The Sum Root to Leaf Numbers interview question is a core problem in binary tree traversal. You are given a binary tree where each node contains a single digit from 0 to 9. Each root-to-leaf path in the tree represents a number. For example, if a path from root to leaf is 1 -> 2 -> 3, it represents the number 123. Your task is to calculate the total sum of all such numbers formed by every possible path from the root to the leaf nodes. This problem requires you to traverse the tree while maintaining the current number formed along the path.
This problem is a favorite for companies like Google, Microsoft, and Meta because it evaluates a candidate's ability to use recursion and tree traversal effectively. It tests whether you can pass and update state (the current number) through recursive calls. Beyond simple traversal, it requires a clear understanding of how leaf nodes are defined and how to combine results from multiple subtrees. Solving the Sum Root to Leaf Numbers coding problem demonstrates that you can think about data flow within a hierarchical structure.
The primary algorithmic pattern used is Depth-First Search (DFS) for Tree traversal. Specifically, a pre-order traversal is most natural here. As you move from a parent to a child, the current number is updated using the formula: current_number = parent_number * 10 + child_node_value. When a leaf node is reached, the accumulated number is added to the total sum. This pattern allows for an elegant recursive solution with a time complexity of O(n), where n is the number of nodes in the tree.
Imagine a small tree:
4
/
9 0
/
5
There are two root-to-leaf paths:
4 -> 9 -> 5 which forms the number 495.4 -> 0 which forms the number 40.
The total sum is 495 + 40 = 535.
During the DFS, we start at 4 (current=4). Moving to 9, we get 4*10 + 9 = 49. Moving to 5, we get 49*10 + 5 = 495. Since 5 is a leaf, we return 495. Then we explore the right child 0, getting 4*10 + 0 = 40. Since 0 is a leaf, we return 40.One frequent mistake is failing to correctly identify leaf nodes, sometimes adding the current sum at intermediate nodes that are not leaves. Another error is not handling the base case of an empty tree (returning 0). Some candidates also struggle with the logic of resetting or passing the state, which can lead to numbers from one branch "bleeding" into another if not using recursion or a proper stack correctly.
When preparing for the Sum Root to Leaf Numbers interview question, practice different types of DFS (pre-order, in-order, post-order) and understand when each is appropriate. Also, familiarize yourself with iterative tree traversal using a stack, as some interviewers might ask you to solve it without recursion to avoid stack overflow on very deep trees. Mastery of the Depth-First Search interview pattern is essential for any tree-based coding challenge.
| Title | Difficulty | Topics | LeetCode |
|---|---|---|---|
| Distribute Coins in Binary Tree | Medium | Solve | |
| Count Nodes Equal to Average of Subtree | Medium | Solve | |
| Binary Tree Pruning | Medium | Solve | |
| Flip Equivalent Binary Trees | Medium | Solve | |
| Binary Tree Longest Consecutive Sequence | Medium | Solve |