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bnsf Railway·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jun 2026

Summary

Interviewed for a software engineering role at BNSF Railway and got hit with a graph traversal problem. Nothing too wild but it required knowing your BFS fundamentals cold.

Questions Asked (1)

Q1

Given an undirected unweighted graph with a set of source nodes and a set of target nodes, how would you compute the shortest distance from every node to its nearest source?

Algorithms & Data Structures
Author's notes

Multi-source BFS is the move here.

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AI HintsAI Generated

Suggested Approach

Use a multi-source BFS starting from all source nodes simultaneously, initializing distances to 0 for sources and infinity for others. Process nodes level by level, updating distances when a shorter path is found. This efficiently computes the shortest distance from each node to its nearest source in O(V+E) time.

Pro tip: Mention that multi-source BFS is optimal for unweighted graphs and can be implemented by enqueuing all sources initially. Also, discuss how to handle disconnected components by leaving distances as infinity.

1. Clarify the problem

Confirm that the graph is undirected and unweighted, and that we need the shortest distance from every node to its nearest source. Ask if there are any constraints on graph size or if multiple sources are allowed.

2. Choose the algorithm

Select multi-source BFS as the optimal approach because it handles multiple sources and unweighted edges efficiently. Explain why BFS is suitable for shortest paths in unweighted graphs.

3. Initialize data structures

Create a distance array initialized to infinity for all nodes, set distance to 0 for all source nodes, and enqueue all sources into a queue.

4. Perform BFS

While the queue is not empty, dequeue a node, and for each unvisited neighbor, set its distance to current distance + 1 and enqueue it. This ensures the first time a node is visited, it gets the shortest distance from any source.

5. Return results

After BFS completes, the distance array contains the shortest distance from each node to its nearest source. Nodes unreachable from any source remain at infinity.

Key Points to Mention

  • Multi-source BFS treats all sources as starting points at distance 0, effectively computing the shortest path from the set of sources.
  • Time complexity is O(V+E) for adjacency list representation, which is optimal for this problem.
  • Space complexity is O(V) for the distance array and queue.
  • Handling disconnected graphs: nodes not reachable from any source will have distance infinity.
  • Alternative approaches like running BFS from each source are less efficient (O(S*(V+E))) and unnecessary.
  • The algorithm naturally handles multiple sources and ensures the nearest source is found due to BFS's level-order traversal.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.