<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) {
        vector<TreeNode*> inorder_list;
        inorderTraversal(root, inorder_list);
        return formTree(inorder_list, 0, inorder_list.size() - 1);
    }
    
    void inorderTraversal(TreeNode* root, vector<TreeNode*>& inorder_list) {
        if (root) {
            inorderTraversal(root->left, inorder_list);
            inorder_list.push_back(root);
            inorderTraversal(root->right, inorder_list);
            root->left = nullptr;
            root->right = nullptr;
        }
    }
    
    TreeNode* formTree(vector<TreeNode*> inorder, int start, int end) {
        if (start == end) {
            return inorder[start];
        }
        if (start > end) return nullptr;
        
        int mid = start + (end - start) / 2;
        inorder[mid]->left = formTree(inorder, start, mid-1);
        inorder[mid]->right = formTree(inorder, mid+1, end);
        return inorder[mid];
    }
};
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