maximum_width_of_binary_tree.py

"""
Given the root of a binary tree, return the maximum width of the given tree.

The maximum width of a tree is the maximum width among all levels.

The width 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.

It is guaranteed that the answer will in the range of a 32-bit signed integer.

 

Example 1:


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).
Example 2:


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).
Example 3:


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

Constraints:

The number of nodes in the tree is in the range [1, 3000].
-100 <= Node.val <= 100

"""

# 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
class Solution:
    def widthOfBinaryTree(self, root: Optional[TreeNode]) -> int:
        queue = deque([(root, 1)])
        maxwidth = 0
        while queue:
            maxwidth = max(maxwidth, queue[-1][1] - queue[0][1] + 1)

            for _ in range(len(queue)):
                node, index = queue.popleft()
                if node and node.left:
                    queue.append((node.left, index * 2))
                if node and node.right:
                    queue.append((node.right, index * 2 + 1))
        
        return maxwidth