543.Diameter of Binary Tree

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。

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int diameterOfBinaryTree(TreeNode* root) 
    {
      res = 1;
      treeDepth(root);
      return res - 1;
    }
    int treeDepth(TreeNode* node)
    {
      if(node == nullptr)
        return 0;
      int L = treeDepth(node->left);
      int R = treeDepth(node->right);
      res = max(res,L+R+1);
      return max(L,R)+1;
    }
  private:
  int res;
};