label"> T</span><span class="z-punctuation"> :</span><span class="z-source"> Type </span><span class="z-keyword z-operator">=</span><span class="z-source"> A</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 这里可以做类型层面的逻辑</span></span> <span class="giallo-l"><span class="z-keyword z-control"> return</span><span class="z-source"> T</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-entity z-name">combine</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-source">a</span><span class="z-punctuation">:</span><span class="z-source"> $A</span><span class="z-punctuation">,</span><span class="z-source"> b</span><span class="z-punctuation">:</span><span class="z-source"> $B</span><span class="z-punctuation">)</span><span class="z-punctuation"> -&gt;</span><span class="z-entity z-name z-function"> Helper</span><span class="z-punctuation">(</span><span class="z-source">A</span><span class="z-punctuation">,</span><span class="z-source"> B</span><span class="z-punctuation">)</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">T</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> ...</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre><h3 id="jin-jie-5-modify-bian-yi-qi-xiao-yan-bian-huan-duo-tai-can-shu">进阶 5：<code>#modify</code>——编译期校验/变换多态参数</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">do_something</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-source">T</span><span class="z-punctuation">:</span><span class="z-source"> Type</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> -</span><span class="z-keyword z-operator">&gt;</span><span class="z-storage z-type"> bool</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-entity z-name z-label"> ti</span><span class="z-punctuation"> :</span><span class="z-keyword z-operator">=</span><span class="z-entity z-name z-function"> cast</span><span class="z-punctuation">(</span><span class="z-keyword z-operator">*</span><span class="z-source">Type_Info</span><span class="z-punctuation">)</span><span class="z-source"> T</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> return</span><span class="z-variable z-other"> ti</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">type</span><span class="z-keyword z-operator"> ==</span><span class="z-source"> .INTEGER </span><span class="z-keyword z-operator">||</span><span class="z-variable z-other"> ti</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">type</span><span class="z-keyword z-operator"> ==</span><span class="z-source"> .ENUM </span><span class="z-keyword z-operator">||</span><span class="z-variable z-other"> ti</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">type</span><span class="z-keyword z-operator"> ==</span><span class="z-source"> .POINTER</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-entity z-name">function</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-source">dest</span><span class="z-punctuation">:</span><span class="z-keyword z-operator"> *</span><span class="z-source">$T</span><span class="z-punctuation">,</span><span class="z-source"> value</span><span class="z-punctuation">:</span><span class="z-source"> T</span><span class="z-punctuation">)</span></span> <span class="giallo-l"><span class="z-variable z-other">#modify</span><span class="z-punctuation"> {</span><span class="z-keyword z-control"> return</span><span class="z-entity z-name z-function"> do_something</span><span class="z-punctuation">(</span><span class="z-source">T</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> false =&gt; 编译错误</span></span> <span class="giallo-l"><span class="z-punctuation">{</span></span> <span class="giallo-l"><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 运行时实现</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <p><code>#modify</code> 在每次调用解析时执行，可检查参数类型、做约束，是 Jai 在“类型层“做特化的入口。</p> <hr /> <h2 id="10-bian-yi-qi-zhi-xing-yuan-bian-cheng-he-xin">10. 编译期执行（元编程核心）</h2> <h3 id="run-bian-yi-qi-yun-xing-ren-yi-dai-ma">#run：编译期运行任意代码</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">generate_table</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> -</span><span class="z-keyword z-operator">&gt;</span><span class="z-punctuation"> [</span><span class="z-constant z-numeric">256</span><span class="z-punctuation">]</span><span class="z-storage z-type"> float</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-entity z-name z-label"> table</span><span class="z-punctuation"> :</span><span class="z-punctuation"> [</span><span class="z-constant z-numeric">256</span><span class="z-punctuation">]</span><span class="z-storage z-type"> float</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> for</span><span class="z-entity z-name z-label"> i</span><span class="z-punctuation"> :</span><span> </span><span class="z-invalid">0..255</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-variable z-other"> table</span><span class="z-punctuation">[</span><span class="z-source">i</span><span class="z-punctuation">]</span><span class="z-keyword z-operator"> =</span><span class="z-entity z-name z-function"> pow</span><span class="z-punctuation">(</span><span class="z-source">i </span><span class="z-keyword z-operator">/</span><span class="z-constant z-numeric"> 255</span><span class="z-constant z-numeric">.</span><span class="z-constant z-numeric">0</span><span class="z-punctuation">,</span><span class="z-constant z-numeric"> 2</span><span class="z-constant z-numeric">.</span><span class="z-constant z-numeric">2</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-keyword z-control"> return</span><span class="z-source"> table</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-source">srgb_table :</span><span class="z-keyword z-operator">=</span><span class="z-variable z-other"> #run</span><span class="z-entity z-name z-function"> generate_table</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 编译期生成，运行期直接查表</span></span></code></pre> <p>编译期函数由编译器解释执行，结果直接烘焙进二进制。</p> <h3 id="if-bian-yi-qi-tiao-jian">#if：编译期条件</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-punctuation">#</span><span class="z-keyword z-control z-directive">if</span><span class="z-entity z-name z-function z-preprocessor"> OS</span><span class="z-keyword z-operator"> ==</span><span class="z-punctuation"> &quot;</span><span class="z-string">windows</span><span class="z-punctuation">&quot;</span><span class="z-meta z-preprocessor"> {</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">Windows build</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-source">}</span><span class="z-keyword z-control"> else</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">Other build</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <p><code>#if</code> 也可用于结构体字段与枚举值的条件定义。</p> <h3 id="bake-can-shu-hong-bei">#bake：参数烘焙</h3> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">add</span><span class="z-punctuation"> ::</span><span class="z-punctuation"> (</span><span class="z-source">a</span><span class="z-punctuation">:</span><span class="z-storage z-type"> int</span><span class="z-punctuation">,</span><span class="z-source"> b</span><span class="z-punctuation">:</span><span class="z-storage z-type"> int</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> -</span><span class="z-keyword z-operator">&gt;</span><span class="z-storage z-type"> int</span><span class="z-punctuation"> {</span><span class="z-keyword z-control"> return</span><span class="z-source"> a </span><span class="z-keyword z-operator">+</span><span class="z-source"> b</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-source">add_one :</span><span class="z-keyword z-operator">=</span><span class="z-variable z-other"> #bake</span><span class="z-entity z-name z-function"> add</span><span class="z-punctuation">(</span><span class="z-constant z-numeric">1</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 等价于单参数函数</span></span></code></pre> <hr /> <h2 id="11-shu-ju-dao-xiang-jie-gou-soa">11. 数据导向结构（SOA）</h2> <p>普通 AoS 与 <code>struct SOA</code> 只差一个关键字，内存布局自动切换：</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-entity z-name">Vector3</span><span class="z-punctuation"> ::</span><span class="z-storage z-type"> struct</span><span class="z-punctuation"> {</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> AoS：x y z x y z ...