docs(docs): add ProblemBadges component, layout slot, and enrich pages with topics/video frontmatter, plus guide placeholders and topic‑landing map.

apps/docs/topic-landings.ts

@@ -0,0 +1,35 @@
+/**
+ * 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:
+ *
+ * - `components/ProblemBadges.astro` links a covered tag's badge to its
+ *   landing page, and every other tag's badge to `/guides/<slug>`;
+ * - `apps/cli/sync.ts` creates a placeholder `content/guides/<slug>.mdx` for
+ *   every tag a problem page carries that is NOT a key here.
+ *
+ * Add a key when a campaign topic starts teaching a tag; its guide page is then
+ * dead weight, delete it by hand. A tag naming two topics (DFS/BFS: tree and
+ * graph; DP: 1-D and grid) lists both; the badge picks per page.
+ */
+export const TOPIC_LANDINGS: Record<string, readonly string[]> = {
+  "hash-table": ["/hash-table"],
+  "prefix-sum": ["/prefix-sum"],
+  "two-pointers": ["/two-pointers"],
+  "sliding-window": ["/sliding-window"],
+  "binary-search": ["/binary-search"],
+  stack: ["/stack"],
+  "monotonic-stack": ["/monotonic-stack"],
+  "linked-list": ["/linked-list"],
+  matrix: ["/matrix-index-math"],
+  "depth-first-search": ["/tree-dfs", "/graph-dfs"],
+  "breadth-first-search": ["/tree-bfs", "/graph-bfs"],
+  "binary-search-tree": ["/binary-search-tree"],
+  "heap-priority-queue": ["/heap-priority-queue"],
+  trie: ["/trie"],
+  "topological-sort": ["/topological-sort"],
+  "union-find": ["/union-find"],
+  backtracking: ["/backtracking"],
+  "dynamic-programming": ["/1d-dynamic-programming", "/multi-d-grid-dp"],
+  greedy: ["/greedy"],
+};