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

apps/docs/content/(01-linear-structures)/prefix-sum/560-subarray-sum-equals-k.mdx

@@ -2,13 +2,16 @@
 title: '560. Subarray Sum Equals K'
 description: Given an array of integers nums and an integer k, return the total number of subarrays whose sum equals to k
 icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Hash Table", slug: "hash-table" }
+  - { name: "Prefix Sum", slug: "prefix-sum" }
+video: "fFVZt-6sgyo"
 sidebar:
   label: 'Subarray Sum Equals K'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Array</Badge>
-
 ### Example 1:
 - Input: `nums = [1,1,1], k = 2`
 - Output: `2`
@@ -65,7 +68,3 @@ var subarraySum = function(nums, k) {
   return count
 };
 ```
-
-## Explanation
-
-<YouTube id="fFVZt-6sgyo" title="Subarray Sum Equals K - Prefix Sums - Leetcode 560 - Python" />