feat(cli): add sidebar icons mapping for topics

apps/cli/sync.ts

@@ -181,6 +181,45 @@ const TOPIC_ALIASES: Record<string, string> = {
   "Hash-Based Lookup": "Hash Table",
 };
 
+/**
+ * Sidebar icon per group, keyed by the (post-alias) topic name — the same key an
+ * unplanned problem's category group uses, so `Stack` the category and `Stack`
+ * the topic share one row. Lucide names; Blume resolves them at build time and
+ * reports a diagnostic for a typo, but an unmapped group is caught here first.
+ */
+const TOPIC_ICONS: Record<string, string> = {
+  // README topics, in curriculum order
+  "Hash Table": "hash",
+  "Prefix Sum": "sigma",
+  "Two Pointers": "arrow-left-right",
+  "Sliding Window": "app-window",
+  "Binary Search": "search",
+  Stack: "layers",
+  "Monotonic Stack": "trending-up",
+  "Linked List": "link",
+  "Hybrid Structures": "combine",
+  "Matrix Index Math": "grid-3x3",
+  "Tree DFS": "folder-tree",
+  "Tree BFS": "network",
+  "Binary Search Tree": "git-fork",
+  "Heap / Priority Queue": "triangle",
+  Trie: "spell-check",
+  "Graph DFS": "waypoints",
+  "Graph BFS": "radar",
+  "Topological Sort": "workflow",
+  "Union-Find": "merge",
+  Backtracking: "undo-2",
+  "1-D Dynamic Programming": "columns-3",
+  "Multi-D / Grid DP": "table",
+  Greedy: "coins",
+  Intervals: "calendar-range",
+  // work/1 categories that can surface as an unplanned group
+  Array: "brackets",
+  String: "type",
+  Tree: "network",
+  "Depth-First Search": "folder-tree",
+};
+
 /** LC number -> topic. A problem listed under two topics keeps the first. */
 async function readmeTopics(): Promise<Map<number, Topic>> {
   const md = await Bun.file(join(ROOT, "README.md")).text();
@@ -197,12 +236,17 @@ async function readmeTopics(): Promise<Map<number, Topic>> {
 }
 
 /**
- * Blume folder meta: exact topic label (the folder slug loses `/` and case) and
+ * Blume folder meta: exact topic label (the folder slug loses `/` and case),
- * curriculum order. An unplanned category group (warm-ups) has no README
+ * curriculum order, and the group's sidebar icon. An unplanned category group
- * number and sorts at 0, ahead of topic 1, so the sidebar opens on the basics.
+ * (warm-ups) has no README number and sorts at 0, ahead of topic 1, so the
+ * sidebar opens on the basics.
  */
 function groupMeta(topic: Topic): string {
-  return `import { defineMeta } from "blume";\n\nexport default defineMeta({ title: ${JSON.stringify(topic.name)}, order: ${topic.order ?? 0} });\n`;
+  const icon = TOPIC_ICONS[topic.name];
+  if (!icon) console.warn(`no icon for group ${JSON.stringify(topic.name)}: add it to TOPIC_ICONS`);
+  const fields = [`title: ${JSON.stringify(topic.name)}`, `order: ${topic.order ?? 0}`];
+  if (icon) fields.push(`icon: ${JSON.stringify(icon)}`);
+  return `import { defineMeta } from "blume";\n\nexport default defineMeta({ ${fields.join(", ")} });\n`;
 }
 
 // ── inline-code formatting heuristics ────────────────────────────