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.

Solution:

/**
 * 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) {
        int dia = 0, height = 0;
        height = helper(root, dia);
        // Get edges from number of nodes.
        return dia > 1 ? dia  - 1: 0;
    }
   
    int helper(TreeNode *root, int& dia) {
        if (root == NULL) {
            return 0;
        }
        int left_height = 0, right_height = 0, left_dia = 0, right_dia = 0;
       
        left_height = helper(root -> left, left_dia);
        right_height = helper(root -> right, right_dia);
       
        dia = max(left_height + right_height + 1, max(left_dia, right_dia));
        return max(left_height, right_height) + 1;
    }
};