173. Binary Search Tree Iterator

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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.
Credits:
Special thanks to @ts for adding this problem and creating all test cases.

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# 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):
    def __init__(self, root):
        """
        :type root: TreeNode
        """
        self.stack = []
        self._pushLeft(root)

    def hasNext(self):
        """
        :rtype: bool
        """
        return self.stack
      

    def next(self):
        """
        :rtype: int
        """
        node = self.stack.pop()
        self._pushLeft(node.right)
        return node.val
      
    def _pushLeft(self, node):
        while node:
            self.stack.append(node)
            node = node.left

# Your BSTIterator will be called like this:
# i, v = BSTIterator(root), []
# while i.hasNext(): v.append(i.next())