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# Time:  O(1)
# Space: O(h), h is height of binary tree
# Implement an iterator over a binary search tree (BST).
# Your iterator will be initialized with the root node of a BST.
# Calling next() will return the next smallest number in the BST.
# Note: next() and hasNext() should run in average O(1) time
# and uses O(h) memory, where h is the height of the tree.
# Definition for a  binary tree node
class TreeNode(object):
    def __init__(self, x):
        self.val = x
        self.left = None
        self.right = None
class BSTIterator(object):
    # @param root, a binary search tree's root node
    def __init__(self, root):
        self.stack = []
        self.cur = root
    # @return a boolean, whether we have a next smallest number
    def hasNext(self):
        return self.stack or self.cur
    # @return an integer, the next smallest number
    def next(self):
        while self.cur:
            self.stack.append(self.cur)
            self.cur = self.cur.left
        self.cur = self.stack.pop()
        node = self.cur
        self.cur = self.cur.right
        return node.val

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