</span></span> <span class="giallo-l"><span class="z-source"> x:</span><span class="z-storage z-type"> float</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 1</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-source"> y:</span><span class="z-storage z-type"> float</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 4</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-source"> z:</span><span class="z-storage z-type"> float</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 9</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-entity z-name">Vector3SOA</span><span class="z-punctuation"> ::</span><span class="z-storage z-type"> struct</span><span class="z-entity z-name z-type"> SOA</span><span class="z-punctuation"> {</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> SoA：x x x y y y z z z</span></span> <span class="giallo-l"><span class="z-source"> x:</span><span class="z-storage z-type"> float</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 1</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-source"> y:</span><span class="z-storage z-type"> float</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 4</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-source"> z:</span><span class="z-storage z-type"> float</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 9</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <p>对缓存友好、批量更新场景（游戏实体、粒子系统）收益明显，且业务代码无需改动。</p> <hr /> <h2 id="12-fan-she-yu-yun-xing-shi-lei-xing-xin-xi">12. 反射与运行时类型信息</h2> <p>程序数据段保存完整类型表，可在运行时遍历：</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-keyword z-control">for</span><span class="z-source"> _type_table </span><span class="z-punctuation">{</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> print</span><span class="z-punctuation">(</span><span class="z-punctuation">&quot;</span><span class="z-string">%</span><span class="z-constant z-character z-escape">\n</span><span class="z-punctuation">&quot;</span><span class="z-punctuation">,</span><span class="z-variable z-other"> it</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">name</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span></span></code></pre> <p>可用于序列化、网络复制、存档、调试器等（C/C++ 需要手写或宏实现）。</p> <hr /> <h2 id="13-mo-kuai-yu-xiang-mu-zu-zhi">13. 模块与项目组织</h2> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-variable z-other">#import</span><span class="z-punctuation"> &quot;</span><span class="z-string">Basic</span><span class="z-punctuation">&quot;</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-variable z-other">#load</span><span class="z-punctuation"> &quot;</span><span class="z-string">part2.jai</span><span class="z-punctuation">&quot;</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 追加编译另一个源文件</span></span></code></pre> <p>大型项目常用 <code>main.jai</code> 作为结构总览：<code>#import</code> 模块、<code>#load</code> 分片源文件，再定义 <code>main()</code>。</p> <hr /> <h2 id="14-xue-xi-lu-jing-jian-yi">14. 学习路径建议</h2> <ol> <li><strong>语法骨架</strong>：变量 → 过程 → 结构体 → 控制流；</li> <li><strong>内存</strong>：指针、<code>new/delete</code>、所有权 <code>!</code>、<code>defer</code>；</li> <li><strong>元编程</strong>：<code>#run</code>、<code>#if</code>、<code>$T</code> 多态、<code>#bake</code>；</li> <li><strong>数据导向</strong>：<code>struct SOA</code>、数组/切片、缓存局部性；</li> <li><strong>实战</strong>：参考 <a class="external" rel="external" href="https://github.com/Ivo-Balbaert/The_Way_to_Jai">The Way to Jai</a> 与 <a class="external" rel="external" href="https://github.com/BSVino/JaiPrimer">JaiPrimer</a> 的示例项目。</li> </ol> <blockquote> <p>注意：Jai 仍处于开发期，语法细节随编译器迭代可能变化，以官方最新文档为准。</p> </blockquote> 2026-08-11T00:00:00+00:00 2026-08-11T00:00:00+00:00 Suchaharcan https://suchaharcan.github.io/01Write_blog_PaperReading/design-patterns-23-cxx/ <h1 id="23-chong-she-ji-mo-shi-c-ban-you-que-dian-yu-ying-yong-chang-jing">23 种设计模式 · C++ 版优缺点与应用场景</h1> <blockquote> <p>GoF《设计模式》23 种，按目的分三类：<strong>创建型（5）· 结构型（7）· 行为型（11）</strong>。本文给出每种模式的意图、C++ 关键代码、优缺点与典型应用场景。</p> </blockquote> <hr /> <h2 id="zong-lan">总览</h2> <table><thead><tr><th>类别</th><th>模式</th><th>一句话</th></tr></thead><tbody> <tr><td>创建型</td><td>单例 Singleton</td><td>全局唯一实例</td></tr> <tr><td>创建型</td><td>工厂方法 Factory Method</td><td>子类决定创建哪个类</td></tr> <tr><td>创建型</td><td>抽象工厂 Abstract Factory</td><td>创建一族相关对象</td></tr> <tr><td>创建型</td><td>建造者 Builder</td><td>分步构建复杂对象</td></tr> <tr><td>创建型</td><td>原型 Prototype</td><td>复制已有对象</td></tr> <tr><td>结构型</td><td>适配器 Adapter</td><td>接口转换</td></tr> <tr><td>结构型</td><td>桥接 Bridge</td><td>抽象与实现分离</td></tr> <tr><td>结构型</td><td>组合 Composite</td><td>树形整体-部分</td></tr> <tr><td>结构型</td><td>装饰 Decorator</td><td>动态附加职责</td></tr> <tr><td>结构型</td><td>外观 Facade</td><td>统一门面接口</td></tr> <tr><td>结构型</td><td>享元 Flyweight</td><td>共享细粒度对象</td></tr> <tr><td>结构型</td><td>代理 Proxy</td><td>替身控制访问</td></tr> <tr><td>行为型</td><td>责任链 Chain of Responsibility</td><td>请求沿链传递</td></tr> <tr><td>行为型</td><td>命令 Command</td><td>请求封装为对象</td></tr> <tr><td>行为型</td><td>解释器 Interpreter</td><td>文法解释</td></tr> <tr><td>行为型</td><td>迭代器 Iterator</td><td>顺序访问集合</td></tr> <tr><td>行为型</td><td>中介者 Mediator</td><td>对象间解耦通信</td></tr> <tr><td>行为型</td><td>备忘录 Memento</td><td>保存/恢复状态</td></tr> <tr><td>行为型</td><td>观察者 Observer</td><td>一对多通知</td></tr> <tr><td>行为型</td><td>状态 State</td><td>状态行为切换</td></tr> <tr><td>行为型</td><td>策略 Strategy</td><td>算法族可替换</td></tr> <tr><td>行为型</td><td>模板方法 Template Method</td><td>骨架固定、步骤可变</td></tr> <tr><td>行为型</td><td>访问者 Visitor</td><td>数据结构与操作分离</td></tr> </tbody></table> <hr /> <h1 id="yi-chuang-jian-xing-mo-shi">一、创建型模式</h1> <h2 id="1-dan-li-singleton">1. 单例 Singleton</h2> <p><strong>意图</strong>：确保一个类只有一个实例，并提供全局访问点。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Logger</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> static</span><span class="z-entity z-name z-type"> Logger</span><span class="z-storage z-modifier">&amp;</span><span class="z-entity z-name z-function"> instance</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> static</span><span class="z-source"> Logger inst</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> C++11 线程安全</span></span> <span class="giallo-l"><span class="z-keyword z-control"> return</span><span class="z-source"> inst</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">private</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> Logger</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-keyword"> default</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>全局唯一、省资源</td><td>隐藏依赖，难测试</td></tr> <tr><td>延迟初始化</td><td>多线程初始化需注意</td></tr> </tbody></table> <p><strong>场景</strong>：日志系统、配置中心、线程池、连接池。</p> <h2 id="2-gong-han-fang-fa-factory-method">2. 工厂方法 Factory Method</h2> <p><strong>意图</strong>：定义一个创建对象的接口，让子类决定实例化哪个类。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">struct</span><span class="z-entity z-name z-type"> Product</span><span class="z-punctuation"> {</span><span class="z-storage z-modifier"> virtual</span><span class="z-keyword z-operator"> ~</span><span class="z-entity z-name z-function">Product</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-keyword z-control"> default</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">struct</span><span class="z-entity z-name z-type"> ConcreteA</span><span class="z-punctuation"> :</span><span class="z-source"> Product </span><span class="z-punctuation">{</span><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Factory</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">unique_ptr</span><span class="z-punctuation">&lt;</span><span class="z-entity z-name z-type">Product</span><span class="z-punctuation">&gt;</span><span class="z-entity z-name z-function"> create</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> FactoryA</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> Factory</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">unique_ptr</span><span class="z-punctuation">&lt;</span><span class="z-entity z-name z-type">Product</span><span class="z-punctuation">&gt;</span><span class="z-entity z-name z-function"> create</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-keyword z-control"> return</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-function">make_unique</span><span class="z-punctuation">&lt;</span><span class="z-entity z-name z-type">ConcreteA</span><span class="z-punctuation">&gt;</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>解耦创建与使用</td><td>每加一个产品需加子类</td></tr> <tr><td>开闭原则友好</td><td>类数量膨胀</td></tr> </tbody></table> <p><strong>场景</strong>：框架中由子类决定对象类型（如游戏单位工厂）。</p> <h2 id="3-chou-xiang-gong-han-abstract-factory">3. 抽象工厂 Abstract Factory</h2> <p><strong>意图</strong>：提供创建<strong>一族</strong>相关对象的接口。