Given a Binary Tree. You need to find and return the vertical width of the tree.
Examples :
Input:
1
/ \
2 3
/ \ / \
4 5 6 7
\ \
8 9
Output: 6
Explanation: The width of a binary tree is
the number of vertical paths in that tree.
The above tree contains 6 vertical lines.
Input:
1
/ \
2 3
Output: 3
Explanation: The above tree has 3 vertical lines, hence the answer is 3.
Expected Time Complexity: O(nlogn)
Expected Auxiliary Space: O(height of the tree).
Constraints:
0 <= number of nodes <= 104
