feat(激励): 知识点地图——每个知识点做对几道、在哪一档、再做几道升级，首页一句话提示本周进步

现有 38 个成就全是累计量（通过几题、提交几次、连续几天），起步的人人都有、往上的够不着，
而且没有一个在说「你学会了什么」。连续打卡在这里结构上做不到：2025 秋学生最长连续交题
天数的中位数是 1 天，连续 7 天的只有 3 人。

- GET /me/knowledge：题数 ≥10 的知识点标签（10 个），每个给做对几道、档位、周一时的档位、
  下一档门槛；四档 入门 1 / 会了 3 / 熟练 题数 40%（≤10）/ 精通 75%（≤20）。
  回测 2025 秋：中位数学生一学期升 5 档；「入门」一档是给只做对一两道的 71 人加的
- 同班 ≥30% 点亮过的知识点才会出现在「还没碰过」里，免得 Python 班看到「C 语言」
- 个人主页加「我的知识点」，只在看自己时显示；首页一句话：本周升级 > 离下一档最近的 >
  去点亮一个班里在学的，点了去按知识点筛的题目列表

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

apps/api/src/routes/account.ts

@@ -6,6 +6,8 @@ import {
   STUDENT_ROLES,
   updateProfileRequestSchema,
   type ActivityRankItem,
+  type KnowledgeLevel,
+  type KnowledgeMap,
   type Metrics,
   type MyRank,
   type ProblemRank,
@@ -499,6 +501,159 @@ accountRoutes.get("/rankings/weekly", optionalAuth, async (c) => {
   } satisfies WeeklyRank)
 })
 
