1120. Maximum Average Subtree

Given the root of a binary tree, find the maximum average value of any subtree of that tree.

(A subtree of a tree is any node of that tree plus all its descendants. The average value of a tree is the sum of its values, divided by the number of nodes.)

Example 1:

Input: 

[5,6,1]

Output: 

6.00000

Explanation: 

For the node with value = 5 we have an average of (5 + 6 + 1) / 3 = 4.
For the node with value = 6 we have an average of 6 / 1 = 6.
For the node with value = 1 we have an average of 1 / 1 = 1.
So the answer is 6 which is the maximum.

Note:

1. The number of nodes in the tree is between 1 and 5000 .
2. Each node will have a value between 0 and 100000 .
3. Answers will be accepted as correct if they are within 10^-5 of the correct answer.

1、题目描述¶

给你一棵二叉树的根节点 root，找出这棵树的 每一棵 子树的 平均值 中的 最大 值。

子树是树中的任意节点和它的所有后代构成的集合。

树的平均值是树中节点值的总和除以节点数。

示例：

输入：[5,6,1]
输出：6.00000
解释： 
以 value = 5 的节点作为子树的根节点，得到的平均值为 (5 + 6 + 1) / 3 = 4。
以 value = 6 的节点作为子树的根节点，得到的平均值为 6 / 1 = 6。
以 value = 1 的节点作为子树的根节点，得到的平均值为 1 / 1 = 1。
所以答案取最大值 6。

提示：

• 树中的节点数介于 1 到 5000之间。
• 每个节点的值介于 0 到 100000 之间。
• 如果结果与标准答案的误差不超过 $10^{-5}$，那么该结果将被视为正确答案。