Convert Binary Search Tree to Sorted Doubly Linked List — Python

# Time:  O(n)
# Space: O(h)

class Node(object):
    def __init__(self, val, left, right):
        self.val = val
        self.left = left
        self.right = right


class Solution(object):
    def treeToDoublyList(self, root):
        """
        :type root: Node
        :rtype: Node
        """
        if not root:
            return None
        left_head, left_tail, right_head, right_tail = root, root, root, root
        if root.left:
            left_head = self.treeToDoublyList(root.left)
            left_tail = left_head.left
        if root.right:
            right_head = self.treeToDoublyList(root.right)
            right_tail = right_head.left
        left_tail.right, right_head.left = root, root
        root.left, root.right = left_tail, right_head
        left_head.left, right_tail.right = right_tail, left_head
        return left_head