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

apps/docs/content/(02-nodal-grid)/matrix-index-math/48-rotate-image.mdx

@@ -2,13 +2,16 @@
 title: '48. Rotate Image'
 description: You are given an n x n 2D matrix representing an image, rotate the image by 90 degrees (clockwise)
 icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Math", slug: "math" }
+  - { name: "Matrix", slug: "matrix" }
+video: "fMSJSS7eO1w"
 sidebar:
   label: 'Rotate Image'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Array</Badge>
-
 ### Example 1:
 - Input: `matrix = [[1,2,3],[4,5,6],[7,8,9]]`
 - Output: `[[7,4,1],[8,5,2],[9,6,3]]`
@@ -52,7 +55,3 @@ class Solution:
         for r in range(n):
             matrix[r].reverse()
 ```
-
-## Explanation
-
-<YouTube id="fMSJSS7eO1w" title="Rotate Image - Matrix - Leetcode 48" />

apps/docs/content/(02-nodal-grid)/matrix-index-math/54-spiral-matrix.mdx

@@ -2,13 +2,16 @@
 title: '54. Spiral Matrix'
 description: Given an m x n matrix, return all elements of the matrix in spiral order
 icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Matrix", slug: "matrix" }
+  - { name: "Simulation", slug: "simulation" }
+video: "BJnMZNwUk1M"
 sidebar:
   label: 'Spiral Matrix'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Array</Badge>
-
 ### Example 1:
 - Input: `matrix = [[1,2,3],[4,5,6],[7,8,9]]`
 - Output: `[1,2,3,6,9,8,7,4,5]`
@@ -76,7 +79,3 @@ class Solution:
 
         return res
 ```
-
-## Explanation
-
-<YouTube id="BJnMZNwUk1M" title="Spiral Matrix - Microsoft Interview Question - Leetcode 54" />

apps/docs/content/(02-nodal-grid)/matrix-index-math/73-set-matrix-zeroes.mdx

@@ -2,13 +2,16 @@
 title: '73. Set Matrix Zeroes'
 description: Given an m x n integer matrix matrix, if an element is 0, set its entire row and column to 0's
 icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Hash Table", slug: "hash-table" }
+  - { name: "Matrix", slug: "matrix" }
+video: "T41rL0L3Pnw"
 sidebar:
   label: 'Set Matrix Zeroes'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Array</Badge>
-
 ::::warning
 You must do it in place.
 ::::
@@ -95,7 +98,3 @@ class Solution:
             for r in range(m):
                 matrix[r][0] = 0
 ```
-
-## Explanation
-
-<YouTube id="T41rL0L3Pnw" title="Set Matrix Zeroes - In-place - Leetcode 73" />