543. 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 longestpath 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].

Analysis:
The possible diameter is the node's left max depth + node's right max depth.

Solution:

class Solution {
    int max;
    public int diameterOfBinaryTree(TreeNode root) {
        if (root == null) return 0;
        max = Integer.MIN_VALUE;
        depth(root);
        return max;
    }
    
    private int depth(TreeNode root) {
        if (root == null) return 0;
        int left = depth(root.left);
        int right = depth(root.right);
        max = Math.max(left + right, max);
        return Math.max(left, right) + 1;
    }
}