+/** 题数少于这个的知识点不参与升级：3 道题的知识点做完就「精通」，没有意义 */
+const KNOWLEDGE_MIN_PROBLEMS = 10
+/** 同班这么多比例的人点亮过，才算「班里在学」，才会出现在「还没碰过」里 */
+const KNOWLEDGE_CLASS_TOUCHED_RATIO = 0.3
+
+/**
+ * 四档门槛：入门 1 道、会了 3 道、熟练 = 题数的 40%（最多 10）、精通 = 75%（最多 20）。
+ * 按题量缩放是因为知识点之间差得很远（循环结构 107 道、数组 15 道）。
+ *
+ * 拿 2025 秋回测过：中位数的学生一学期升 5 档，前 25% 升 9 档；加上「入门」这一档之前，
+ * 26% 的学生一档都没升，其中一半做对过带标签的题、只是没到 3 道。
+ */
+function levelThresholds(problemCount: number) {
+  return [
+    1,
+    3,
+    Math.max(4, Math.min(10, Math.round(problemCount * 0.4))),
+    Math.max(5, Math.min(20, Math.round(problemCount * 0.75))),
+  ]
+}
+
+function levelOf(solved: number, thresholds: number[]) {
+  return thresholds.filter((threshold) => solved >= threshold).length
+}
+
+/**
+ * 我的知识点地图。「做对」按题目算（同一题只算一次），不含比赛提交，
+ * 题目只算公开的题库题 —— 和 problemCount 同一个口径，不然会出现 12/10。
+ */
+accountRoutes.get("/me/knowledge", requireAuth, async (c) => {
+  const user = c.get("user")!
+  const tags = await db
+    .select({
+      id: schema.problemTag.id,
+      name: schema.problemTag.name,
+      problemCount: count(),
+    })
+    .from(schema.problemTag)
+    .innerJoin(schema.problemTags, eq(schema.problemTags.problemtagId, schema.problemTag.id))
+    .innerJoin(schema.problem, eq(schema.problem.id, schema.problemTags.problemId))
+    .where(
+      and(
+        eq(schema.problemTag.category, "knowledge"),
+        eq(schema.problem.visible, true),
+        isNull(schema.problem.contestId),
+      ),
+    )
+    .groupBy(schema.problemTag.id, schema.problemTag.name)
+    .having(sql`count(*) >= ${KNOWLEDGE_MIN_PROBLEMS}`)
+  const tagIds = tags.map((tag) => tag.id)
+  if (!tagIds.length) return success(c, { tags: [], classTouched: [] } satisfies KnowledgeMap)
+
+  const firstAccepted = db
+    .select({
+      problemId: schema.submission.problemId,
+      firstAt: min(schema.submission.createTime).as("first_at"),
+    })
+    .from(schema.submission)
+    .where(
+      and(
+        eq(schema.submission.userId, user.id),
+        isNull(schema.submission.contestId),
+        inArray(schema.submission.result, ACCEPTED_RESULTS),
+      ),
+    )
+    .groupBy(schema.submission.problemId)
+    .as("first_accepted")
+
+  const start = weekStart()
+  const [mine, classTouchedRows, classSize] = await Promise.all([
+    db
+      .select({
+        tagId: schema.problemTags.problemtagId,
+        solved: count(),
+        solvedBeforeWeek: sql<number>`count(*) filter (where ${firstAccepted.firstAt} < ${start})::int`,
+      })
+      .from(firstAccepted)
+      .innerJoin(schema.problemTags, eq(schema.problemTags.problemId, firstAccepted.problemId))
+      .innerJoin(schema.problem, eq(schema.problem.id, firstAccepted.problemId))
+      .where(
+        and(
+          inArray(schema.problemTags.problemtagId, tagIds),
+          eq(schema.problem.visible, true),
+          isNull(schema.problem.contestId),
+        ),
+      )
+      .groupBy(schema.problemTags.problemtagId),
+    user.className
+      ? db
+          .select({
+            tagId: schema.problemTags.problemtagId,
+            users: countDistinct(schema.submission.userId),
+          })
+          .from(schema.submission)
+          .innerJoin(schema.user, eq(schema.user.id, schema.submission.userId))
+          .innerJoin(
+            schema.problemTags,
+            eq(schema.problemTags.problemId, schema.submission.problemId),
+          )
+          .where(
+            and(
+              eq(schema.user.className, user.className),
+              eq(schema.user.isDisabled, false),
+              inArray(schema.user.adminType, [...STUDENT_ROLES]),
+              isNull(schema.submission.contestId),
+              inArray(schema.submission.result, ACCEPTED_RESULTS),
+              inArray(schema.problemTags.problemtagId, tagIds),
+            ),
+          )
+          .groupBy(schema.problemTags.problemtagId)
+      : [],
+    user.className
+      ? db
+          .select({ total: count() })
+          .from(schema.user)
+          .where(
+            and(
+              eq(schema.user.className, user.className),
+              eq(schema.user.isDisabled, false),
+              inArray(schema.user.adminType, [...STUDENT_ROLES]),
+            ),
+          )
+      : [],
+  ])
+
+  const mineByTag = new Map(mine.map((row) => [row.tagId, row]))
+  const total = classSize[0]?.total ?? 0
+  const touchedIds = new Set(
+    classTouchedRows
+      .filter((row) => total > 0 && row.users / total >= KNOWLEDGE_CLASS_TOUCHED_RATIO)
+      .map((row) => row.tagId),
+  )
+
+  return success(c, {
+    tags: tags
+      .sort((a, b) => b.problemCount - a.problemCount)
+      .map((tag) => {
+        const thresholds = levelThresholds(tag.problemCount)
+        const solved = mineByTag.get(tag.id)?.solved ?? 0
+        const level = levelOf(solved, thresholds)
+        return {
+          name: tag.name,
+          problemCount: tag.problemCount,
+          solved,
+          level,
+          levelAtWeekStart: levelOf(mineByTag.get(tag.id)?.solvedBeforeWeek ?? 0, thresholds),
+          nextAt: thresholds[level] ?? null,
+        } satisfies KnowledgeLevel
+      }),
+    classTouched: tags.filter((tag) => touchedIds.has(tag.id)).map((tag) => tag.name),
+  } satisfies KnowledgeMap)
+})
+
 accountRoutes.get("/problems/:displayId/rank", requireAuth, async (c) => {
   const user = c.get("user")!
   const [problem] = await db

apps/web/src/oj/api.ts

@@ -10,6 +10,7 @@ import {
   type TutorialSummary,
   type ClassActivity,
   type ClassBoard,
+  type KnowledgeMap,
   type ClassComparisonResponse,
   type ClassRankItem,
   type ClassUserRank,
@@ -228,6 +229,11 @@ export function setClassLesson(className: string, problemDisplayIds: string[]) {
   return api.put<null>("classroom/lesson", { className, problemDisplayIds })
 }
 
