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11

Maximum Width In Binary Tree

Difficulty: MEDIUM
Contributed By
Avg. time to solve
38 min
Success Rate
50%

Problem Statement

You have been given a Binary Tree of integers. You are supposed to return the maximum width of the given Binary Tree. The maximum width of the tree is the maximum width among all the levels of the given tree.

The width of one level is defined as the length between the leftmost and the rightmost, non-null nodes in the level, where the null nodes in between the leftmost and rightmost are excluded into length calculation.

For example :
For the given binary tree

Example

The maximum width will be at the third level with the length of 3, i.e. {4, 5, 6}.
Input Format :
The only line of input contains elements in the level order form. The line consists of values of nodes separated by a single space. In case a node is null, we take -1 in its place.

For example, the input for the tree depicted in the below image would be :

Example

1
2 3
4 -1 5 6
-1 7 -1 -1 -1 -1
-1 -1

Explanation :

Level 1 :
The root node of the tree is 1

Level 2 :
Left child of 1 = 2
Right child of 1 = 3

Level 3 :
Left child of 2 = 4
Right child of 2 = null (-1)
Left child of 3 = 5
Right child of 3 = 6

Level 4 :
Left child of 4 = null (-1)
Right child of 4 = 7
Left child of 5 = null (-1)
Right child of 5 = null (-1)
Left child of 6 = null (-1)
Right child of 6 = null (-1)

Level 5 :
Left child of 7 = null (-1)
Right child of 7 = null (-1)

The first not-null node(of the previous level) is treated as the parent of the first two nodes of the current level. The second not-null node (of the previous level) is treated as the parent node for the next two nodes of the current level and so on.
The input ends when all nodes at the last level are null(-1).
Note :
The above format was just to provide clarity on how the input is formed for a given tree. 
The sequence will be put together in a single line separated by a single space. Hence, for the above-depicted tree, the input will be given as:

1 2 3 4 -1 5 6 -1 7 -1 -1 -1 -1 -1 -1
Output Format :
For each input, print a single line that contains a single integer that denotes the maximum width for the given tree.
Note :
You do not need to print anything; it has already been taken care of. Just implement the given function.
Constraints :
0 <= 'N' <= 5 * 10 ^ 5
0 <= 'DATA' <= 10 ^ 6 and data != -1
Where ‘N’ is the total number of nodes in the binary tree, and 'DATA' is the value of the binary tree node.

Time Limit: 1sec.
Sample Input 1 :
1 2 3 4 -1 5 6 -1 7 -1 -1 -1 -1 -1 -1
Sample Output 1 :
3
Explanation of Sample Input 1 :
The maximum width will be at the third level with the length of 3, i.e. {4, 5, 6}.
Sample Input 2 :
2 7 5 2 6 -1 9 -1 -1 5 11 4 -1 -1 -1 -1 -1 -1 -1
Sample Output 2 :
3
Explanation of Sample Input 2 :
The maximum width will be at the third level i.e. {2, 6, 9} and the fourth level with the length of 3, i.e. {5, 11, 4}. So the maximum width will be 3.
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