235. Lowest Common Ancestor of a Binary Search Tree

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https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/

Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST.
According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”
Given binary search tree:  root = [6,2,8,0,4,7,9,null,null,3,5]


Example 1:
Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8
Output: 6
Explanation: The LCA of nodes 2 and 8 is 6.
Example 2:
Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4
Output: 2
Explanation: The LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

Note:
  • All of the nodes' values will be unique.
  • p and q are different and both values will exist in the BST.
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Clarifying questions
Is a solution guaranteed
Are p, q guaranteed to exist in the tree
If nodes are in direct parent, child, which node is answer ?
 
Intuition
Binary Search Tree - All nodes to left are less than root, all nodes to right are greater than root

Goal - find first node from top, which is between p, and q

if both p, q are less than root, recurse left
if both p, q are greater than root, recurse right

otherwise the root lies between p, q and return root
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Complexity
Space - O(N) - worst case - skewed tree - all nodes in one line
Time - O(N)
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