+/** 我的知识点地图（只有自己的，不能查别人） */
+export function getKnowledgeMap() {
+  return api.get<KnowledgeMap>("me/knowledge")
+}
+
 export function getClassActivity() {
   return api.get<ClassActivity>("me/class-activity")
 }

apps/web/src/oj/home/dashboard.vue

@@ -4,6 +4,7 @@ import {
   getAnnouncement,
   getAnnouncementList,
   getClassActivity,
+  getKnowledgeMap,
   getContestList,
   getLearnProgress,
   getSubmissions,
@@ -13,6 +14,7 @@ import {
 import SubmissionResultTag from "shared/components/SubmissionResultTag.vue"
 import { useBreakpoints } from "shared/composables/breakpoints"
 import { useProblemJump } from "shared/composables/problemJump"
+import { pickHeadline, type Headline } from "oj/user/knowledge"
 import { useUserStore } from "shared/store/user"
 import { ContestStatus, CONTEST_STATUS } from "utils/constants"
 import { duration, parseTime, zonedParts } from "utils/functions"
@@ -49,6 +51,8 @@ const submissions = ref<SubmissionListItem[]>([])
 const announcements = ref<AnnouncementListItem[]>([])
 const weekly = ref<WeeklyRank | null>(null)
 const classActivity = ref<ClassActivity | null>(null)
+/** 知识点地图挑出来的那一句（本周升级 / 再做几道升档 / 去点亮一个），见 oj/user/knowledge.ts */
+const knowledgeHeadline = ref<Headline | null>(null)
 const loaded = ref(false)
 const keyword = ref("")
 
@@ -121,6 +125,10 @@ async function loadAnnouncements() {
   announcements.value = res.results
 }
 
+async function loadKnowledge() {
+  knowledgeHeadline.value = pickHeadline(await getKnowledgeMap())
+}
+
 async function loadClassActivity() {
   classActivity.value = await getClassActivity()
 }
@@ -160,6 +168,7 @@ async function load() {
     loadAnnouncements(),
     loadWeekly(),
     loadClassActivity(),
+    loadKnowledge(),
   ])
   loaded.value = true
 }
@@ -226,6 +235,13 @@ async function openAnnouncement(item: AnnouncementListItem) {
             <router-link to="/rank" class="plain-link">{{ weeklyText }}</router-link>
           </template>
         </n-text>
+        <div v-if="knowledgeHeadline" class="knowledge-line">
+          <router-link v-if="knowledgeHeadline.to" :to="knowledgeHeadline.to" class="plain-link">
+            {{ knowledgeHeadline.text }}
+          </router-link>
+          <span v-else>{{ knowledgeHeadline.text }}</span>
+          <router-link to="/user" class="more">我的知识点</router-link>
+        </div>
       </div>
       <n-input-group class="search">
         <n-input
@@ -421,6 +437,21 @@ async function openAnnouncement(item: AnnouncementListItem) {
   margin: 0 0 6px;
 }
 
+.knowledge-line {
+  margin-top: 6px;
+  display: flex;
+  gap: 12px;
+  align-items: baseline;
+  color: #18a058;
+}
+
+/* 这一行本身就是链接（去按知识点筛的题目列表），下划线说明它能点 */
+.knowledge-line .plain-link {
+  color: #18a058;
+  text-decoration: underline;
+  text-underline-offset: 3px;
+}
+
 .search {
   width: 320px;
   max-width: 100%;

