285 Inorder Successor in BST

Given a binary search tree and a node in it, find the in-order successor of that node in the BST.
Note: If the given node has no in-order successor in the tree, returnnull.
The Idea: The problem can be summed up into two cases. In the first case when p has a right child, then the next in order successor is the smallest value of that right subtree. Otherwise, we have to ascend down from the root of the tree and find p using plain old binary search. In this case, maintain a previous node that follows root.left, since this will be the the first largest node that is larger than root once p is found.
Complexity: O(logn) time and O(1) space
# Definition for a binary tree node.
# class TreeNode(object):
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution(object):
def inorderSuccessor(self, root, p):
:type root: TreeNode - the actual root of the tree
:type p: TreeNode - find the next in order successor of this node
:rtype: TreeNode
if not root or not p:
return None
# case 1
if p.right:
p = p.right
while p.left:
p = p.left
return p
# case 2
prev = None
while root != p:
if p.val > root.val:
root = root.right
prev = root
root = root.left
return prev