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].

思路：

求二叉树的高度，左子树的高度加上右子树的高度就为最大的直径。

int height(TreeNode* root, int& diameter)
     {
         if (root == NULL) return 0;
         int left = height(root->left, diameter);
         int right = height(root->right, diameter);
         diameter = max(diameter, left + right);
         return 1 + max(left, right);
     }
     int diameterOfBinaryTree(TreeNode* root)
     {
         int diameter = 0;
         height(root, diameter);
         return diameter;
     }

参考：

https://discuss.leetcode.com/topic/83569/543-diameter-of-binary-tree-c-_recursive_with-brief-explanation

[leetcode-543-Diameter of Binary Tree]