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">struct</span><span class="z-entity z-name z-type"> Button</span><span class="z-punctuation"> {</span><span class="z-storage z-modifier"> virtual</span><span class="z-keyword z-operator"> ~</span><span class="z-entity z-name z-function">Button</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-keyword z-control"> default</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">struct</span><span class="z-entity z-name z-type"> WinButton</span><span class="z-punctuation"> :</span><span class="z-source"> Button </span><span class="z-punctuation">{</span><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> UIFactory</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">unique_ptr</span><span class="z-punctuation">&lt;</span><span class="z-entity z-name z-type">Button</span><span class="z-punctuation">&gt;</span><span class="z-entity z-name z-function"> makeButton</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> WinFactory</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> UIFactory</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">unique_ptr</span><span class="z-punctuation">&lt;</span><span class="z-entity z-name z-type">Button</span><span class="z-punctuation">&gt;</span><span class="z-entity z-name z-function"> makeButton</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-keyword z-control"> return</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-function">make_unique</span><span class="z-punctuation">&lt;</span><span class="z-entity z-name z-type">WinButton</span><span class="z-punctuation">&gt;</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>保证产品族一致</td><td>新增产品族类型困难</td></tr> <tr><td>隔离具体类</td><td>新增产品（方法）违反开闭</td></tr> </tbody></table> <p><strong>场景</strong>：跨平台 UI 组件、数据库访问层（不同方言）。</p> <h2 id="4-jian-zao-zhe-builder">4. 建造者 Builder</h2> <p><strong>意图</strong>：分步骤构建复杂对象，步骤可复用于不同表示。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> PizzaBuilder</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-entity z-name z-type"> PizzaBuilder</span><span class="z-storage z-modifier">&amp;</span><span class="z-entity z-name z-function"> size</span><span class="z-punctuation">(</span><span class="z-storage z-type">int</span><span class="z-variable z-parameter"> s</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-source"> size_ </span><span class="z-keyword z-operator">=</span><span class="z-source"> s</span><span class="z-punctuation z-terminator">;</span><span class="z-keyword z-control"> return</span><span class="z-keyword z-operator"> *</span><span class="z-variable z-language">this</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-entity z-name z-type"> Pizza</span><span class="z-entity z-name z-function"> build</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-keyword z-control"> return</span><span class="z-entity z-name z-function"> Pizza</span><span class="z-punctuation">(</span><span class="z-source">size_</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">private</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-type"> int</span><span class="z-source"> size_ </span><span class="z-keyword z-operator">=</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation z-definition z-comment">//</span><span class="z-comment"> 使用：PizzaBuilder{}.size(12).build();</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>构造参数可读、不可变</td><td>需要额外类</td></tr> <tr><td>复用构建流程</td><td>简单对象反而过度设计</td></tr> </tbody></table> <p><strong>场景</strong>：复杂配置对象、文档/查询构建器。</p> <h2 id="5-yuan-xing-prototype">5. 原型 Prototype</h2> <p><strong>意图</strong>：通过克隆已有对象创建新对象。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">struct</span><span class="z-entity z-name z-type"> Shape</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-entity z-name z-function"> ~Shape</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-keyword"> default</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">unique_ptr</span><span class="z-punctuation">&lt;</span><span class="z-entity z-name z-type">Shape</span><span class="z-punctuation">&gt;</span><span class="z-entity z-name z-function"> clone</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> const</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">struct</span><span class="z-entity z-name z-type"> Circle</span><span class="z-punctuation"> :</span><span class="z-source"> Shape </span><span class="z-punctuation">{</span></span> <span class="giallo-l"><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">unique_ptr</span><span class="z-punctuation">&lt;</span><span class="z-entity z-name z-type">Shape</span><span class="z-punctuation">&gt;</span><span class="z-entity z-name z-function"> clone</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> const</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-keyword z-control"> return</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-function">make_unique</span><span class="z-punctuation">&lt;</span><span class="z-entity z-name z-type">Circle</span><span class="z-punctuation">&gt;</span><span class="z-punctuation">(</span><span class="z-keyword z-operator">*</span><span class="z-variable z-language">this</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>避免重复构造开销</td><td>深拷贝语义易出错</td></tr> <tr><td>动态类型克隆</td><td>含资源成员需自定义拷贝</td></tr> </tbody></table> <p><strong>场景</strong>：编辑器复制图形、游戏单位克隆、配置模板。</p> <hr /> <h1 id="er-jie-gou-xing-mo-shi">二、结构型模式</h1> <h2 id="6-gua-pei-qi-adapter">6. 适配器 Adapter</h2> <p><strong>意图</strong>：将不兼容接口转换为客户端期望的接口。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Target</span><span class="z-punctuation"> {</span><span class="z-storage z-type z-modifier"> public</span><span class="z-punctuation">:</span><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> request</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Adaptee</span><span class="z-punctuation"> {</span><span class="z-storage z-type z-modifier"> public</span><span class="z-punctuation">:</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> specific</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Adapter</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> Target</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> request</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-variable z-other"> adaptee_</span><span class="z-punctuation">.</span><span class="z-entity z-name z-function">specific</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">private</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-source"> Adaptee adaptee_</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>复用已有类，不改源码</td><td>过度使用使架构混乱</td></tr> <tr><td>符合开闭原则</td><td>有性能微开销</td></tr> </tbody></table> <p><strong>场景</strong>：接入第三方库、新旧接口桥接。</p> <h2 id="7-qiao-jie-bridge">7. 桥接 Bridge</h2> <p><strong>意图</strong>：将抽象部分与实现部分分离，各自独立变化。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Renderer</span><span class="z-punctuation"> {</span><span class="z-storage z-type z-modifier"> public</span><span class="z-punctuation">:</span><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> draw</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Shape</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> explicit</span><span class="z-entity z-name z-function"> Shape</span><span class="z-punctuation">(</span><span class="z-entity z-name z-type">Renderer</span><span class="z-storage z-modifier">*</span><span class="z-variable z-parameter"> r</span><span class="z-punctuation">)</span><span class="z-punctuation"> :</span><span class="z-entity z-name z-function"> r_</span><span class="z-punctuation">(</span><span class="z-source">r</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">protected</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-source"> Renderer</span><span class="z-keyword z-operator">*</span><span class="z-source"> r_</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Circle</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> Shape</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-keyword"> using</span><span class="z-entity z-name"> Shape</span><span class="z-punctuation">::</span><span class="z-source">Shape</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> draw</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-variable z-other"> r_</span><span class="z-punctuation">-&gt;</span><span class="z-entity z-name z-function">draw</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>抽象与实现可独立扩展</td><td>增加系统复杂度</td></tr> <tr><td>符合开闭原则</td><td>需提前识别维度</td></tr> </tbody></table> <p><strong>场景</strong>：图形渲染后端（OpenGL/Vulkan）、跨平台设备驱动。</p> <h2 id="8-zu-he-composite">8. 组合 Composite</h2> <p><strong>意图</strong>：将对象组织成树形结构，一致对待叶子与容器。