<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) {
        // Special case: if the depth is 1, we need to create a new root
        if (depth == 1) {
            TreeNode* newRoot = new TreeNode(val);
            newRoot->left = root;
            return newRoot;
        }
        
        // BFS queue to traverse the tree level by level
        queue<TreeNode*> q;
        q.push(root);
        int currentDepth = 1;

        // Traverse the tree until reaching the level just above the target depth
        while (!q.empty() && currentDepth < depth - 1) {
            int size = q.size();
            for (int i = 0; i < size; ++i) {
                TreeNode* node = q.front();
                q.pop();
                
                // Add children to the queue if they exist
                if (node->left) q.push(node->left);
                if (node->right) q.push(node->right);
            }
            currentDepth++;
        }
        
        // Now we are at the level just above the target depth
        while (!q.empty()) {
            TreeNode* node = q.front();
            q.pop();

            // Insert new nodes with value 'val' as the new children
            TreeNode* newLeft = new TreeNode(val);
            TreeNode* newRight = new TreeNode(val);

            newLeft->left = node->left;  // The original left child becomes the new left's left child
            newRight->right = node->right;  // The original right child becomes the new right's right child

            node->left = newLeft;  // Attach new left node
            node->right = newRight;  // Attach new right node
        }

        return root;
    }
};

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