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.

思路

这个问题可以分两个方面来考虑： 
1. 最长路径经过根节点：那么根节点的左子树的深度和右子树的深度就是我们的结果 
2. 最长路径没有经过根节点：这个问题就分为两个子问题，分别设置新的根节点为其左子节点和右子节点，然后重复步骤 1

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