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)/backtracking/39-combination-sum.mdx

@@ -2,13 +2,14 @@
 title: '39. Combination Sum'
 description: Given an array of distinct integers candidates and a target integer target, return a list of all unique combinations of candidates where the chosen numbers sum to target. You may return the combinations in any order
 icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Backtracking", slug: "backtracking" }
 sidebar:
   label: 'Combination Sum'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Array</Badge>
-
 ### Example 1:
 - Input: `candidates = [2,3,6,7], target = 7`
 - Output: `[[2,2,3],[7]]`

apps/docs/content/(05-decision-space)/backtracking/46-permutations.mdx

@@ -2,13 +2,14 @@
 title: '46. Permutations'
 description: Given an array nums of distinct integers, return all the possible permutations. You can return the answer in any order
 icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Backtracking", slug: "backtracking" }
 sidebar:
   label: 'Permutations'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Array</Badge>
-
 ### Example 1:
 - Input: `nums = [1,2,3]`
 - Output: `[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]`

apps/docs/content/(05-decision-space)/backtracking/78-subsets.mdx

@@ -2,13 +2,15 @@
 title: '78. Subsets'
 description: Given an integer array nums of unique elements, return all possible subsets (the power set)
 icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Backtracking", slug: "backtracking" }
+  - { name: "Bit Manipulation", slug: "bit-manipulation" }
 sidebar:
   label: 'Subsets'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Array</Badge>
-
 ### Example 1:
 - Input: `nums = [1,2,3]`
 - Output: `[[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]]`