<p>Given the <code>root</code> of a binary search tree and an integer <code>k</code>, return <code>true</code> <em>if there exist two elements in the BST such that their sum is equal to</em> <code>k</code>, <em>or</em> <code>false</code> <em>otherwise</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/21/sum_tree_1.jpg" style="width: 400px; height: 229px;" />
<pre>
<strong>Input:</strong> root = [5,3,6,2,4,null,7], k = 9
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/21/sum_tree_2.jpg" style="width: 400px; height: 229px;" />
<pre>
<strong>Input:</strong> root = [5,3,6,2,4,null,7], k = 28
<strong>Output:</strong> false
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 10<sup>4</sup>]</code>.</li>
	<li><code>-10<sup>4</sup> &lt;= Node.val &lt;= 10<sup>4</sup></code></li>
	<li><code>root</code> is guaranteed to be a <strong>valid</strong> binary search tree.</li>
	<li><code>-10<sup>5</sup> &lt;= k &lt;= 10<sup>5</sup></code></li>
</ul>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */


class BSTIterator{
    private:
        TreeNode* root;
        int reverse;
        std::stack< TreeNode* > st;

        void Push(TreeNode* root, std::stack< TreeNode* > &st, bool reverse) {
            TreeNode* temp = root;
            while(temp) {
                if(!reverse) { st.push(temp); temp = temp -> left; }
                if(reverse) { st.push(temp); temp = temp -> right; }
            }
        }

    public:
        BSTIterator(TreeNode* root, int _f) {
            this -> root = root;
            this -> reverse = _f;
            Push(root, st, _f);
        }

        int next(){
            TreeNode* temp = st.top(); st.pop();
            
            if(!reverse && temp->right) {
                TreeNode* curr = temp -> right;
                while(curr){
                    st.push(curr);
                    curr = curr -> left;
                }
            }

            if(reverse && temp->left) {
                TreeNode* curr = temp -> left;
                while(curr){
                    st.push(curr);
                    curr = curr -> right;
                }
            }

            return temp -> val;
        }

        bool has_elements(){
            return !st.empty();
        } 
};

class Solution {
public:
    bool findTarget(TreeNode* root, int k) {
        BSTIterator* asc = new BSTIterator(root, false);
        BSTIterator* dsc = new BSTIterator(root, true);

        int ele1 = asc->next();
        int ele2 = dsc->next();
        while(ele1 < ele2) {
            int sum = ele1 + ele2;
            if(sum == k)
                return true;
            else if(sum > k)
                ele2 = dsc->next();
            else
                ele1 = asc->next();
        }

        return false;
    }
};
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