543. Diameter of Binary Tree

Example:
Given a binary tree

          1
         /         2   3
       / \     
      4   5    

Return 3, which is the length of the path [4,2,1,3] or [5,2,1,3].

Note: The length of path between two nodes is represented by the number of edges between them. 

路径未必经过root结点，

参考

1

2

34

5678

最长的跨度是第四层的结点之间，比如5和8的跨度是4，53248

经过观察可以发现，最大路径存在于，左子结点和右子结点之间。

比如上面第一个例子的34和35，

第二个例子根结点的右结点不存在

 还有一种情况

1

2

3

单层的，叶结点和根结点距离最大

https://www.geeksforgeeks.org/diameter-of-a-binary-tree/

The diameter of a tree T is the largest of the following quantities:

* the diameter of T’s left subtree
* the diameter of T’s right subtree
* the longest path between leaves that goes through the root of T (this can be computed from the heights of the subtrees of T)