235. 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).”

Example 1:

1
2
3

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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2
3

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:

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

lowest common ancestor (LCA)找節點共同祖先，確認順序後找root

# Definition for a binary tree node.
# class TreeNode:
#     def init(self, x):
#         self.val = x
#         self.left = None
#         self.right = None
T:O(n), S:O(1)
class Solution:
    def lowestCommonAncestor(self, root: 'TreeNode', p: 'TreeNode', q: 'TreeNode') -> 'TreeNode':
        if q.val < p.val: p,q = q,p # p must small than q
        while True:
            if q.val < root.val:
                root = root.left
            elif p.val > root.val:
                root = root.right
            elif p.val <= root.val <= q.val:
                return root

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