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.

BSTIterator.java

public class BSTIterator {
    private Stack<TreeNode> stack;

    public BSTIterator(TreeNode root) {
        stack = new Stack<TreeNode>();
        pushLeft(root);
    }

    /** @return whether we have a next smallest number */
    public boolean hasNext() {
        return !stack.isEmpty();
    }

    /** @return the next smallest number */
    public int next() {
        if(!hasNext())
            throw new java.util.EmptyStackException();

        TreeNode root = stack.pop();
        pushLeft(root.right);
        return root.val;
    }

    private void pushLeft(TreeNode root) {
        while(root!=null) {
            stack.push(root);
            root = root.left;
        }
    }
}