# Maximum Width Of Binary Tree Problem

## Description

LeetCode Problem 662.

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 are also counted into the length calculation.

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

Example 1:

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

Example 2:

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

Example 3:

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

Example 4:

``````1
2
3
Input: root = [1,3,2,5,null,null,9,6,null,null,7]
Output: 8
Explanation: The maximum width existing in the fourth level with the length 8 (6,null,null,null,null,null,null,7).
``````

Constraints:

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

``````1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
/**
* Definition for a binary tree node.
* struct TreeNode {
*     int val;
*     TreeNode *left;
*     TreeNode *right;
*     TreeNode() : val(0), left(nullptr), right(nullptr) {}
*     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
*     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution {
public:
int widthOfBinaryTree(TreeNode* root) {
if (!root)
return 0;

queue<pair<TreeNode*, unsigned long long int>> que;
que.push({ root, 0 });
int width = 0;

while (que.size() != 0) {
unsigned long long int left = que.front().second, right = 0;
int size = que.size();

while (size-- > 0) {
pair<TreeNode*, unsigned long long int> rNode = que.front();
que.pop();
right = rNode.second;
if (rNode.first->left) {
que.push({rNode.first->left, 2 * rNode.second + 1});
}
if (rNode.first->right) {
que.push({rNode.first->right, 2 * rNode.second + 2});
}
}

width = max(width, int(right - left + 1));
}

return width;
}
};
``````