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

apps/docs/content/(05-decision-space)/1d-dynamic-programming/322-coin-change.mdx

@@ -2,13 +2,17 @@
 title: '322. Coin Change'
 description: You are given an integer array coins representing coins of different denominations and an integer amount representing a total amount of money
 icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Dynamic Programming", slug: "dynamic-programming" }
+  - { name: "Breadth-First Search", slug: "breadth-first-search" }
+  - { name: "Knapsack Problem", slug: "knapsack-problem" }
+  - { name: "Complete Knapsack", slug: "complete-knapsack" }
 sidebar:
   label: 'Coin Change'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Array</Badge>
-
 ### Example 1:
 - Input: `coins = [1,2,5], amount = 11`
 - Output: `3`