Bloomberg·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Bloomberg technical screen focused on graph algorithms, specifically DAG traversal and path computation. The question had layers to it and pushed toward optimization in a way I wasn't fully ready for.

Questions Asked (1)

Given a directed acyclic graph with weighted edges and a source node, compute either the number of distinct paths from the source to each node, or the minimum total edge cost to reach each node (returning infinity if unreachable). How do you optimize beyond naive DFS?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I started with brute-force DFS and they let me finish before asking about performance on large graphs.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem: DAG with weighted edges, source node, and two possible computations (path count or min cost). Explain that naive DFS is exponential due to overlapping subproblems, then propose topological sort to process nodes in linear order, using DP to accumulate results. Discuss time and space complexity, and mention edge cases like unreachable nodes and zero-weight edges.

Pro tip: Emphasize that topological sort ensures each node is processed after all its predecessors, eliminating redundant work and enabling O(V+E) time. Mention that for path counting, use modulo if numbers can be huge, and for min cost, initialize distances to infinity and relax edges.

1. Clarify the problem and constraints

Confirm whether to compute path count or min cost, and note that the graph is a DAG with weighted edges. Ask about potential large numbers, negative weights, and unreachable nodes.

2. Identify inefficiency of naive DFS

Explain that naive DFS explores all paths, leading to exponential time due to overlapping subproblems. For example, a diamond-shaped DAG causes repeated computations.

3. Propose topological sort + DP

Use Kahn's algorithm or DFS-based topological sort to order nodes. Then process nodes in topological order, using DP to compute either the number of paths or minimum cost from the source.

4. Define DP recurrence and initialization

For path count: initialize count[source]=1, others 0; for each edge u->v, count[v] += count[u]. For min cost: initialize dist[source]=0, others infinity; for each edge u->v, dist[v] = min(dist[v], dist[u] + weight).

5. Analyze complexity and edge cases

Time O(V+E), space O(V+E). Handle unreachable nodes (infinity or 0 paths), zero-weight edges, and large path counts with modulo if needed.

Key Points to Mention

Topological sort ensures linear processing order and avoids redundant computations.
DP recurrence for path counting: sum of paths from predecessors.
DP recurrence for min cost: relaxation of edges from predecessors.
Time and space complexity: O(V+E) vs exponential for naive DFS.
Handling unreachable nodes: return infinity for min cost, 0 for path count.
Potential need for modulo when counting paths due to large numbers.

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