// Time:  O(1), amortized
// Space: O(h)

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class BSTIterator {
public:
    BSTIterator(TreeNode *root) : cur_(root) {
    }

    /** @return whether we have a next smallest number */
    bool hasNext() {
        return !s_.empty() || cur_ != nullptr;
    }

    /** @return the next smallest number */
    int next() {
        // Go to the left most descendant.
        while (cur_ != nullptr) {
            s_.emplace(cur_);
            cur_ = cur_->left;
        }
        cur_ = s_.top();  // Left most node.
        s_.pop();

        const auto *node = cur_;
        cur_ = cur_->right;  // Visit right child.

        return node->val;
    }

private:
    stack<TreeNode *> s_;
    TreeNode *cur_;
};

/**
 * Your BSTIterator will be called like this:
 * BSTIterator i = BSTIterator(root);
 * while (i.hasNext()) cout << i.next();
 */