Sum Root to Leaf Numbers

Given a binary tree containing digits from 0-9 only, each root-to-leaf path could represent a number.

An example is the root-to-leaf path 1->2->3 which represents the number 123.

Find the total sum of all root-to-leaf numbers.

For example,

    1
   / \
  2   3

The root-to-leaf path 1->2 represents the number 12.
The root-to-leaf path 1->3 represents the number 13.

Return the sum = 12 + 13 = 25.

Solution: Recursion. Similar as [LeetCode] Binary Tree Maximum Path Sum Solution, the difference here is only adding a track variable to sum all the paths.

问题处理：

1 分情况就是: (1)空节点, (2)到了叶子节点, (3)一般节点（包括只有左孩子，只有右孩子，两个孩子都有）

2 递归到该点的时候就把这点的值与前面的值乘以10，然后相加

3 需要如何保存前面的值？以参数传递的方式保存，以供下一层使用。总值可以以两种方式保存：参数传递方式，返回函数值方式。
算法的本质是一次先序遍历，所以时间是O(n)，空间是栈大小，O(logn)。

/**
 * Definition for binary tree
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public int sumNumbers(TreeNode root) {
        return helper(root, 0);
    }
    
    public int helper(TreeNode root, int sum) {
        if(root == null) { //terminate condition, root == null, just return 0
            return 0;
        }
        
        if(root.left == null && root.right == null) { //terminate condition, if root == leaf, add the value to sum and return
            return sum * 10 + root.val;
        }
            
        return helper(root.left, sum*10+root.val) + helper(root.right, sum*10+root.val);
        
    }
}