Lowest Common Ancestor of a Binary Search Tree
Given a binary search tree (BST), find the lowest common ancestor (LCA) node 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)."
Example 1:
6
/ \
2 8
/ \ / \
0 4 7 9
/ \
3 5
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:
6
/ \
2 8
/ \ / \
0 4 7 9
/ \
3 5
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.
Example 3:
Input: root = [2,1], p = 2, q = 1
Output: 2
Examples
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. Node 2 is in the left subtree and node 8 is in the right subtree, so the root (6) is their lowest common ancestor.
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. Node 4 is a descendant of node 2, and a node can be a descendant of itself according to the LCA definition.
Example 3
Input: root = [2,1], p = 2, q = 1
Output: 2
Explanation: The root node 2 is the ancestor of node 1, and since a node is its own descendant, the LCA is 2.
Constraints
- -The number of nodes in the tree is in the range [2, 10^5].
- --10^9 <= Node.val <= 10^9
- -All Node.val are unique.
- -p != q
- -p and q will exist in the BST.
Optimal Complexity
Time
O(h)
Space
O(1)
Choose between solo practice and interview simulation
Practice Mode keeps things simple with code + tests. AI Interview Mode adds voice, pressure, and a post-round score summary.