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Component</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> render</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> add</span><span class="z-punctuation">(</span><span class="z-entity z-name z-type">Component</span><span class="z-storage z-modifier">*</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Leaf</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> Component</span><span class="z-punctuation"> {</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> render</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Composite</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> Component</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> add</span><span class="z-punctuation">(</span><span class="z-entity z-name z-type">Component</span><span class="z-storage z-modifier">*</span><span class="z-variable z-parameter"> c</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-variable z-other"> children_</span><span class="z-punctuation">.</span><span class="z-entity z-name z-function">push_back</span><span class="z-punctuation">(</span><span class="z-source">c</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> render</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-keyword z-control"> for</span><span class="z-punctuation"> (</span><span class="z-storage z-type">auto</span><span class="z-keyword z-operator">*</span><span class="z-source"> c </span><span class="z-punctuation">:</span><span class="z-source"> children_</span><span class="z-punctuation">)</span><span class="z-variable z-other"> c</span><span class="z-punctuation">-&gt;</span><span class="z-entity z-name z-function">render</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">private</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-source">vector</span><span class="z-keyword z-operator">&lt;</span><span class="z-source">Component</span><span class="z-keyword z-operator">*</span><span class="z-keyword z-operator">&gt;</span><span class="z-source"> children_</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>树形结构统一操作</td><td>叶子与容器接口耦合</td></tr> <tr><td>易扩展新节点</td><td>违反接口隔离</td></tr> </tbody></table> <p><strong>场景</strong>：文件系统、UI 控件树、组织架构。</p> <h2 id="9-zhuang-shi-decorator">9. 装饰 Decorator</h2> <p><strong>意图</strong>：动态给对象添加职责，替代继承。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Stream</span><span class="z-punctuation"> {</span><span class="z-storage z-type z-modifier"> public</span><span class="z-punctuation">:</span><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> write</span><span class="z-punctuation">(</span><span class="z-storage z-modifier">const</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-source">string</span><span class="z-keyword z-operator">&amp;</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> FileStream</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> Stream</span><span class="z-punctuation"> {</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> write</span><span class="z-punctuation">(</span><span class="z-storage z-modifier">const</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">string</span><span class="z-storage z-modifier">&amp;</span><span class="z-variable z-parameter"> s</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> EncryptedStream</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> Stream</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> explicit</span><span class="z-entity z-name z-function"> EncryptedStream</span><span class="z-punctuation">(</span><span class="z-entity z-name z-type">Stream</span><span class="z-storage z-modifier">*</span><span class="z-variable z-parameter"> s</span><span class="z-punctuation">)</span><span class="z-punctuation"> :</span><span class="z-entity z-name z-function"> s_</span><span class="z-punctuation">(</span><span class="z-source">s</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> write</span><span class="z-punctuation">(</span><span class="z-storage z-modifier">const</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">string</span><span class="z-storage z-modifier">&amp;</span><span class="z-variable z-parameter"> s</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-variable z-other"> s_</span><span class="z-punctuation">-&gt;</span><span class="z-entity z-name z-function">write</span><span class="z-punctuation">(</span><span class="z-entity z-name z-function">encrypt</span><span class="z-punctuation">(</span><span class="z-source">s</span><span class="z-punctuation">)</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">private</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-source"> Stream</span><span class="z-keyword z-operator">*</span><span class="z-source"> s_</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>组合优于继承，灵活</td><td>层数多时难调试</td></tr> <tr><td>运行时叠加能力</td><td>小对象过多</td></tr> </tbody></table> <p><strong>场景</strong>：IO 流加缓冲/加密/压缩、中间件管道。</p> <h2 id="10-wai-guan-facade">10. 外观 Facade</h2> <p><strong>意图</strong>：为复杂子系统提供统一简化的入口。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> VideoConverter</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> convert</span><span class="z-punctuation">(</span><span class="z-storage z-modifier">const</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">string</span><span class="z-storage z-modifier">&amp;</span><span class="z-variable z-parameter"> file</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-variable z-other"> codec_</span><span class="z-punctuation">.</span><span class="z-entity z-name z-function">load</span><span class="z-punctuation">(</span><span class="z-source">file</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-variable z-other"> filter_</span><span class="z-punctuation">.</span><span class="z-entity z-name z-function">apply</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-variable z-other"> mux_</span><span class="z-punctuation">.</span><span class="z-entity z-name z-function">save</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">private</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-source"> Codec codec_</span><span class="z-punctuation z-terminator">;</span><span class="z-source"> Filter filter_</span><span class="z-punctuation z-terminator">;</span><span class="z-source"> Muxer mux_</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>客户端使用简单</td><td>可能变成“上帝对象“</td></tr> <tr><td>隔离子系统变化</td><td>隐藏了灵活性</td></tr> </tbody></table> <p><strong>场景</strong>：编译模块入口、播放器/转换器统一 API。</p> <h2 id="11-xiang-yuan-flyweight">11. 享元 Flyweight</h2> <p><strong>意图</strong>：共享细粒度对象，减少内存占用。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">struct</span><span class="z-entity z-name z-type"> CharStyle</span><span class="z-punctuation"> {</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-source">string font</span><span class="z-punctuation z-terminator">;</span><span class="z-storage z-type"> int</span><span class="z-source"> size</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> StyleCache</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> const</span><span class="z-entity z-name z-type"> CharStyle</span><span class="z-storage z-modifier">&amp;</span><span class="z-entity z-name z-function"> get</span><span class="z-punctuation">(</span><span class="z-storage z-modifier">const</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">string</span><span class="z-storage z-modifier">&amp;</span><span class="z-variable z-parameter"> font</span><span class="z-punctuation">,</span><span class="z-storage z-type"> int</span><span class="z-variable z-parameter"> size</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type"> auto</span><span class="z-source"> key </span><span class="z-keyword z-operator">=</span><span class="z-source"> font </span><span class="z-keyword z-operator">+</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-function">to_string</span><span class="z-punctuation">(</span><span class="z-source">size</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type"> auto</span><span class="z-source"> it </span><span class="z-keyword z-operator">=</span><span class="z-variable z-other"> cache_</span><span class="z-punctuation">.</span><span class="z-entity z-name z-function">find</span><span class="z-punctuation">(</span><span class="z-source">key</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> if</span><span class="z-punctuation"> (</span><span class="z-source">it </span><span class="z-keyword z-operator">==</span><span class="z-variable z-other"> cache_</span><span class="z-punctuation">.</span><span class="z-entity z-name z-function">end</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation">)</span></span> <span class="giallo-l"><span class="z-source"> it </span><span class="z-keyword z-operator">=</span><span class="z-variable z-other"> cache_</span><span class="z-punctuation">.