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)/union-find/323-number-of-connected-components-in-an-undirected-graph.mdx

@@ -2,13 +2,16 @@
 title: '323. Number of Connected Components in an Undirected Graph'
 description: You have a graph of n nodes. You are given an integer n and an array edges where edges[i] = [ai, bi] indicates that there is an edge between ai and bi in the graph
 icon: dot
+topics:
+  - { name: "Depth-First Search", slug: "depth-first-search" }
+  - { name: "Breadth-First Search", slug: "breadth-first-search" }
+  - { name: "Union-Find", slug: "union-find" }
+  - { name: "Graph Theory", slug: "graph" }
 sidebar:
   label: 'Number of Connected Components in an Undirected Graph'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Depth-First Search</Badge>
-
 ### Example 1:
 - Input: `n = 5, edges = [[0,1],[1,2],[3,4]]`
 - Output: `2`

apps/docs/content/(04-relational)/union-find/684-redundant-connection.mdx

@@ -2,13 +2,16 @@
 title: '684. Redundant Connection'
 description: In this problem, a tree is an undirected graph that is connected and has no cycles
 icon: dot
+topics:
+  - { name: "Depth-First Search", slug: "depth-first-search" }
+  - { name: "Breadth-First Search", slug: "breadth-first-search" }
+  - { name: "Union-Find", slug: "union-find" }
+  - { name: "Graph Theory", slug: "graph" }
 sidebar:
   label: 'Redundant Connection'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Depth-First Search</Badge>
-
 ### Example 1:
 - Input: `edges = [[1,2],[1,3],[2,3]]`
 - Output: `[2,3]`