apps/web/src/oj/user/components/KnowledgeMap.vue

@@ -0,0 +1,135 @@
+<script setup lang="ts">
+import { getKnowledgeMap } from "oj/api"
+import { levelName, MAX_LEVEL, remainingToNext, tagLink } from "oj/user/knowledge"
+import type { KnowledgeLevel, KnowledgeMap } from "utils/types"
+
+/**
+ * 个人主页上的知识点地图：「我学会了什么」，只和自己比。
+ *
+ * 只在看**自己的**主页时挂（index.vue 判断），不开放给别人看 —— 开放了它就成了
+ * 另一张排行榜，基础弱的学生最不想被看到的就是这个。
+ */
+const map = ref<KnowledgeMap | null>(null)
+
+onMounted(async () => {
+  map.value = await getKnowledgeMap().catch(() => null)
+})
+
+const learned = computed(() =>
+  (map.value?.tags ?? [])
+    .filter((tag) => tag.level >= 1)
+    .sort((a, b) => b.level - a.level || b.solved - a.solved),
+)
+
+/** 班里同学在学、自己还没碰过的。别的（比如 Python 班的「C 语言」）不列 */
+const untouched = computed(() => {
+  const touched = new Set(map.value?.classTouched ?? [])
+  return (map.value?.tags ?? []).filter((tag) => tag.level === 0 && touched.has(tag.name))
+})
+
+function progress(tag: KnowledgeLevel) {
+  if (tag.nextAt === null) return 100
+  return Math.min(100, Math.round((tag.solved / tag.nextAt) * 100))
+}
+
+function hint(tag: KnowledgeLevel) {
+  const left = remainingToNext(tag)
+  if (left === null) return `做对了 ${tag.solved} 道，已经精通了`
+  return `做对 ${tag.solved} 道 · 再做 ${left} 道到「${levelName(tag.level + 1)}」`
+}
+</script>
+
+<template>
+  <n-card v-if="map && (learned.length || untouched.length)" class="knowledge" title="我的知识点">
+    <template #header-extra>
+      <n-text depth="3" class="meta">入门 → 会了 → 熟练 → 精通</n-text>
+    </template>
+    <n-flex vertical :size="14">
+      <router-link v-for="tag in learned" :key="tag.name" :to="tagLink(tag.name)" class="row">
+        <div class="head">
+          <span class="name">{{ tag.name }}</span>
+          <span class="dots" :title="levelName(tag.level)">
+            <span v-for="i in MAX_LEVEL" :key="i" class="dot" :class="{ on: i <= tag.level }" />
+          </span>
+          <span class="level">{{ levelName(tag.level) }}</span>
+          <n-tag
+            v-if="tag.level > tag.levelAtWeekStart"
+            size="small"
+            type="success"
+            :bordered="false"
+          >
+            本周升级
+          </n-tag>
+        </div>
+        <n-progress
+          type="line"
+          :percentage="progress(tag)"
+          :show-indicator="false"
+          :height="6"
+          status="success"
+        />
+        <n-text depth="3" class="meta">{{ hint(tag) }}</n-text>
+      </router-link>
+
+      <div v-if="untouched.length">
+        <n-text depth="3" class="meta">班里同学在学、你还没碰过：</n-text>
+        <n-flex :size="8" style="margin-top: 6px">
+          <router-link v-for="tag in untouched" :key="tag.name" :to="tagLink(tag.name)">
+            <n-tag size="small">{{ tag.name }}</n-tag>
+          </router-link>
+        </n-flex>
+      </div>
+    </n-flex>
+  </n-card>
+</template>
+
+<style scoped>
+.knowledge {
+  max-width: 610px;
+  margin: 16px auto 0;
+}
+
+.row {
+  display: flex;
+  flex-direction: column;
+  gap: 4px;
+  color: inherit;
+  text-decoration: none;
+}
+
+.head {
+  display: flex;
+  align-items: center;
+  gap: 8px;
+}
+
+.name {
+  font-weight: 500;
+  min-width: 5em;
+}
+
+.dots {
+  display: inline-flex;
+  gap: 3px;
+}
+
+.dot {
+  width: 8px;
+  height: 8px;
+  border-radius: 50%;
+  background-color: rgba(128, 128, 128, 0.25);
+}
+
+.dot.on {
+  background-color: #18a058;
+}
+
+.level {
+  font-size: 13px;
+  color: #18a058;
+}
+
+.meta {
+  font-size: 12px;
+}
+</style>

apps/web/src/oj/user/index.vue

@@ -1,4 +1,5 @@
 <script setup lang="ts">
+import KnowledgeMap from "./components/KnowledgeMap.vue"
 import { Icon } from "@iconify/vue"
 import { getProfile } from "shared/api"
 import { durationToDays, parseTime } from "utils/functions"
@@ -11,6 +12,15 @@ import { useUserStore } from "shared/store/user"
 const route = useRoute()
 const router = useRouter()
 const userStore = useUserStore()
+
+/**
+ * 在看自己的主页。知识点地图只在这时候挂：它不给别人看（见 KnowledgeMap.vue），
+ * 后端 /me/knowledge 也只认当前登录的人。带 ?name= 看的是别人，除非名字就是自己。
+ */
+const isSelf = computed(() => {
+  const name = route.query.name as string | undefined
+  return !name || name === userStore.user?.username
+})
 const profile = ref<Profile | null>(null)
 const problems = ref<string[]>([])
 const firstSubmissionAt = ref("")
@@ -219,6 +229,7 @@ onMounted(() => {
     </n-flex>
   </n-card>
 
