<p>Given the <code>root</code> of a binary search tree, and an integer <code>k</code>, return <em>the</em> <code>k<sup>th</sup></code> <em>smallest value (<strong>1-indexed</strong>) of all the values of the nodes in the tree</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/28/kthtree1.jpg" style="width: 212px; height: 301px;" />
<pre>
<strong>Input:</strong> root = [3,1,4,null,2], k = 1
<strong>Output:</strong> 1
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/28/kthtree2.jpg" style="width: 382px; height: 302px;" />
<pre>
<strong>Input:</strong> root = [5,3,6,2,4,null,null,1], k = 3
<strong>Output:</strong> 3
</pre>

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

<ul>
	<li>The number of nodes in the tree is <code>n</code>.</li>
	<li><code>1 &lt;= k &lt;= n &lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= Node.val &lt;= 10<sup>4</sup></code></li>
</ul>

<p>&nbsp;</p>
<p><strong>Follow up:</strong> If the BST is modified often (i.e., we can do insert and delete operations) and you need to find the kth smallest frequently, how would you optimize?</p>

/**
 * 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 Solution {
public:
    int vali;
    int kthSmallest(TreeNode* root, int k) {
        if (root == NULL)
            return 0;
        int v = 0;
        findk(root, v, k);
        root->left = root->right = NULL;
        return vali;
    }
    void findk(TreeNode* root, int& v, int k) {

        if (root == NULL)
            return;
        findk(root->left, v, k);
        v++;
        if (v == k) {
            vali = root->val;
            return;
        }
        findk(root->right, v, k);
    }
};
/*auto init = []()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    return 'c';
}();*/
16700