題目：

Given a binary tree, find the length of the longest path where each node in the path has the same value. This path may or may not pass through the root.

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

Example 1:

Input:

              5
             / \
            4   5
           / \   \
          1   1   5

Output:

2

Example 2:

Input:

              1
             / \
            4   5
           / \   \
          4   4   5

Output:

2

Note:The given binary tree has not more than 10000 nodes. The height of the tree is not more than 1000.

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    private int max=0;
    public int longestUnivaluePath(TreeNode root) {
        //給定二叉樹，找出一條所有節點均為相同值的最長路徑。
        //思路：遞迴查詢是否同根節點相同。定義一個全域性變數
        //注意：遞迴返回最長的一邊，即單邊最大值
        if(root==null) return 0;
        backtrace(root);
        return max;
    }
    
    //遞迴
    public int backtrace(TreeNode root){
        int left=root.left!=null?backtrace(root.left):0;
        int right=root.right!=null?backtrace(root.right):0;
        //遞迴判斷是否根節點等於左右
        int resLeft=root.left!=null&&root.val==root.left.val?left+1:0;
        int resRight=root.right!=null&&root.val==root.right.val?right+1:0;
        
        max=Math.max(max,resLeft+resRight);
        //返回最長的一邊
        return Math.max(resLeft,resRight);
    }
}