Diameter of Binary Tree

Problem

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

Tail-Recursive Solution

public class Solution {

    int max = 0;
    public int diameterOfBinaryTree(TreeNode root) {
        helper(root);
        return max;
    }

    private int helper(TreeNode node) {
        if (node == null) return 0;
        int left = helper(node.left);
        int right = helper(node.right);
        max = Math.max(left + right, max);
        return Math.max(left, right) + 1; //For each node, we return only one longest path plus one 
    }
}

Solution

In the recursive method, we visit each node in pre-order traversal(root, left, right)
Then we update our max if we find left + right > max
At the end, we return the longer path of current node with adding one