</span><span class="z-entity z-name z-function">emplace</span><span class="z-punctuation">(</span><span class="z-source">key</span><span class="z-punctuation">,</span><span class="z-source"> CharStyle{font</span><span class="z-punctuation">,</span><span class="z-source"> size}</span><span class="z-punctuation">)</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">first</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> return</span><span class="z-variable z-other"> it</span><span class="z-punctuation">-&gt;</span><span class="z-variable z-other z-property">second</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">private</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-source">unordered_map</span><span class="z-keyword z-operator">&lt;</span><span class="z-entity z-name">std</span><span class="z-punctuation">::</span><span class="z-source">string</span><span class="z-punctuation">,</span><span class="z-source"> CharStyle</span><span class="z-keyword z-operator">&gt;</span><span class="z-source"> cache_</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>大幅减少内存</td><td>外部状态管理复杂</td></tr> <tr><td>提高缓存命中</td><td>引入共享对象并发问题</td></tr> </tbody></table> <p><strong>场景</strong>：文本编辑器字符样式、游戏贴图/粒子模板、连接池。</p> <h2 id="12-dai-li-proxy">12. 代理 Proxy</h2> <p><strong>意图</strong>：提供替身控制对真实对象的访问（延迟/权限/缓存）。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Image</span><span class="z-punctuation"> {</span><span class="z-storage z-type z-modifier"> public</span><span class="z-punctuation">:</span><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> show</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> RealImage</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> Image</span><span class="z-punctuation"> {</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> show</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> ImageProxy</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> Image</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> show</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-keyword z-control"> if</span><span class="z-punctuation"> (</span><span class="z-keyword z-operator">!</span><span class="z-source">real_</span><span class="z-punctuation">)</span><span class="z-source"> real_ </span><span class="z-keyword z-operator">=</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-function">make_unique</span><span class="z-punctuation">&lt;</span><span class="z-entity z-name z-type">RealImage</span><span class="z-punctuation">&gt;</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-variable z-other"> real_</span><span class="z-punctuation">-&gt;</span><span class="z-entity z-name z-function">show</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 延迟加载</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">private</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-source">unique_ptr</span><span class="z-keyword z-operator">&lt;</span><span class="z-source">RealImage</span><span class="z-keyword z-operator">&gt;</span><span class="z-source"> real_</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>延迟加载、访问控制、日志</td><td>增加间接层</td></tr> <tr><td>透明代理</td><td>过度代理增加延迟</td></tr> </tbody></table> <p><strong>场景</strong>：懒加载图片、智能指针、远程调用（RPC stub）。</p> <hr /> <h1 id="san-xing-wei-xing-mo-shi">三、行为型模式</h1> <h2 id="13-ze-ren-lian-chain-of-responsibility">13. 责任链 Chain of Responsibility</h2> <p><strong>意图</strong>：多个处理者串成链，请求沿链传递直到被处理。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Handler</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-entity z-name z-type"> Handler</span><span class="z-storage z-modifier">*</span><span class="z-entity z-name z-function"> next</span><span class="z-punctuation">(</span><span class="z-entity z-name z-type">Handler</span><span class="z-storage z-modifier">*</span><span class="z-variable z-parameter"> n</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-source"> next_ </span><span class="z-keyword z-operator">=</span><span class="z-source"> n</span><span class="z-punctuation z-terminator">;</span><span class="z-keyword z-control"> return</span><span class="z-variable z-language"> this</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> handle</span><span class="z-punctuation">(</span><span class="z-storage z-type">int</span><span class="z-variable z-parameter"> level</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-keyword z-control"> if</span><span class="z-punctuation"> (</span><span class="z-entity z-name z-function">canHandle</span><span class="z-punctuation">(</span><span class="z-source">level</span><span class="z-punctuation">)</span><span class="z-punctuation">)</span><span class="z-entity z-name z-function"> process</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-keyword z-control"> else</span><span class="z-keyword z-control"> if</span><span class="z-punctuation"> (</span><span class="z-source">next_</span><span class="z-punctuation">)</span><span class="z-variable z-other"> next_</span><span class="z-punctuation">-&gt;</span><span class="z-entity z-name z-function">handle</span><span class="z-punctuation">(</span><span class="z-source">level</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">private</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> bool</span><span class="z-entity z-name z-function"> canHandle</span><span class="z-punctuation">(</span><span class="z-storage z-type">int</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> process</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-source"> Handler</span><span class="z-keyword z-operator">*</span><span class="z-source"> next_ </span><span class="z-keyword z-operator">=</span><span class="z-constant z-language"> nullptr</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>发送者与处理者解耦</td><td>请求可能无人处理</td></tr> <tr><td>灵活增删处理者</td><td>调试链长时困难</td></tr> </tbody></table> <p><strong>场景</strong>：日志级别过滤、事件冒泡、中间件管道。</p> <h2 id="14-ming-ling-command">14. 命令 Command</h2> <p><strong>意图</strong>：把请求封装成对象，支持参数化、队列、撤销。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Command</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> execute</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> undo</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> CopyCommand</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> Command</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> execute</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> undo</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>支持撤销/重做、任务队列</td><td>每个操作一个类</td></tr> <tr><td>请求可参数化延迟执行</td><td>类数量增加</td></tr> </tbody></table> <p><strong>场景</strong>：编辑器撤销栈、事务、宏录制、线程任务。</p> <h2 id="15-jie-shi-qi-interpreter">15. 解释器 Interpreter</h2> <p><strong>意图</strong>：为文法定义解释器，求值表达式。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">struct</span><span class="z-entity z-name z-type"> Expr</span><span class="z-punctuation"> {</span><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> int</span><span class="z-entity z-name z-function"> eval</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> const</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">struct</span><span class="z-entity z-name z-type"> Num</span><span class="z-punctuation"> :</span><span class="z-source"> Expr </span><span class="z-punctuation">{</span><span class="z-storage z-type"> int</span><span class="z-source"> v</span><span class="z-punctuation z-terminator">;</span><span class="z-storage z-type"> int</span><span class="z-entity z-name z-function"> eval</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> const</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-keyword z-control"> return</span><span class="z-source"> v</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">struct</span><span class="z-entity z-name z-type"> Add</span><span class="z-punctuation"> :</span><span class="z-source"> Expr </span><span class="z-punctuation">{</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> const</span><span class="z-source"> Expr </span><span class="z-keyword z-operator">*</span><span class="z-source">l</span><span class="z-punctuation">,</span><span class="z-keyword z-operator"> *</span><span class="z-source">r</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type"> int</span><span class="z-entity z-name z-function"> eval</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> const</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-keyword z-control"> return</span><span class="z-variable z-other"> l</span><span class="z-punctuation">-&gt;</span><span class="z-entity z-name z-function">eval</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> +</span><span class="z-variable z-other"> r</span><span class="z-punctuation">-&gt;</span><span class="z-entity z-name z-function">eval</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>文法易扩展</td><td>复杂文法维护困难</td></tr> <tr><td>领域语言表达力强</td><td>性能较低</td></tr> </tbody></table> <p><strong>场景</strong>：SQL/正则/数学表达式引擎、脚本解析。