給定一個非空二叉樹，返回其最大路徑和。

本題中，路徑被定義為一條從樹中任意節點出發，達到任意節點的序列。該路徑至少包含一個節點，且不一定經過根節點。

示例 1:

輸入: [1,2,3]

       1
      / \
     2   3

輸出: 6

示例 2:

輸入: [-10,9,20,null,null,15,7]

   -10
   / \
  9  20
    /  \
   15   7

輸出: 42

Java程式碼：

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public int maxSum = Integer.MIN_VALUE;
    public int maxPathSum(TreeNode root) {
        if(null == root)
            return 0;
        dfs(root);
        return maxSum;
    }
    private int dfs(TreeNode root){
        if(null == root)
            return 0;

        int curVal = root.val, leftSum = dfs(root.left), rightSum = dfs(root.right);
        if(0 < leftSum)
            curVal += leftSum;
        if(0 < rightSum)
            curVal += rightSum;
        maxSum = Math.max(maxSum, curVal);
        return Math.max(root.val, Math.max(root.val+leftSum, root.val+rightSum));
    }
}