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.

time: O(n^2)　　-- worst case, space: O(n)

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public int diameterOfBinaryTree(TreeNode root) {
        if(root == null) {
            return 0;
        }
        int d = depth(root.left) + depth(root.right);
        int left = diameterOfBinaryTree(root.left);
        int right = diameterOfBinaryTree(root.right);
        
        return Math.max(d, Math.max(left, right));
    }
    
    public int depth(TreeNode node) {
        if(node == null) {
            return 0;
        }
        return 1 + Math.max(depth(node.left), depth(node.right));
    }
}

optimized:

time: O(n)　　-- post order traverse, visited each node once,

space: O(height)

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    int max = 1;
    
    public int diameterOfBinaryTree(TreeNode root) {
        maxDiamter(root);
        return max - 1;
    }
    
    public int maxDiamter(TreeNode node) {
        if (node == null) {
            return 0;
        }
        int left = maxDiamter(node.left);
        int right = maxDiamter(node.right);

        max = Math.max(max, left + right + 1);
        return 1 + Math.max(left, right);
    }
}