> For the complete documentation index, see [llms.txt](https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/tree/129.-sum-root-to-leaf-numbers.md).

# 129. 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.

**Note:** A leaf is a node with no children.

**Example:**

```
Input: [1,2,3]
    1
   / \
  2   3
Output: 25
Explanation:
The root-to-leaf path 1->2 represents the number 12.
The root-to-leaf path 1->3 represents the number 13.
Therefore, sum = 12 + 13 = 25.
```

**Example 2:**

```
Input: [4,9,0,5,1]
    4
   / \
  9   0
 / \
5   1
Output: 1026
Explanation:
The root-to-leaf path 4->9->5 represents the number 495.
The root-to-leaf path 4->9->1 represents the number 491.
The root-to-leaf path 4->0 represents the number 40.
Therefore, sum = 495 + 491 + 40 = 1026.
```

```cpp
// Preorder traversal
void helper(TreeNode* node, int cur, int& res) {
    if (!node) return;
    cur = cur * 10 + node->val;
    if (!node->left && !node->right) {
        res += cur;
        return;
    }
    helper(node->left, cur, res);
    helper(node->right, cur, res);
}
int sumNumbers(TreeNode* root) { // time: O(n); space: O(n)
    if (!root) return 0;
    int res = 0;
    helper(root, 0, res);
    return res;
}
```