<p>Given the <code>root</code> of a binary tree and two integers <code>val</code> and <code>depth</code>, add a row of nodes with value <code>val</code> at the given depth <code>depth</code>.</p>

<p>Note that the <code>root</code> node is at depth <code>1</code>.</p>

<p>The adding rule is:</p>

<ul>
	<li>Given the integer <code>depth</code>, for each not null tree node <code>cur</code> at the depth <code>depth - 1</code>, create two tree nodes with value <code>val</code> as <code>cur</code>&#39;s left subtree root and right subtree root.</li>
	<li><code>cur</code>&#39;s original left subtree should be the left subtree of the new left subtree root.</li>
	<li><code>cur</code>&#39;s original right subtree should be the right subtree of the new right subtree root.</li>
	<li>If <code>depth == 1</code> that means there is no depth <code>depth - 1</code> at all, then create a tree node with value <code>val</code> as the new root of the whole original tree, and the original tree is the new root&#39;s left subtree.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/15/addrow-tree.jpg" style="width: 500px; height: 231px;" />
<pre>
<strong>Input:</strong> root = [4,2,6,3,1,5], val = 1, depth = 2
<strong>Output:</strong> [4,1,1,2,null,null,6,3,1,5]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/11/add2-tree.jpg" style="width: 500px; height: 277px;" />
<pre>
<strong>Input:</strong> root = [4,2,null,3,1], val = 1, depth = 3
<strong>Output:</strong> [4,2,null,1,1,3,null,null,1]
</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>The depth of the tree is in the range <code>[1, 10<sup>4</sup>]</code>.</li>
	<li><code>-100 &lt;= Node.val &lt;= 100</code></li>
	<li><code>-10<sup>5</sup> &lt;= val &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= depth &lt;= the depth of tree + 1</code></li>
</ul>

class Solution {
public:
    TreeNode* addOneRow(TreeNode* root, int val, int depth) {
        TreeNode* sentinel = new TreeNode();
        sentinel->left = root;

        DFS(sentinel, val, depth);

        TreeNode* result = sentinel->left;
        delete sentinel;

        return result;
    }

private:
    void DFS(TreeNode* current, int val, int depth) {
        if (current == nullptr) return;

        if (depth == 1) {
            TreeNode* new_left = new TreeNode(val, current->left, nullptr);
            TreeNode* new_right = new TreeNode(val, nullptr, current->right);

            current->left = new_left;
            current->right = new_right;

            return;
        }

        DFS(current->left, val, depth - 1);
        DFS(current->right, val, depth - 1);
    }
};
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