<p>Given the <code>root</code> of a binary tree, return <em>the <strong>maximum width</strong> of the given tree</em>.</p>

<p>The <strong>maximum width</strong> of a tree is the maximum <strong>width</strong> among all levels.</p>

<p>The <strong>width</strong> of one level is defined as the length between the end-nodes (the leftmost and rightmost non-null nodes), where the null nodes between the end-nodes that would be present in a complete binary tree extending down to that level are also counted into the length calculation.</p>

<p>It is <strong>guaranteed</strong> that the answer will in the range of a <strong>32-bit</strong> signed integer.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/05/03/width1-tree.jpg" style="width: 359px; height: 302px;" />
<pre>
<strong>Input:</strong> root = [1,3,2,5,3,null,9]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The maximum width exists in the third level with length 4 (5,3,null,9).
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/14/maximum-width-of-binary-tree-v3.jpg" style="width: 442px; height: 422px;" />
<pre>
<strong>Input:</strong> root = [1,3,2,5,null,null,9,6,null,7]
<strong>Output:</strong> 7
<strong>Explanation:</strong> The maximum width exists in the fourth level with length 7 (6,null,null,null,null,null,7).
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/05/03/width3-tree.jpg" style="width: 289px; height: 299px;" />
<pre>
<strong>Input:</strong> root = [1,3,2,5]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The maximum width exists in the second level with length 2 (3,2).
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 3000]</code>.</li>
	<li><code>-100 &lt;= Node.val &lt;= 100</code></li>
</ul>

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
import queue

class Solution:
    def widthOfBinaryTree(self, root: Optional[TreeNode]) -> int:

        if not root:
            return 0

        max_width = 0
        queue = deque()
        queue.append((root, 0)) # node, number

        while queue:
            _, root_level = queue[0]
            for _ in range(len(queue)):
                node, num = queue.popleft()

                if node.left:
                    queue.append((node.left, 2 * num))
                if node.right:
                    queue.append((node.right, 2 * num + 1))
            
            max_width = max(max_width, num - root_level + 1)
        
        return max_width
17500