refactor(categories-service): optimize path building in findFlattened method

backend/src/categories/categories.service.ts

@@ -39,12 +39,31 @@ export class CategoriesService {
 
   async findFlattened(): Promise<FlatCategory[]> {
     const all = await this.prisma.category.findMany({ orderBy: { name: 'asc' } });
-    const nameMap = new Map<number, string>();
-    all.forEach((c) => nameMap.set(c.id, c.name));
+
+    const byId = new Map<number, { id: number; name: string; parentId: number | null }>();
+    all.forEach((c) => byId.set(c.id, c));
+
+    const pathCache = new Map<number, string>();
+
+    const buildPath = (id: number): string => {
+      const cached = pathCache.get(id);
+      if (cached) return cached;
+
+      const current = byId.get(id);
+      if (!current) return '';
+
+      const path = current.parentId == null
+        ? current.name
+        : `${buildPath(current.parentId)} > ${current.name}`;
+
+      pathCache.set(id, path);
+      return path;
+    };
+
     return all.map((c) => ({
       id: c.id,
       name: c.name,
-      path: c.parentId ? `${nameMap.get(c.parentId) ?? ''} > ${c.name}` : c.name,
+      path: buildPath(c.id),
     }));
   }
 }