docs(docs): add BacklinksList component and shared tagTarget logic for badge routing, update docs pages

apps/docs/topic-landings.ts

@@ -1,10 +1,12 @@
 /**
  * LeetCode topic-tag slug → the campaign landing routes that teach it, in
  * default preference order. The one answer to "does the campaign cover this
- * tag", read by two sides that must agree:
+ * tag", read by the sides that must agree:
  *
  * - `components/ProblemBadges.astro` links a covered tag's badge to its
  *   landing page, and every other tag's badge to `/guides/<slug>`;
+ * - `components/BacklinksList.astro` lists, under a landing or guide page,
+ *   every problem whose badge links there — both via `tagTarget()`;
  * - `apps/cli/sync.ts` creates a placeholder `content/guides/<slug>.mdx` for
  *   every tag a problem page carries that is NOT a key here.
  *
@@ -33,3 +35,33 @@ export const TOPIC_LANDINGS: Record<string, readonly string[]> = {
   "dynamic-programming": ["/1d-dynamic-programming", "/multi-d-grid-dp"],
   greedy: ["/greedy"],
 };
+
+/** One of LeetCode's topic tags, as a problem page's `topics:` frontmatter carries it. */
+export interface TopicTag {
+  name: string;
+  slug: string;
+}
+
+/**
+ * Where a problem page's badge for `tag` points: a root-relative landing or
+ * guide route (the caller adds the base), or LeetCode's problem list when the
+ * site serves neither, so a badge never links to a 404.
+ *
+ * A tag naming two landings links to the page's own topic — its route's first
+ * segment — when that is one of them; otherwise DFS/BFS prefer the tree topic
+ * for a problem LeetCode also tags `Tree` and the graph topic for the rest.
+ */
+export function tagTarget(
+  tag: TopicTag,
+  page: { route: string; tags: readonly TopicTag[] },
+  served: ReadonlySet<string>,
+): { href: string; kind: "landing" | "guide" | "external" } {
+  const landings = (TOPIC_LANDINGS[tag.slug] ?? []).filter((path) => served.has(path));
+  const own = `/${page.route.split("/")[1]}`;
+  const prefer = page.tags.some((t) => t.slug === "tree") ? "/tree-" : "/graph-";
+  const landing = landings.includes(own) ? own : (landings.find((p) => p.startsWith(prefer)) ?? landings[0]);
+  if (landing) return { href: landing, kind: "landing" };
+  const guide = `/guides/${tag.slug}`;
+  if (served.has(guide)) return { href: guide, kind: "guide" };
+  return { href: `https://leetcode.com/problem-list/${tag.slug}/`, kind: "external" };
+}