</p> <h2 id="16-die-dai-qi-iterator">16. 迭代器 Iterator</h2> <p><strong>意图</strong>：不暴露内部结构，顺序访问集合元素。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Iter</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> bool</span><span class="z-entity z-name z-function"> hasNext</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> int</span><span class="z-entity z-name z-function"> next</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> RangeIter</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> Iter</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type"> int</span><span class="z-source"> cur_</span><span class="z-punctuation">,</span><span class="z-source"> end_</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> RangeIter</span><span class="z-punctuation">(</span><span class="z-storage z-type">int</span><span class="z-variable z-parameter"> a</span><span class="z-punctuation">,</span><span class="z-storage z-type"> int</span><span class="z-variable z-parameter"> b</span><span class="z-punctuation">)</span><span class="z-punctuation"> :</span><span class="z-entity z-name z-function"> cur_</span><span class="z-punctuation">(</span><span class="z-source">a</span><span class="z-punctuation">)</span><span class="z-punctuation">,</span><span class="z-entity z-name z-function"> end_</span><span class="z-punctuation">(</span><span class="z-source">b</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span></span> <span class="giallo-l"><span class="z-storage z-type"> bool</span><span class="z-entity z-name z-function"> hasNext</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-keyword z-control"> return</span><span class="z-source"> cur_ </span><span class="z-keyword z-operator">&lt;=</span><span class="z-source"> end_</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type"> int</span><span class="z-entity z-name z-function"> next</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-keyword z-control"> return</span><span class="z-source"> cur_</span><span class="z-keyword z-operator">++</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>集合遍历与结构解耦</td><td>简单集合反而多余</td></tr> <tr><td>支持多种遍历策略</td><td>遍历中修改集合需约定</td></tr> </tbody></table> <p><strong>场景</strong>：STL 迭代器、分页遍历、树遍历。</p> <h2 id="17-zhong-jie-zhe-mediator">17. 中介者 Mediator</h2> <p><strong>意图</strong>：用一个中介对象协调多个对象的交互。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Mediator</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> notify</span><span class="z-punctuation">(</span><span class="z-storage z-modifier">const</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">string</span><span class="z-storage z-modifier">&amp;</span><span class="z-variable z-parameter"> from</span><span class="z-punctuation">,</span><span class="z-storage z-modifier"> const</span><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">string</span><span class="z-storage z-modifier">&amp;</span><span class="z-variable z-parameter"> msg</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-keyword z-control"> for</span><span class="z-punctuation"> (</span><span class="z-storage z-type">auto</span><span class="z-keyword z-operator">*</span><span class="z-source"> c </span><span class="z-punctuation">:</span><span class="z-source"> colleagues_</span><span class="z-punctuation">)</span><span class="z-keyword z-control"> if</span><span class="z-punctuation"> (</span><span class="z-variable z-other">c</span><span class="z-punctuation">-&gt;</span><span class="z-entity z-name z-function">name</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> !=</span><span class="z-source"> from</span><span class="z-punctuation">)</span><span class="z-variable z-other"> c</span><span class="z-punctuation">-&gt;</span><span class="z-entity z-name z-function">receive</span><span class="z-punctuation">(</span><span class="z-source">msg</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> add</span><span class="z-punctuation">(</span><span class="z-entity z-name z-type">Colleague</span><span class="z-storage z-modifier">*</span><span class="z-variable z-parameter"> c</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-variable z-other"> colleagues_</span><span class="z-punctuation">.</span><span class="z-entity z-name z-function">push_back</span><span class="z-punctuation">(</span><span class="z-source">c</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">private</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-source">vector</span><span class="z-keyword z-operator">&lt;</span><span class="z-source">Colleague</span><span class="z-keyword z-operator">*</span><span class="z-keyword z-operator">&gt;</span><span class="z-source"> colleagues_</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>减少对象间网状依赖</td><td>中介者可能过于庞大</td></tr> <tr><td>交互集中管理</td><td>单点故障</td></tr> </tbody></table> <p><strong>场景</strong>：聊天室、UI 控件协调、航班调度。</p> <h2 id="18-bei-wang-lu-memento">18. 备忘录 Memento</h2> <p><strong>意图</strong>：在不破坏封装的前提下保存并恢复对象状态。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">struct</span><span class="z-entity z-name z-type"> Memento</span><span class="z-punctuation"> {</span><span class="z-storage z-type"> int</span><span class="z-source"> state</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Originator</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-entity z-name z-type"> Memento</span><span class="z-entity z-name z-function"> save</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> const</span><span class="z-punctuation"> {</span><span class="z-keyword z-control"> return</span><span class="z-punctuation"> {</span><span class="z-source">state_</span><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> restore</span><span class="z-punctuation">(</span><span class="z-storage z-modifier">const</span><span class="z-entity z-name z-type"> Memento</span><span class="z-storage z-modifier">&amp;</span><span class="z-variable z-parameter"> m</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-source"> state_ </span><span class="z-keyword z-operator">=</span><span class="z-variable z-other"> m</span><span class="z-punctuation">.</span><span class="z-variable z-other z-property">state</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">private</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-type"> int</span><span class="z-source"> state_ </span><span class="z-keyword z-operator">=</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>状态快照与恢复简单</td><td>大对象快照开销高</td></tr> <tr><td>不破坏封装</td><td>历史过多占内存</td></tr> </tbody></table> <p><strong>场景</strong>：编辑器撤销、游戏存档、事务回滚。</p> <h2 id="19-guan-cha-zhe-observer">19. 观察者 Observer</h2> <p><strong>意图</strong>：定义一对多依赖，状态变化自动通知。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Observer</span><span class="z-punctuation"> {</span><span class="z-storage z-type z-modifier"> public</span><span class="z-punctuation">:</span><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> update</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Subject</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> attach</span><span class="z-punctuation">(</span><span class="z-entity z-name z-type">Observer</span><span class="z-storage z-modifier">*</span><span class="z-variable z-parameter"> o</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-variable z-other"> obs_</span><span class="z-punctuation">.</span><span class="z-entity z-name z-function">push_back</span><span class="z-punctuation">(</span><span class="z-source">o</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> notify</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-keyword z-control"> for</span><span class="z-punctuation"> (</span><span class="z-storage z-type">auto</span><span class="z-keyword z-operator">*</span><span class="z-source"> o </span><span class="z-punctuation">:</span><span class="z-source"> obs_</span><span class="z-punctuation">)</span><span class="z-variable z-other"> o</span><span class="z-punctuation">-&gt;</span><span class="z-entity z-name z-function">update</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">private</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-entity z-name"> std</span><span class="z-punctuation">::</span><span class="z-source">vector</span><span class="z-keyword z-operator">&lt;</span><span class="z-source">Observer</span><span class="z-keyword z-operator">*</span><span class="z-keyword z-operator">&gt;</span><span class="z-source"> obs_</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>主题与观察者解耦</td><td>通知顺序不确定</td></tr> <tr><td>广播机制天然</td><td>级联更新难排查</td></tr> </tbody></table> <p><strong>场景</strong>：事件总线、MVC 视图刷新、发布订阅。</p> <h2 id="20-zhuang-tai-state">20. 状态 State</h2> <p><strong>意图</strong>：对象状态改变时行为随之改变，替代大量 if-else。