Maximum Width of Binary Tree Python Solution

lcpy gen -n 662   # by problem number
lcpy gen -s maximum_width_of_binary_tree   # by problem name

Input: root = [1,3,2,5,3,null,9]
Output: 4
Explanation: The maximum width exists in the third level with length 4 (5,3,null,9).

Input: root = [1,3,2,5,null,null,9,6,null,7]
Output: 7
Explanation: The maximum width exists in the fourth level with length 7 (6,null,null,null,null,null,7).

Input: root = [1,3,2,5]
Output: 2
Explanation: The maximum width exists in the second level with length 2 (3,2).

from collections import deque

from leetcode_py import TreeNode


class Solution:
    # Time: O(n)
    # Space: O(w) where w is maximum width
    def width_of_binary_tree(self, root: TreeNode[int] | None) -> int:
        if not root:
            return 0

        max_width = 1
        queue = deque([(root, 0)])

        while queue:
            level_size = len(queue)
            _, first_pos = queue[0]
            last_pos = first_pos

            for _ in range(level_size):
                node, pos = queue.popleft()
                last_pos = pos

                if node.left:
                    queue.append((node.left, 2 * pos))
                if node.right:
                    queue.append((node.right, 2 * pos + 1))

            max_width = max(max_width, last_pos - first_pos + 1)

        return max_width