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.

方法1：（這是一個深度優先的演算法）

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    int  maxDiameter= 1;
    public int diameterOfBinaryTree(TreeNode root) {
        depth(root);
        // 兩次都算了頂點，要進行減1操作
        return maxDiameter- 1;
    }
    public int depth(TreeNode node) {
        if (node == null) return 0;
        // 遍歷左右子樹的最大高度
        int L = depth(node.left);
        int R = depth(node.right);
        // 不斷去更新maxDiameter的值，使他最大化
        maxDiameter= Math.max(maxDiameter, L+R+1);
        return Math.max(L, R) + 1;
    }
}
 

時間複雜度：O(n^2)

空間複雜度：O(n)