662.Maximum Width of Binary Tree
===

###### tags: `Medium`,`Tree`,`BFS`,`DFS`

[662. Maximum Width of Binary Tree](https://leetcode.com/problems/maximum-width-of-binary-tree/)

### 題目描述

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.

### 範例

**Example 1:**


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

**Example 2:**


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

**Example 3:**


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

**Constraints**:

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

### 解答
#### Python

class Solution:
    def widthOfBinaryTree(self, root: Optional[TreeNode]) -> int:
        q = deque([(root, 0, 0)])
        dic = defaultdict(list)

        while q:
            node, level, idx = q.popleft()
            dic[level].append(idx)

            if node.left:
                q.append((node.left, level + 1, 2 * idx))
            if node.right:
                q.append((node.right, level + 1, 2 * idx + 1))

        max_width = 0
        for nodes in dic.values():
            width = nodes[-1] - nodes[0] + 1
            max_width = max(max_width, width)

        return max_width

> [name=Ron Chen][time=Thu, Apr 20, 2023]

#### Javascript

function widthOfBinaryTree(root) {
  let max = 1;
  const queue = [[root, 0]];
  while (queue.length) {
    const n = queue.length;
    if (n === 1) queue[0][1] = 1;

    const [left, right] = [queue[0][1], queue[n - 1][1]];
    max = Math.max(max, right - left + 1);

    for (let i = 0; i < n; i++) {
      const [node, index] = queue.shift();
      if (node.left) queue.push([node.left, index * 2]);
      if (node.right) queue.push([node.right, index * 2 + 1]);
    }
  }

  return max;
}

> [name=Marsgoat][time=Thu, Apr 20, 2023]

### Reference

[回到題目列表](https://hackmd.io/@Marsgoat/leetcode_every_day)