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.

//Will the root be NULL?
//Will the result be very large? Exceed 2^23?
//Will root be 0?

//DFS algorithm, preorder traversal
/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int sumNumbers(TreeNode* root) {
        return _sumNumbers(root, 0);
    }
    int _sumNumbers(TreeNode * root, int preNumber){
    
        if(root == NULL) return 0;
    
        //leaf node
        if(root->left == NULL && root->right == NULL){
            return preNumber * 10 + root->val;
        }
        
        //non-leaf node
        return _sumNumbers(root->left, preNumber * 10 + root->val) + _sumNumbers(root->right, preNumber * 10 + root->val);
    }
};