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> State</span><span class="z-punctuation"> {</span><span class="z-storage z-type z-modifier"> public</span><span class="z-punctuation">:</span><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> handle</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> IdleState</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> State</span><span class="z-punctuation"> {</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> handle</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> RunningState</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> State</span><span class="z-punctuation"> {</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> handle</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>状态行为内聚、可扩展</td><td>状态类数量多</td></tr> <tr><td>消除巨型条件分支</td><td>状态转换逻辑分散</td></tr> </tbody></table> <p><strong>场景</strong>：播放器状态、订单状态机、网络连接状态。</p> <h2 id="21-ce-lue-strategy">21. 策略 Strategy</h2> <p><strong>意图</strong>：定义算法族并封装，运行时切换。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> SortStrategy</span><span class="z-punctuation"> {</span><span class="z-storage z-type z-modifier"> public</span><span class="z-punctuation">:</span><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> sort</span><span class="z-punctuation">(</span><span class="z-entity z-name">std</span><span class="z-punctuation">::</span><span class="z-source">vector</span><span class="z-keyword z-operator">&lt;</span><span class="z-storage z-type">int</span><span class="z-keyword z-operator">&gt;</span><span class="z-keyword z-operator">&amp;</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> QuickSort</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> SortStrategy</span><span class="z-punctuation"> {</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> sort</span><span class="z-punctuation">(</span><span class="z-entity z-name">std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">vector</span><span class="z-punctuation">&lt;</span><span class="z-storage z-type">int</span><span class="z-punctuation">&gt;</span><span class="z-storage z-modifier">&amp;</span><span class="z-variable z-parameter"> v</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> MergeSort</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> SortStrategy</span><span class="z-punctuation"> {</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> sort</span><span class="z-punctuation">(</span><span class="z-entity z-name">std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">vector</span><span class="z-punctuation">&lt;</span><span class="z-storage z-type">int</span><span class="z-punctuation">&gt;</span><span class="z-storage z-modifier">&amp;</span><span class="z-variable z-parameter"> v</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span><span class="z-punctuation"> }</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Sorter</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> setStrategy</span><span class="z-punctuation">(</span><span class="z-entity z-name z-type">SortStrategy</span><span class="z-storage z-modifier">*</span><span class="z-variable z-parameter"> s</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-source"> s_ </span><span class="z-keyword z-operator">=</span><span class="z-source"> s</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> run</span><span class="z-punctuation">(</span><span class="z-entity z-name">std</span><span class="z-punctuation">::</span><span class="z-entity z-name z-type">vector</span><span class="z-punctuation">&lt;</span><span class="z-storage z-type">int</span><span class="z-punctuation">&gt;</span><span class="z-storage z-modifier">&amp;</span><span class="z-variable z-parameter"> v</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-variable z-other"> s_</span><span class="z-punctuation">-&gt;</span><span class="z-entity z-name z-function">sort</span><span class="z-punctuation">(</span><span class="z-source">v</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">private</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-source"> SortStrategy</span><span class="z-keyword z-operator">*</span><span class="z-source"> s_</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>算法可替换、开闭原则</td><td>客户端需了解策略差异</td></tr> <tr><td>消除条件分支</td><td>策略对象数量增加</td></tr> </tbody></table> <p><strong>场景</strong>：排序算法选择、压缩/加密算法、价格计算。</p> <h2 id="22-mo-ban-fang-fa-template-method">22. 模板方法 Template Method</h2> <p><strong>意图</strong>：定义算法骨架，子类实现可变步骤。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> DataParser</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> parse</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 骨架固定</span></span> <span class="giallo-l"><span class="z-entity z-name z-function"> open</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-entity z-name z-function"> read</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-entity z-name z-function"> process</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span><span class="z-entity z-name z-function"> close</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation"> }</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">protected</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> process</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span><span class="z-punctuation z-definition z-comment"> //</span><span class="z-comment"> 可变步骤</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">private</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> open</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> read</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> close</span><span class="z-punctuation">(</span><span class="z-punctuation">)</span><span class="z-punctuation"> {</span><span class="z-punctuation">}</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>复用公共流程</td><td>骨架修改影响全部子类</td></tr> <tr><td>约束子类实现范围</td><td>违反 LSP 风险（子类改变骨架）</td></tr> </tbody></table> <p><strong>场景</strong>：框架生命周期（初始化-运行-清理）、解析器流程。</p> <h2 id="23-fang-wen-zhe-visitor">23. 访问者 Visitor</h2> <p><strong>意图</strong>：在不修改类的前提下，为对象结构增加新操作。</p> <pre class="giallo z-code"><code data-lang="cpp"><span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Visitor</span><span class="z-punctuation z-terminator">;</span><span class="z-source"> </span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Node</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> accept</span><span class="z-punctuation">(</span><span class="z-entity z-name z-type">Visitor</span><span class="z-storage z-modifier">&amp;</span><span class="z-variable z-parameter"> v</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> TextNode</span><span class="z-punctuation"> :</span><span class="z-storage z-type z-modifier"> public</span><span class="z-entity z-name z-type"> Node</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> accept</span><span class="z-punctuation">(</span><span class="z-entity z-name z-type">Visitor</span><span class="z-storage z-modifier">&amp;</span><span class="z-variable z-parameter"> v</span><span class="z-punctuation">)</span><span class="z-storage z-modifier"> override</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-storage z-type">class</span><span class="z-entity z-name z-type"> Visitor</span><span class="z-punctuation"> {</span></span> <span class="giallo-l"><span class="z-storage z-type z-modifier">public</span><span class="z-punctuation">:</span></span> <span class="giallo-l"><span class="z-storage z-modifier"> virtual</span><span class="z-storage z-type"> void</span><span class="z-entity z-name z-function"> visit</span><span class="z-punctuation">(</span><span class="z-entity z-name z-type">TextNode</span><span class="z-storage z-modifier">&amp;</span><span class="z-punctuation">)</span><span class="z-keyword z-operator"> =</span><span class="z-constant z-numeric"> 0</span><span class="z-punctuation z-terminator">;</span></span> <span class="giallo-l"><span class="z-punctuation">}</span><span class="z-punctuation z-terminator">;</span></span></code></pre><table><thead><tr><th>优点</th><th>缺点</th></tr></thead><tbody> <tr><td>数据结构与操作分离，易加操作</td><td>新增节点类型需改所有访问者</td></tr> <tr><td>操作内聚</td><td>破坏封装（需暴露内部）</td></tr> </tbody></table> <p><strong>场景</strong>：AST 编译/解释、对象结构统计与序列化。</p> <hr /> <h2 id="xuan-xing-su-cha">选型速查</h2> <table><thead><tr><th>问题</th><th>推荐模式</th></tr></thead><tbody> <tr><td>全局唯一</td><td>单例</td></tr> <tr><td>创建复杂对象</td><td>建造者 / 工厂 / 抽象工厂</td></tr> <tr><td>接口不兼容</td><td>适配器</td></tr> <tr><td>动态加职责</td><td>装饰</td></tr> <tr><td>树形结构</td><td>组合</td></tr> <tr><td>延迟/控制访问</td><td>代理</td></tr> <tr><td>一对多通知</td><td>观察者</td></tr> <tr><td>运行时换算法</td><td>策略</td></tr> <tr><td>状态行为切换</td><td>状态</td></tr> <tr><td>撤销重做</td><td>命令 + 备忘录</td></tr> <tr><td>为结构加新操作</td><td>访问者</td></tr> </tbody></table> <blockquote> <p>原则提醒：<strong>优先组合而非继承、面向接口而非实现、对扩展开放对修改关闭</strong>。