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

apps/docs/content/(03-hierarchical)/heap-priority-queue/215-kth-largest-element-in-an-array.mdx

@@ -2,13 +2,18 @@
 title: '215. Kth Largest Element in an Array'
 description: Given an integer array nums and an integer k, return the k^th largest element in the array
 icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Divide and Conquer", slug: "divide-and-conquer" }
+  - { name: "Sorting", slug: "sorting" }
+  - { name: "Heap (Priority Queue)", slug: "heap-priority-queue" }
+  - { name: "Quickselect", slug: "quickselect" }
+video: "XEmy13g1Qxc"
 sidebar:
   label: 'Kth Largest Element in an Array'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Array</Badge>
-
 ### Example 1:
 - Input: `nums = [3,2,1,5,6,4], k = 2`
 - Output: `5`
@@ -54,7 +59,3 @@ class Solution:
 
         return -heapq.heappop(nums)
 ```
-
-## Explanation
-
-<YouTube id="XEmy13g1Qxc" title="Kth Largest Element in an Array - Quick Select - Leetcode 215 - Python" />

apps/docs/content/(03-hierarchical)/heap-priority-queue/23-merge-k-sorted-lists.mdx

@@ -2,13 +2,18 @@
 title: '23. Merge k Sorted Lists'
 description: You are given an array of k linked-lists lists, each linked-list is sorted in ascending order
 icon: dot
+topics:
+  - { name: "Linked List", slug: "linked-list" }
+  - { name: "Divide and Conquer", slug: "divide-and-conquer" }
+  - { name: "Heap (Priority Queue)", slug: "heap-priority-queue" }
+  - { name: "Merge Sort", slug: "merge-sort" }
+  - { name: "Tournament Sort", slug: "tournament-sort" }
+video: "q5a5OiGbT6Q"
 sidebar:
   label: 'Merge k Sorted Lists'
   badge: 'Hard'
 ---
 
-<Badge variant="accent">Linked List</Badge>
-
 ### Example 1:
 - Input: `lists = [[1,4,5],[1,3,4],[2,6]]`
 - Output: `[1,1,2,3,4,4,5,6]`
@@ -89,7 +94,3 @@ class Solution:
         # Space: O(n)
         return D.next
 ```
-
-## Explanation
-
-<YouTube id="q5a5OiGbT6Q" title="Merge K Sorted Lists - Leetcode 23 - Python" />

apps/docs/content/(03-hierarchical)/heap-priority-queue/973-k-closest-points-to-origin.mdx

@@ -2,13 +2,21 @@
 title: '973. K Closest Points to Origin'
 description: Given an array of points where points[i] = [xi, yi] represents a point on the X-Y plane and an integer k, return the k closest points to the origin (0, 0)
 icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Math", slug: "math" }
+  - { name: "Divide and Conquer", slug: "divide-and-conquer" }
+  - { name: "Geometry", slug: "geometry" }
+  - { name: "Sorting", slug: "sorting" }
+  - { name: "Heap (Priority Queue)", slug: "heap-priority-queue" }
+  - { name: "Quickselect", slug: "quickselect" }
+  - { name: "K-D Tree", slug: "k-d-tree" }
+video: "rI2EBUEMfTk"
 sidebar:
   label: 'K Closest Points to Origin'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Array</Badge>
-
 ### Example 1:
 - Input: `points = [[1,3],[-2,2]], k = 1`
 - Output: `[[-2,2]]`
@@ -64,7 +72,3 @@ class Solution:
 
         return res
 ```
-
-## Explanation
-
-<YouTube id="rI2EBUEMfTk" title="K Closest Points to Origin - Heap / Priority Queue - Leetcode 973 - Python" />