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# Binary Search Tree Iterator

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.

**Example:**

![](https://assets.leetcode.com/uploads/2018/12/25/bst-tree.png)

```
BSTIterator iterator = new BSTIterator(root);
iterator.next();    // return 3
iterator.next();    // return 7
iterator.hasNext(); // return true
iterator.next();    // return 9
iterator.hasNext(); // return true
iterator.next();    // return 15
iterator.hasNext(); // return true
iterator.next();    // return 20
iterator.hasNext(); // return false
```

**Note:**

* `next()` and `hasNext()` should run in average O(1) time and uses O(h) memory, where h is the height of the tree.
* You may assume that `next()` call will always be valid, that is, there will be at least a next smallest number in the BST when `next()` is called.

```java
class BSTIterator {
    Deque<TreeNode> stack = new LinkedList<>();

    public BSTIterator(TreeNode root) {
        adder(root);
    }

    public int next() {
        TreeNode next = stack.pop();
        adder(next.right); // This will work because in the end the AVERAGE time complexity will be O(1).
        return next.val;
    }

    public boolean hasNext() {
        return stack.size() == 0 ? false : true;
    }

    private void adder(TreeNode temp) {
        while (temp != null) {
            stack.push(temp);
            temp = temp.left;
        }
    }
}
```