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).”

Given binary search tree: root = [6,2,8,4,7,9,null,3,5]

_______6______
       /                  ___2__          ___8__
   /              /         0      _4       7       9
         /           3   5

Example 1:

Input: root = [6,5],p = 2,q = 8
Output: 6
Explanation: The LCA of nodes 2 and 8 is 6.

Example 2:

Input: root = [6,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.

# Definition for a binary tree node.
class TreeNode:
    def __init__(self,x):
        self.val = x
        self.left = None
        self.right = None

class Solution:
    def lowestCommonAncestor(self,root,p,q):
        """
        :type root: TreeNode
        :type p: TreeNode
        :type q: TreeNode
        :rtype: TreeNode
        """
        if not root:
            return None
        if root.val > p.val and root.val > q.val:
            return self.lowestCommonAncestor(root.left,q) #这里需要return，因为不需要回溯，找到就可以了
        elif root.val < p.val and root.val < q.val:
            return self.lowestCommonAncestor(root.right,q)
        else:
            return root