How would you modify this solution for a very large binary tree, like a distributed system where each part of the tree is on different servers?

Interviewee: For a distributed system, we’d need to divide the tree into parts and process each part concurrently. Each server could handle traversal for its subtree and communicate the results back to a central system that aggregates the level order lists.

We’d also need to ensure proper synchronization between servers, as they may finish processing at different times. A message-passing system or a distributed queue could help manage the traversal between different parts of the tree.

Interviewer: Interesting. How would you handle balancing the workload across servers?

Interviewee: I would start by distributing the workload based on tree size. We could estimate the number of nodes in each subtree and allocate more resources to larger subtrees. Alternatively, we could divide the tree breadth-wise, so each level of the tree is handled independently by different servers, which might better distribute the workload.

Interviewer: That’s a good approach. One final question—how would you handle errors in a distributed system like this, such as a server going down?

Interviewee: If a server goes down, we could implement retries for the part of the tree that server was processing. We’d keep track of which nodes have been processed and which haven’t, so that another server could take over the failed part. We could also store the state of each server periodically so that in case of failure, recovery would be easier.