Sum Numbers Formed by Root-to-Leaf Paths

Question

This question asks the candidate to calculate the sum of numbers formed by all root-to-leaf paths in a binary tree.

Codemia · Accepted Answer

To solve the problem of summing numbers formed by root-to-leaf paths, we can use a depth-first search (DFS) approach. As we traverse the tree, we maintain a running total that represents the number formed by the path from the root to the current node. When we reach a leaf node, we add the total to our final sum.

We can implement the algorithm using a recursive function that takes the current node and the current number as parameters. The base case will handle the leaf nodes, while the recursive case will continue traversing left and right children. Here's a Python implementation:

```python
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

class Solution:
    def sumNumbers(self, root: TreeNode) -> int:
        def dfs(node, current_number):
            if not node:
                return 0
            current_number = current_number * 10 + node.val
            if not node.left and not node.right:
                return current_number
            return dfs(node.left, current_number) + dfs(node.right, current_number)

return dfs(root, 0)
```
This code defines a TreeNode class and a Solution class with the `sumNumbers` method that initializes the DFS traversal.

The time complexity of this algorithm is O(N), where N is the number of nodes in the binary tree, as we visit each node exactly once. The space complexity is O(H), where H is the height of the tree, due to the recursion stack. In the worst case (a skewed tree), this could be O(N), but for a balanced tree, it would be O(log N).

It is important to consider edge cases such as an empty tree, where the sum should be 0. Additionally, if the tree consists of a single node, the sum should simply be the value of that node. These cases should be handled in the implementation to ensure robustness.

Interviewers will look for clarity in your explanation and code, as well as your ability to think through edge cases. They may also assess your understanding of recursion and tree traversal techniques. Demonstrating a structured thought process and the ability to discuss time and space complexity will strengthen your response.

Sum Numbers Formed by Root-to-Leaf Paths

Meta

What the Interviewer Expects

Key Topics to Cover

How to Approach This

Possible Follow-up Questions

Sharpen Your Skills on Codemia

Sample Answer

Approach

Algorithm

Submit Your Answer

Meta Software Engineer Interview Guide

Related Questions

Binary Search on graph

Count kth largest element in array

Find connected components in string

Merge Three Sorted strings

Binary Search on string