模式是工具，不要为模式而模式。</p> </blockquote> 2026-08-11T00:00:00+00:00 2026-08-11T00:00:00+00:00 Suchaharcan https://suchaharcan.github.io/01Write_blog_ReadingNotes/readingnotes-kant-critique/ <h1 id="chun-cui-li-xing-pi-pan-du-hou-gan">《纯粹理性批判》读后感</h1> <blockquote> <p>康德（Immanuel Kant）1781 年初版《纯粹理性批判》。本次精读<strong>先验感性论</strong>与<strong>先验分析论</strong>，兼及辩证论的开头部分。</p> </blockquote> <hr /> <h2 id="yi-wen-ti-yi-shi-xian-tian-zong-he-pan-duan-ru-he-ke-neng">一、问题意识：先天综合判断如何可能</h2> <p>康德面对两派：</p> <table><thead><tr><th>学派</th><th>立场</th><th>问题</th></tr></thead><tbody> <tr><td>唯理论（莱布尼茨）</td><td>理性演绎一切</td><td>脱离经验，独断</td></tr> <tr><td>经验论（休谟）</td><td>一切知识来自经验</td><td>因果等必然性无法保证</td></tr> </tbody></table> <p>康德的问题是：<strong>存在既先于经验（先天）、又扩展知识（综合）的判断吗？</strong> 数学与自然科学就是例子：</p> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>7 + 5 = 12 先天综合（不靠经验，却扩展了知识）</span></span> <span class="giallo-l"><span>一切事件都有原因 先天综合（因果性不能从经验归纳出来）</span></span></code></pre> <p>回答这个问题，需要<strong>批判理性自身的能力与边界</strong>——这就是“纯粹理性批判“。</p> <hr /> <h2 id="er-ge-bai-ni-shi-ge-ming">二、哥白尼式革命</h2> <p>传统认为认识必须符合对象；康德反转为：<strong>对象必须符合我们的认识形式</strong>。</p> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>不是知识围绕对象转，而是对象围绕我们的认知结构转</span></span></code></pre> <p>我们只能认识“对我们显现的现象“，而不能认识独立于我们的“物自体（Ding an sich）“。物自体不可知，但它的存在被设定为现象的根据。</p> <hr /> <h2 id="san-xian-yan-gan-xing-lun-shi-kong">三、先验感性论：时空</h2> <h3 id="1-shi-jian-yu-kong-jian-shi-zhi-guan-xing-shi">1. 时间与空间是直观形式</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>空间：外感官的形式——外部事物必须在空间中呈现</span></span> <span class="giallo-l"><span>时间：内感官的形式——一切表象（含思维）都在时间中</span></span></code></pre> <p>时空不是经验中抽象出来的概念，而是<strong>感性的先天形式</strong>：它们使经验成为可能，也因此只适用于现象。</p> <h3 id="2-shu-xue-wei-shen-me-ke-neng">2. 数学为什么可能</h3> <p>几何基于空间的先天直观，算术基于时间的先天直观——这解释了数学的“普遍必然性“。</p> <hr /> <h2 id="si-xian-yan-fen-xi-lun-fan-chou-yu-zhi-xing">四、先验分析论：范畴与知性</h2> <h3 id="1-zhi-guan-wu-gai-nian-ze-mang-gai-nian-wu-zhi-guan-ze-kong">1. 直观无概念则盲，概念无直观则空</h3> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>思维无内容则空，直观无概念则盲</span></span></code></pre> <p>感性提供材料，知性用<strong>范畴</strong>整理材料，两者结合才产生知识。</p> <h3 id="2-shi-er-fan-chou-zhi-xing-de-xian-tian-gai-nian">2. 十二范畴（知性的先天概念）</h3> <table><thead><tr><th>量</th><th>质</th><th>关系</th><th>样式</th></tr></thead><tbody> <tr><td>单一性</td><td>实在性</td><td>依存性与实体</td><td>可能性</td></tr> <tr><td>多数性</td><td>否定性</td><td>因果性与依存</td><td>现实性</td></tr> <tr><td>全体性</td><td>限制性</td><td>协同性（共联）</td><td>必然性</td></tr> </tbody></table> <h3 id="3-tong-jue-de-xian-yan-tong-yi">3. 统觉的先验统一</h3> <p>“我思“必须能够伴随我的一切表象——这是知识统一的最高原理。范畴通过<strong>先验统觉</strong>把杂多表象综合为对象。</p> <h3 id="4-ren-wei-zi-ran-li-fa">4. 人为自然立法</h3> <p>因果性、实体性等范畴是<strong>知性加到现象上</strong>的，而不是从自然里“读出来“的。因此：</p> <blockquote> <p>自然界的普遍规律，是知性先天地规定的——“人为自然立法”。</p> </blockquote> <hr /> <h2 id="wu-xian-yan-bian-zheng-lun-yin-zi-li-xing-de-yue-jie">五、先验辩证论（引子）：理性的越界</h2> <p>理性不满足于现象，总想把握“无条件者“，于是产生三类理念：<strong>灵魂、世界、上帝</strong>。理性把它们当作对象去认识，就会陷入幻相（如二律背反：世界有无开端、自由与必然等矛盾）。康德的任务不是消灭理性，而是<strong>为理性划界</strong>：</p> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>现象界：可认识（知性 + 感性）</span></span> <span class="giallo-l"><span>本体界（物自体）：不可认识，只能思维（实践理性另论）</span></span></code></pre> <hr /> <h2 id="liu-yue-du-ti-hui">六、阅读体会</h2> <h3 id="1-hua-jie-bi-hui-da-geng-shen-ke">1. “划界“比“回答“更深刻</h3> <p>康德最打动我的不是某个结论，而是<strong>问题的提法</strong>：与其争论上帝存在与否，不如先问“我们能认识什么“。这种“先问能力边界“的姿态，和工程中的“先定义问题域“非常接近——很多争论之所以无解，是因为双方在错误的层面争论。</p> <h3 id="2-shi-kong-yu-jie-kou">2. 时空与“接口“</h3> <p>把时空理解为“认知的接口“，是一个现代比喻：我们永远只能通过这个接口读取“外部系统“的数据，接口之外（物自体）只能假设其存在。这与软件中“接口隔离““内部实现不可见“的思想惊人地同构。</p> <h3 id="3-fan-chou-ren-zhi-de-nei-zhi-dsl">3. 范畴 = 认知的“内置 DSL“</h3> <p>因果、实体、必然等范畴，像是人类认知系统内置的“领域语言“：没有它们，经验只是杂乱的数据流。这也提醒我：<strong>工具（语言、框架）不仅描述世界，也在塑造我们能“看见“什么</strong>——正如范畴塑造经验。</p> <h3 id="4-dui-ke-xue-bian-jie-de-qing-xing">4. 对科学边界的清醒</h3> <p>康德既为科学辩护（先天综合判断使牛顿力学成为可能），又为科学划界（物自体不可知）。这种“既肯定又限制“的平衡，在今天（AI 与科学的边界、数学公理系统的哥德尔界限）依然有回响。</p> <h3 id="5-yue-du-nan-du-yu-ce-lue">5. 阅读难度与策略</h3> <p>《纯粹理性批判》公认难读：术语密集、论证层层嵌套。我的策略是：</p> <ol> <li>先读导论与感性论（约前 80 页）建立框架；</li> <li>用“表格化“整理十二范畴与判断表；</li> <li>配合二手导读（如邓晓芒《康德&lt;纯粹理性批判&gt;句读》）逐段对照；</li> <li>不求一次读通，先抓住“先天综合判断、现象/物自体、范畴、统觉“四个锚点。</li> </ol> <hr /> <h2 id="qi-zhi-de-hui-wei-de-ju-zi">七、值得回味的句子</h2> <blockquote> <p>哥白尼式的革命：不是知识依照对象，而是对象依照知识。</p> <p>思维无内容则空，直观无概念则盲。</p> <p>我不得不限制知识，以便为信仰留出地盘。</p> </blockquote> <hr /> <h2 id="ba-yan-shen-yue-du">八、延伸阅读</h2> <ul> <li>邓晓芒《康德哲学讲演录》；</li> <li>韩水法译《实践理性批判》；</li> <li>叔本华《作为意志和表象的世界》（康德批判哲学的继承与反叛）；</li> <li>波普尔《客观知识》（康德的“人为自然立法“在科学哲学中的回声）。</li> </ul> <blockquote> <p>上一篇：<a href="https://suchaharcan.github.io/01Write_blog_ReadingNotes/readingnotes-schopenhauer-world/">《作为意志和表象的世界》读后感</a></p> </blockquote> 2026-08-11T00:00:00+00:00 2026-08-11T00:00:00+00:00 Suchaharcan https://suchaharcan.github.io/01Write_blog_ReadingNotes/readingnotes-schopenhauer-world/ <h1 id="zuo-wei-yi-zhi-he-biao-xiang-de-shi-jie-du-hou-gan">《作为意志和表象的世界》读后感</h1> <blockquote> <p>叔本华（Arthur Schopenhauer）1818 年出版《作为意志和表象的世界》。本次精读第一、二篇（世界作为表象 / 世界作为意志），兼及第三篇的审美思想。</p> </blockquote> <hr /> <h2 id="yi-zuo-zhe-yu-xie-zuo-bei-jing">一、作者与写作背景</h2> <p>叔本华在 30 岁前完成此书，自视极高，却长期无人问津；直到晚年（《附录与补遗》）才获得声誉。他承康德之余绪，却把康德“物自体“推演为<strong>意志</strong>，由此建立了一套以“痛苦与解脱“为核心的哲学。</p> <hr /> <h2 id="er-di-yi-pian-shi-jie-zuo-wei-biao-xiang">二、第一篇：世界作为表象</h2> <h3 id="1-biao-xiang-de-shi-jie">1. 表象的世界</h3> <p>叔本华开篇即断言：</p> <blockquote> <p>“世界是我的表象。”</p> </blockquote> <p>我所能经验到的一切，都是<strong>我的表象</strong>——颜色、声音、时间、空间，都离不开认识主体而独立存在。这继承了康德的“现象/物自体“之分：我们能认识的只是显现给我们的现象。</p> <h3 id="2-chong-zu-li-you-lu">2. 充足理由律</h3> <p>表象世界受<strong>充足理由律</strong>支配：</p> <pre class="giallo z-code"><code data-lang="plain"><span class="giallo-l"><span>生成的理由（因果律）：万物皆有其因</span></span> <span class="giallo-l"><span>认识的理由：判断须有依据</span></span> <span class="giallo-l"><span>存在的理由：时间与空间中的位置关系</span></span> <span class="giallo-l"><span>行为的理由（动机律）：人的行动有其动机</span></span></code></pre> <p>充足理由律是现象世界的“形式骨架“，但它只在表象领域有效。</p> <h3 id="3-zhi-guan-xian-yu-gai-nian">3. 直观先于概念</h3> <p>叔本华特别强调**直观（Anschauung）**先于概念：概念是直观的抽象，是“表象的表象“。真正的认识从直观开始，科学是对直观关系的整理。这一立场使他与黑格尔式的抽象思辨划清界限，也预示了后来的现象学思路。</p> <hr /> <h2 id="san-di-er-pian-shi-jie-zuo-wei-yi-zhi">三、第二篇：世界作为意志</h2> <h3 id="1-cong-biao-xiang-shen-ru-dao-yi-zhi">1. 从表象深入到意志</h3> <p>表象背后是什么？叔本华认为：<strong>世界的内核是意志（Wille）</strong>——一种无意识、无目的的欲求与冲动。现象世界的“物自体“就是意志。</p> <h3 id="2-shen-ti-shi-yi-zhi-de-ke-jian-xing">2. 身体是意志的可见性</h3> <p>身体是理解意志的钥匙：</p> <ul> <li>我的身体同时是<strong>表象</strong>（对象）与<strong>意志</strong>（内在体验）；</li> <li>牙齿的“咬合欲“、胃的“消化欲“、性欲——器官本身就是客体化的意志；</li> <li>饥饿、疼痛、欲望，都是意志的直接显现。</li> </ul> <p>由此，<strong>一切现象都是意志的客体化</strong>：从低级无机物到高级动物，层层上升，直到人。</p> <h3 id="3-yi-zhi-de-te-zheng">3. 意志的特征</h3> <table><thead><tr><th>特征</th><th>说明</th></tr></thead><tbody> <tr><td>无目的</td><td>意志没有终极目标，欲求永不停息</td></tr> <tr><td>盲目</td><td>不服从理性，理性只是它的工具</td></tr> <tr><td>不可满足</td><td>满足一个欲望，立刻生出新的欲望</td></tr> </tbody></table> <h3 id="4-tong-ku-yu-wu-liao">4. 痛苦与无聊</h3> <p>由此推出叔本华著名的<strong>钟摆论</strong>：</p> <blockquote> <p>人生就是欲望与满足之间的钟摆：欲望不得满足则痛苦，得到满足则无聊。</p> </blockquote> <hr /> <h2 id="si-di-san-pian-yan-shen-shen-mei-zuo-wei-jie-tuo">四、第三篇（延伸）：审美作为解脱</h2> <p>审美是暂时的解脱：当主体沉浸于直观，忘记欲望，对象脱离功利关系时，主体与客体都“上升“为纯粹的理念。音乐尤其如此——它不是表象的摹本，而是意志本身的直接写照。</p> <hr /> <h2 id="wu-yue-du-ti-hui">五、阅读体会</h2> <h3 id="1-yu-kang-de-de-guan-xi">1. 与康德的关系</h3> <p>叔本华把康德“物自体不可知“的谨慎立场，替换为“物自体就是意志“的大胆断言。这种替换使形而上学重新可能，但也把康德批判哲学留下的“知识边界“再次跨越了。读此书最好先读过康德《纯粹理性批判》的先验感性论与分析论，否则“表象/物自体“这对概念会缺少锚点。</p> <h3 id="2-dui-xian-dai-ren-de-hong-dong">2. 对现代人的触动</h3> <p>在消费主义与效率至上的今天，“意志永不满足“几乎可以翻译为：<strong>欲望是生产与消费的动力系统</strong>。广告、算法推荐都在制造新的欲求；而叔本华提醒我们，满足之后是空虚。这不是要人禁欲，而是让人看清欲望的结构，从而获得一点抽离。</p> <h3 id="3-bei-guan-zhu-yi-de-ji-ji-mian">3. 悲观主义的积极面</h3> <p>叔本华的悲观不是消沉，而是<strong>清醒</strong>：把人生的底色看清楚，反而能减少不切实际的期待。正如他说的，期望是痛苦的来源之一；降低对“外部世界必然回报“的预期，是一种心理上的减震。</p> <h3 id="4-dui-ji-shu-gong-zuo-de-qi-fa">4. 对技术工作的启发</h3> <p>作为程序员，我常把“意志的客体化“读成<strong>系统的演化逻辑</strong>：商业系统的目标是增长（无目的的意志），个体在其中只是功能单元（客体化的器官）。理解这一点，有助于在工程决策中区分“系统自身的欲求“与“真实的需求“，避免被卷进盲目迭代。</p> <hr /> <h2 id="liu-zhi-de-hui-wei-de-ju-zi">六、值得回味的句子</h2> <blockquote> <p>世界是我的表象。——这不是说世界是幻觉，而是说我们对世界的认识离不开认识的形式。</p> <p>生命意志的本质就是挣扎。</p> <p>一切满足都只是暂时的，新的欲求立刻接踵而至。</p> </blockquote> <hr /> <h2 id="qi-yan-shen-yue-du">七、延伸阅读</h2> <ul> <li>康德《纯粹理性批判》（先验感性论、分析论）；</li> <li>尼采《悲剧的诞生》（意志哲学的反转：肯定生命）；</li> <li>张汝伦《现代西方哲学十五讲》（叔本华章）；</li> <li>叔本华《附录与补遗》（更易读的通俗篇）。</li> </ul> <blockquote> <p>下一篇：<a href="https://suchaharcan.github.io/01Write_blog_ReadingNotes/readingnotes-kant-critique/">《纯粹理性批判》读后感</a></p> 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