<p>Given the <code>root</code> of a binary search tree, return <em>a <strong>balanced</strong> binary search tree with the same node values</em>. If there is more than one answer, return <strong>any of them</strong>.</p>

<p>A binary search tree is <strong>balanced</strong> if the depth of the two subtrees of every node never differs by more than <code>1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/balance1-tree.jpg" style="width: 500px; height: 319px;" />
<pre>
<strong>Input:</strong> root = [1,null,2,null,3,null,4,null,null]
<strong>Output:</strong> [2,1,3,null,null,null,4]
<b>Explanation:</b> This is not the only correct answer, [3,1,4,null,2] is also correct.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/balanced2-tree.jpg" style="width: 224px; height: 145px;" />
<pre>
<strong>Input:</strong> root = [2,1,3]
<strong>Output:</strong> [2,1,3]
</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>1 &lt;= Node.val &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 Solution {
public:
    
    TreeNode* balanceBST(TreeNode* root)
    {
        inorder(root);
        return createTree(v_nodes);
    }

    TreeNode* createTree(const std::vector<int>& nums)
    {
        if(nums.size() == 0) return nullptr;

        int mid = std::round((0 + nums.size() - 1) / 2);
        auto midIt = std::find(nums.begin(), nums.end(), nums.at(mid));
        TreeNode* node = new TreeNode(nums.at(mid));

        std::vector<int> lnums, rnums;
        std::copy(nums.begin(), midIt,  std::back_inserter(lnums));
        std::copy(midIt + 1, nums.end(), std::back_inserter(rnums));

        node->left  = createTree(lnums);
        node->right = createTree(rnums);

        return node;
    }

    std::vector<int> v_nodes;

    void inorder(TreeNode* rt)
    {
        if(!rt) return;
        inorder(rt->left);
        v_nodes.push_back(rt->val);
        inorder(rt->right);
    }
};
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