+  <KnowledgeMap v-if="!loading && profile && isSelf" />
   <n-descriptions v-if="!loading && profile" class="wrapper" bordered>
     <n-descriptions-item v-if="!!problems.length">
       <template #label>

apps/web/src/oj/user/knowledge.ts

@@ -0,0 +1,72 @@
+import type { KnowledgeLevel, KnowledgeMap } from "utils/types"
+
+/**
+ * 知识点地图的档位名（后端 routes/account.ts 的 levelThresholds 定门槛）。
+ * 用「会了」「熟练」这种学生听得懂的词，不用「Lv.3」—— 这张图要说的是「我会了什么」，
+ * 不是又一套积分。
+ */
+export const LEVEL_NAMES = ["没碰过", "入门", "会了", "熟练", "精通"] as const
+
+export const MAX_LEVEL = LEVEL_NAMES.length - 1
+
+export function levelName(level: number) {
+  return LEVEL_NAMES[Math.max(0, Math.min(MAX_LEVEL, level))]!
+}
+
+/** 离下一档还差几道；已经最高档为 null */
+export function remainingToNext(tag: KnowledgeLevel) {
+  return tag.nextAt === null ? null : Math.max(1, tag.nextAt - tag.solved)
+}
+
+export function tagLink(name: string) {
+  return { path: "/problem", query: { tag: name } }
+}
+
+export interface Headline {
+  text: string
+  /** 点了去哪：按这个知识点筛的题目列表 */
+  to?: ReturnType<typeof tagLink>
+}
+
+/**
+ * 首页「你好」下面那一行：一次只说一件事，挑最能让人想再做一道的那件。
+ *
+ * 1. 本周升级了 —— 刚发生的进步，最值得说
+ * 2. 正在学的里面，离下一档最近的那个（班里在学的优先）—— 给一个很近的目标
+ * 3. 一个都没点亮：挑一个班里同学在学的，让他去点亮
+ */
+export function pickHeadline(map: KnowledgeMap): Headline | null {
+  const upgraded = map.tags
+    .filter((tag) => tag.level > tag.levelAtWeekStart)
+    .sort((a, b) => b.level - a.level)
+  if (upgraded.length === 1) {
+    const tag = upgraded[0]!
+    return { text: `本周升级：${tag.name} → ${levelName(tag.level)}`, to: tagLink(tag.name) }
+  }
+  if (upgraded.length > 1) {
+    const list = upgraded.map((tag) => `${tag.name}「${levelName(tag.level)}」`).join("、")
+    return { text: `本周升级了 ${upgraded.length} 个知识点：${list}` }
+  }
+
+  const touched = new Set(map.classTouched)
+  const learning = map.tags
+    .filter((tag) => tag.level >= 1 && tag.level < MAX_LEVEL)
+    .sort(
+      (a, b) =>
+        Number(touched.has(b.name)) - Number(touched.has(a.name)) ||
+        remainingToNext(a)! - remainingToNext(b)!,
+    )
+  const next = learning[0]
+  if (next) {
+    return {
+      text: `正在学${next.name}，再做 ${remainingToNext(next)} 道就到「${levelName(next.level + 1)}」`,
+      to: tagLink(next.name),
+    }
+  }
+
+  const fresh = map.tags.find((tag) => tag.level === 0 && touched.has(tag.name))
+  if (fresh) {
+    return { text: `班里同学在学${fresh.name}，去做一道点亮它`, to: tagLink(fresh.name) }
+  }
+  return null
+}

apps/web/src/utils/types.ts

@@ -293,6 +293,9 @@ export type { ClassActivity, ClassActivityProblem } from "@oj2/contract"
 /** 课堂看板：一个班今天这节课的题 × 全班学生 */
 export type { ClassBoard, ClassBoardStudent, ClassBoardCell } from "@oj2/contract"
 
+/** 知识点地图：每个知识点做对几道、在第几档，只给自己看 */
+export type { KnowledgeLevel, KnowledgeMap } from "@oj2/contract"
+
 /**
  * 学生侧的比赛：不含 password / visible。后台用 `AdminContest` ——
  * oj 侧的 contestSchema 永远不含 password，后台要能看到（告诉学生）