# 662. Maximum Width of Binary Tree

## Problem Statement

<br>

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.

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**Example 1:**

![](https://assets.leetcode.com/uploads/2021/05/03/width1-tree.jpg)

<pre><code><strong>Input: root = [1,3,2,5,3,null,9]
</strong><strong>Output: 4
</strong><strong>Explanation: The maximum width exists in the third level with length 4 (5,3,null,9).
</strong></code></pre>

**Example 2:**

![](https://assets.leetcode.com/uploads/2022/03/14/maximum-width-of-binary-tree-v3.jpg)

<pre><code><strong>Input: root = [1,3,2,5,null,null,9,6,null,7]
</strong><strong>Output: 7
</strong><strong>Explanation: The maximum width exists in the fourth level with length 7 (6,null,null,null,null,null,7).
</strong></code></pre>

**Example 3:**

![](https://assets.leetcode.com/uploads/2021/05/03/width3-tree.jpg)

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

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**Constraints:**

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

## Intuition

```
Approach:

1) Do a BFS traversal, as we want the width, builing the intuition
2) Now, we can index the tree nodes like

   0
  / \
  1 2
  .. son

if index = i
Left = 2*i+1
right = 2*i+2

in 0 based indexing

now we can maintain a queue to track the indices

Now to avoid overflow, We do a trick 
For skewed tree, i - 2i - 4i .. can cause overflow

So mmin trick
```

### Links

<https://leetcode.com/problems/maximum-width-of-binary-tree/description/>

### Video Links

<https://www.youtube.com/watch?v=ZbybYvcVLks&ab_channel=takeUforward>

### Approach 1:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
class Solution {
public:
    int widthOfBinaryTree(TreeNode* root) {
        queue<pair<TreeNode*, long long int>> q;
        q.push({root, 0});
        long long int len=0;

        while(!q.empty()){
            int size = q.size();
            int mmin = q.front().second;
            long long int left, right;
            
            for(int i=0; i<size; i++){
                TreeNode* temp = q.front().first;
                long long int index = q.front().second;

                if(i==0)
                    left = index;
                if(i==size-1)
                    right = index;

                if(temp->left){
                    long long int node_idx = (2*index+1) - mmin;
                    q.push({temp->left, node_idx}); 
                }
                if(temp->right){
                    long long int node_idx = (2*index+2) - mmin;
                    q.push({temp->right, node_idx}); 
                }
                q.pop();
            }
            len = max(len, right-left+1);
        }

        return len;
    }
};
```

{% endcode %}

### Approach 2:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Approach 3:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Approach 4:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Similar Problems

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