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

apps/docs/content/(04-relational)/graph-dfs/200-number-of-islands.mdx

@@ -2,13 +2,17 @@
 title: '200. Number of Islands'
 description: Given an m x n 2D binary grid grid which represents a map of '1's (land) and '0's (water), return the number of islands
 icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Depth-First Search", slug: "depth-first-search" }
+  - { name: "Breadth-First Search", slug: "breadth-first-search" }
+  - { name: "Union-Find", slug: "union-find" }
+  - { name: "Matrix", slug: "matrix" }
 sidebar:
   label: 'Number of Islands'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Array</Badge>
-
 ### Example 1:
 - Input: `grid = [ ["1","1","1","1","0"], ["1","1","0","1","0"], ["1","1","0","0","0"], ["0","0","0","0","0"] ]`
 - Output: `1`