feat(cli): add backlink badge generation for guides

apps/cli/sync.ts

@@ -21,11 +21,13 @@
  * - Every tag a page carries that no campaign topic teaches (not a key of
  *   `apps/docs/topic-landings.ts`) gets a placeholder guide page,
  *   `guides/<slug>.mdx`, with `list:` pointing at LeetCode's problem list for
- *   the tag. Created once (a missing or empty file), then hand-owned; the tag's
- *   badge on a problem page links to it. A guide may be filed into a category
- *   `(group)` folder (e.g. `guides/(2-algorithms)/`) — no route segment, so
+ *   the tag. Created once (a missing or empty file), then hand-owned except
+ *   for `sidebar.badge`, which sync keeps at the guide's backlink count (the
+ *   problem pages carrying the tag; dropped at zero); the tag's badge on a
+ *   problem page links to it. A guide may be filed into a category `(group)`
+ *   folder (e.g. `guides/(2-algorithms)/`) — no route segment, so
  *   `/guides/<slug>` holds — and is found there by slug; a new placeholder
- *   lands at the `guides/` root for a human to file.
+ *   lands at the `guides/` root for a human to file (and give an `icon:`).
  *
  * The sidebar group is the campaign TOPIC from the README table (`tree-dfs/`,
  * ordered by topic number via a script-owned `meta.ts`). A problem outside the
@@ -418,6 +420,27 @@ function guidePage(tag: TopicTag): string {
 /** Folder meta for `guides/`: its own header tab (`navigation.tabs` in blume.config.ts), so only the label. */
 const GUIDES_META = `import { defineMeta } from "blume";\n\nexport default defineMeta({ title: "Guides" });\n`;
 
+/**
+ * A guide's frontmatter with `sidebar.badge` set to its backlink count — the
+ * one key sync owns on a hand-owned guide — or dropped (with a `sidebar:` left
+ * empty) at zero, so the sidebar shows a count only where there is something
+ * to count.
+ */
+function withBacklinkBadge(page: string, count: number): string {
+  const fm = page.match(/^---\n[\s\S]*?\n---/);
+  if (!fm) return page;
+  let head = fm[0].replace(/^ {2}badge: .*\n/m, "");
+  if (count > 0) {
+    const line = `  badge: '${count}'`;
+    head = /^sidebar:$/m.test(head)
+      ? head.replace(/^sidebar:$/m, `sidebar:\n${line}`)
+      : head.replace(/\n---$/, `\nsidebar:\n${line}\n---`);
+  } else {
+    head = head.replace(/^sidebar:\n(?! {2})/m, "");
+  }
+  return head + page.slice(fm[0].length);
+}
+
 // ── inline-code formatting heuristics ────────────────────────────
 
 /** Identifiers worth backticking in prose, harvested from the code. */
@@ -662,6 +685,7 @@ const phases = new Map<string, Phase>(); // phase folder -> phase, for meta.ts
 const vacated = new Set<string>(); // folders a page moved out of; removed below if empty
 const redirects: string[] = []; // `{ from: "/<num>", to: "/<topic>/<slug>" }` rows, numeric order
 const tags = new Map<string, TopicTag>(); // every tag slug any problem page carries -> tag
+const tagged = new Map<string, number>(); // tag slug -> how many problem pages carry it
 
 for (const sol of ordered) {
   const langs = Object.keys(sol.code).sort().join("+");
@@ -677,6 +701,7 @@ for (const sol of ordered) {
   const existing = pages.get(sol.num);
   await mkdir(join(DOCS, dir), { recursive: true });
 
+  let written: string; // the page as it stands after this run, for its topics
   if (existing) {
     const page = await Bun.file(join(DOCS, existing)).text();
     const at = page.indexOf("## Solution");
@@ -698,12 +723,16 @@ for (const sol of ordered) {
       actions.push("updated");
     }
     report.push([workRef, name, actions.join(" + ") || "skipped (in sync)"]);
-    for (const tag of frontmatterTopics(next)) tags.set(tag.slug, tag);
+    written = next;
   } else {
     const page = renderPage(sol, await fetchTopicTags(sol));
     await Bun.write(join(DOCS, name), page);
     report.push([workRef, name, "created"]);
-    for (const tag of frontmatterTopics(page)) tags.set(tag.slug, tag);
+    written = page;
+  }
+  for (const tag of frontmatterTopics(written)) {
+    tags.set(tag.slug, tag);
+    tagged.set(tag.slug, (tagged.get(tag.slug) ?? 0) + 1);
   }
   // The route drops the phase `(group)` and the page's number prefix.
   redirects.push(`  { from: "/${sol.num}", to: ${JSON.stringify(`/${slugify(topic.name)}/${sol.slug}`)} },`);
@@ -743,6 +772,26 @@ for (const tag of guideTags) {
   report.push([`tag ${tag.slug}`, rel, "created"]);
 }
 
+// Every guide's sidebar badge is its backlink count: the problem pages whose
+// tag badge links to it, which is every page carrying the tag, since a guide's
+// tag has no landing (`tagTarget()`). A guide whose tag a landing has since
+// claimed has no backlinks left. Counts move with every solved problem, so the
+// badge is rewritten whenever it differs; the rest of the guide is untouched.
+// The same pass warns when a guide's hand-picked `icon:` is one a topic group
+// owns (`TOPIC_ICONS`), so a guide row never reads as a topic row.
+const topicIcons = new Set(Object.values(TOPIC_ICONS));
+for await (const rel of new Bun.Glob("guides/**/*.mdx").scan(DOCS)) {
+  const slug = basename(rel, ".mdx");
+  const count = TOPIC_LANDINGS[slug] ? 0 : (tagged.get(slug) ?? 0);
+  const page = await Bun.file(join(DOCS, rel)).text();
+  const icon = page.match(/^---\n[\s\S]*?\n---/)?.[0].match(/^icon: (\S+)$/m)?.[1];
+  if (icon && topicIcons.has(icon)) console.warn(`${rel}: icon ${JSON.stringify(icon)} is a topic's (TOPIC_ICONS); pick another`);
+  const next = withBacklinkBadge(page, count);
+  if (next === page) continue;
+  await Bun.write(join(DOCS, rel), next);
+  report.push([`${count} backlinks`, rel, "badged"]);
+}
+
 // Phase metas: created when missing (an empty file counts as missing), never
 // rewritten, so a renamed phase title survives every sync.
 for (const [dir, phase] of phases) {