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Lowest Common Ancestor of a Binary Search Tree

Problem Statement​

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).”

Leetcode Link

Example 1:​

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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:​

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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.

Example 3:​

Input: root = [2,1], p = 2, q = 1
Output: 2

Constraints:​

  • The number of nodes in the tree is in the range [2, 105].
  • -109 <= Node.val <= 109
  • All Node.val are unique.
  • p != q
  • p and q will exist in the BST.

Code​

Python
class Solution:
    def lowestCommonAncestor(self, root: 'TreeNode', p: 'TreeNode', q: 'TreeNode') -> 'TreeNode':
        small = min(p.val, q.val)
        large = max(p.val, q.val)
        while root:
            if root.val > large:  # p, q belong to the left subtree
                root = root.left
            elif root.val < small:  # p, q belong to the right subtree
                root = root.right
            else:  # Now, small <= root.val <= large -> This is the LCA between p and q
                return root
        return None