feat(布置作业): 能布置「画流程图」「先画再写」，看板分清卡在画图还是写代码

布置时多一个「做什么」：写代码 / 先画再写 / 画流程图（只能选打开了画流程图的题）。
- 先画再写：一道题图画到 A/S、代码也交对才算做完；学生画一道写一道、全画完再写都行，
  打开题目自动停在该做的那一步（图没画对停画布，画对了换到布置的语言）
- 也能分开布置：先一节画流程图，看板上「用这几道题写代码」再开一节；学生那边把今天
  几节课的要求合起来，还没画完的照样看得到要画
- 看板格子是一条进度：图 1/6 → 空心「图 ✓」→ 代码 ✗ → ✓，先写代码没画图的写「缺图」；
  卡在画图上的点开讲那张图（要改的框标红 + AI 的哪里错/怎么改），按走对几组归堆
- 写代码的课不再拿画对的流程图顶替做完；数据统计里画流程图的课数流程图提交

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

apps/api/src/routes/admin/lesson.ts

@@ -34,6 +34,7 @@ adminLessonRoutes.get('/lessons', requireTeacher, async (c) => {
         day: schema.classLesson.day,
         problemIds: schema.classLesson.problemIds,
         language: schema.classLesson.language,
+        mode: schema.classLesson.mode,
         createdAt: schema.classLesson.createdAt,
         updatedAt: schema.classLesson.updatedAt,
         createdBy: teacherName,
@@ -85,6 +86,7 @@ adminLessonRoutes.get('/lessons', requireTeacher, async (c) => {
       updatedAt: row.updatedAt,
       createdBy: row.createdBy,
       language: row.language ?? null,
+      mode: row.mode,
       // 题被删掉的（problem_ids 不挂外键）直接不列
       problems: row.problemIds.flatMap((id) => {
         const problem = problemById.get(id)
@@ -98,23 +100,33 @@ adminLessonRoutes.get('/lessons', requireTeacher, async (c) => {
   } satisfies AdminLessonList)
 })
 
-/** 新补一节、改一节共用的校验：班得有人、题号都对得上、语言每道都能交 */
-async function lessonValues(
-  body: AdminLessonRequest,
-): Promise<
+/** 新补一节、改一节共用的校验：班得有人、题号都对得上、语言每道都能交、要画的都打开了画流程图 */
+async function lessonValues(body: AdminLessonRequest): Promise<
   | { code: string; message: string }
-  | { values: { className: string; day: string; problemIds: number[]; language: AdminLessonRequest['language']; createdAt: string } }
+  | {
+      values: {
+        className: string
+        day: string
+        problemIds: number[]
+        language: AdminLessonRequest['language']
+        mode: AdminLessonRequest['mode']
+        createdAt: string
+      }
+    }
 > {
   const [exists] = await db.select({ id: schema.user.id }).from(schema.user).where(eq(schema.user.className, body.className)).limit(1)
   if (!exists) return { code: 'class-not-found', message: `没有 ${body.className} 这个班` }
-  const resolved = await resolveLessonProblems(body.problemDisplayIds, body.language)
+  // 只画流程图不用语言，存成 null（和看板布置一样）
+  const language = body.mode === 'flowchart' ? null : body.language
+  const resolved = await resolveLessonProblems(body.problemDisplayIds, language, body.mode)
   if ('code' in resolved) return resolved
   return {
     values: {
       className: body.className,
       day: body.day,
       problemIds: resolved.problemIds,
-      language: body.language,
+      language,
+      mode: body.mode,
       createdAt: localDateTime(body.day, body.time),
     },
   }