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# Maximum Width of Binary Tree

Given a binary tree, write a function to get the maximum width of the given tree. The width of a tree is the maximum width among all levels. The binary tree has the same structure as a **full binary tree**, but some nodes are null.

The width of one level is defined as the length between the end-nodes (the leftmost and right most non-null nodes in the level, where the `null` nodes between the end-nodes are also counted into the length calculation.

**Example 1:**

```
Input: 

           1
         /   \
        3     2
       / \     \  
      5   3     9 

Output: 4
Explanation: The maximum width existing in the third level with the length 4 (5,3,null,9).
```

**Example 2:**

```
Input: 

          1
         /  
        3    
       / \       
      5   3     

Output: 2
Explanation: The maximum width existing in the third level with the length 2 (5,3).
```

**Example 3:**

```
Input: 

          1
         / \
        3   2 
       /        
      5      

Output: 2
Explanation: The maximum width existing in the second level with the length 2 (3,2).
```

**Example 4:**

```
Input: 

          1
         / \
        3   2
       /     \  
      5       9 
     /         \
    6           7
Output: 8
Explanation:The maximum width existing in the fourth level with the length 8 (6,null,null,null,null,null,null,7).


```

**Note:** Answer will in the range of 32-bit signed integer.

```java
class Solution {
    public int widthOfBinaryTree(TreeNode root) {
        if (root == null)
            return 0;
        Queue<TreeNode> q = new LinkedList<TreeNode>();
        Map<TreeNode, Integer> m = new HashMap<TreeNode, Integer>();
        q.offer(root);
        m.put(root, 1);
        int curW = 0;
        int maxW = 0;
        while (!q.isEmpty()) {
            int size = q.size();
            int start = 0;
            int end = 0;
            for (int i = 0; i < size; i++) {
                TreeNode node = q.poll();
                if (i == 0)
                    start = m.get(node);
                if (i == size - 1)
                    end = m.get(node);
                if (node.left != null) {
                    m.put(node.left, m.get(node) * 2);
                    q.offer(node.left);
                }
                if (node.right != null) {
                    m.put(node.right, m.get(node) * 2 + 1);
                    q.offer(node.right);
                }
            }
            curW = end - start + 1;
            maxW = Math.max(curW, maxW);
        }
        return maxW;
    }
}
```


---

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