docs: restructure problem paths, change section display to groups, and improve documentation content

apps/docs/content/(03-hierarchical)/binary-search-tree/98_validate-binary-search-tree.mdx

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+---
+title: '98. Validate Binary Search Tree'
+description: Given the root of a binary tree, determine if it is a valid binary search tree (BST)
+icon: dot
+topics:
+  - { name: "Tree", slug: "tree" }
+  - { name: "Depth-First Search", slug: "depth-first-search" }
+  - { name: "Binary Search Tree", slug: "binary-search-tree" }
+  - { name: "Binary Tree", slug: "binary-tree" }
+video: "s6ATEkipzow"
+issue: "https://github.com/prdlk/leetcode/issues/111"
+sidebar:
+  label: 'Validate Binary Search Tree'
+  badge: 'Medium'
+---
+
+### Example 1:
+- Input: `root = [2,1,3]`
+- Output: `true`
+
+### Example 2:
+- Input: `root = [5,1,4,null,null,3,6]`
+- Output: `false`
+- Explanation: The `root` node's value is `5` but its right child's value is `4`.
+
+### Constraints:
+
+- The number of nodes in the tree is in the range [1, 10^4].
+- `-2^31 <= Node.val <= 2^31 - 1`
+
+## Approach
+
+```mermaid
+flowchart TD
+  S(["isValidBST(root)"]) --> C["valid(root, float('-inf'), float('inf')) — the root may hold any value"]
+  C --> E(["return that result"])
+  subgraph valid["valid(node, low, high)"]
+    V1{"not node?"}
+    V1 -- yes --> V2(["return True"])
+    V1 -- no --> V3{"not (low < node.val < high)?"}
+    V3 -- yes --> V4(["return False — node breaks a bound set by an ancestor"])
+    V3 -- no --> V5["valid(node.left, low, node.val) and valid(node.right, node.val, high) — each child tightens one bound"]
+    V5 --> V6(["return that result"])
+  end
+  C --> V1
+```
+
+## Solution
+
+```py
+# Definition for a binary tree node.
+# class TreeNode:
+#     def __init__(self, val=0, left=None, right=None):
+#         self.val = val
+#         self.left = left
+#         self.right = right
+class Solution:
+    def isValidBST(self, root: Optional[TreeNode]) -> bool:
+        def valid(node, low, high):
+            if not node:
+                return True
+
+            if not (low < node.val < high):
+                return False
+
+            return valid(node.left, low, node.val) and valid(node.right, node.val, high)
+
+        return valid(root, float("-inf"), float("inf"))
+```