Given a binary tree, you need to compute the length of the diameter of the tree. The diameter of a binary tree is the length of the longest path between any two nodes in a tree. This path may or may not pass through the root.

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.

思路：其实所谓的二叉树的“直径”其实就是节点左右子树的最大深度和，而现在需要求出这个和的最大值。在递归求二叉树的深度时，记录下当前每个节点的深度，比较出最大值即可。

 1 /**
 2  * Definition for a binary tree node.
 3  * struct TreeNode {
 4  *     int val;
 5  *     TreeNode *left;
 6  *     TreeNode *right;
 7  *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 8  * };
 9  */
10 class Solution {
11 public:
12     int diameterOfBinaryTree(TreeNode* root) 
13     {
14       res = 1;
15       treeDepth(root);
16       return res - 1;
17     }
18     int treeDepth(TreeNode* node)
19     {
20       if(node == nullptr)
21         return 0;
22       int L = treeDepth(node->left);
23       int R = treeDepth(node->right);
24       res = max(res,L+R+1);
25       return max(L,R)+1;
26     }
27   private:
28   int res;
29 };