use bfs to search level by level. The width of a level is the last element index - the first element index. The index can be calculated by its parent nodes, that is if the parent node index is i, then in binary tree its left child 2i-1 and right child 2i

```
# Definition for a binary tree node.
# class TreeNode(object):
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution(object):
def widthOfBinaryTree(self, root):
"""
:type root: TreeNode
:rtype: int
"""
if not root:
return 0
q = [(root, 1)]
res = 1
while q:
nextlevel = []
for node in q:
if node[0].left:
nextlevel.append((node[0].left, 2 * node[1] - 1))
if node[0].right:
nextlevel.append((node[0].right, 2 * node[1]))
if len(nextlevel) >= 2:
res = max(res, nextlevel[-1][1] - nextlevel[0][1] + 1)
q = nextlevel
return res
```