[leetcode] 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 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].

Note: The length of path between two nodes is represented by the number of edges between them.

---

分析：题目翻译一下：一个二叉树，要求找二叉树中最远的两个节点之间的距离，距离定义为路径上连边的个数。

两个点的距离，很容易想到最远的两个点肯定在某个树的左右子树上，因此想到计算树的高度。用res来保存以某个节点root为根节点的子树上最远的距离。DFS方法其实也就是对求树的高度算法的改变，还是很容易想到的，代码如下：

class Solution {
   int res = 0;
    public int diameterOfBinaryTree(TreeNode root) {
        if ( root == null ) return 0;
        helper(root);
        return res-1;
    }
    private int helper(TreeNode root) {
        if ( root == null ) return 0;
        int left_high = helper(root.left);
        int right_high = helper(root.right);
        res = Math.max(res,left_high+right_high+1);
//        System.out.println(root.val+"   "+res);
        return Math.max(left_high,right_high)+1;
    }
}

      我们以上面的例子来讲解一下代码的流程：

4   1
5   1
2   3
3   3
1   4

      13行的输出语句格式：第一列是遍历的节点，第二列是res值。可以看到从叶节点向上遍历，先左子树，后右子树。