Given the <code>root</code> of a binary tree, return <em>the average value of the nodes on each level in the form of an array</em>. Answers within <code>10<sup>-5</sup></code> of the actual answer will be accepted.
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/09/avg1-tree.jpg" style="width: 277px; height: 302px;" />
<pre>
<strong>Input:</strong> root = [3,9,20,null,null,15,7]
<strong>Output:</strong> [3.00000,14.50000,11.00000]
Explanation: The average value of nodes on level 0 is 3, on level 1 is 14.5, and on level 2 is 11.
Hence return [3, 14.5, 11].
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/09/avg2-tree.jpg" style="width: 292px; height: 302px;" />
<pre>
<strong>Input:</strong> root = [3,9,20,15,7]
<strong>Output:</strong> [3.00000,14.50000,11.00000]
</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>-2<sup>31</sup> &lt;= Node.val &lt;= 2<sup>31</sup> - 1</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:
   vector<double> averageOfLevels(TreeNode* root) 
{
    vector<double> toReturn;
    vector<double> totals, amounts;
    if (root != NULL) func(root, 0, totals, amounts);

    for (int i = 0; i < totals.size(); ++i)
    {
        double toAdd = totals[i] / amounts[i];
        toReturn.push_back(toAdd);
    }
    return toReturn;
}


void func(TreeNode* root, int layer, vector<double>& totals, vector<double>& amounts)
{
    if (layer >= totals.size())
    {
        totals.push_back(root->val);
        amounts.push_back(1);
    }
    else
    {
        totals[layer] += root->val;
        amounts[layer] += 1;
    }

    if (root->left != NULL) func(root->left, layer + 1, totals, amounts);
    if (root->right != NULL) func(root->right, layer + 1, totals, amounts);
}
};
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