Microsoft·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Microsoft SWE interview with a graph traversal problem that's basically a TSP variant. Pretty classic bitmask DP territory if you recognize what it is, which is the whole challenge.

Questions Asked (1)

Given a weighted graph, a starting node, and a set of required nodes, find the minimum total distance for a tour that starts at the origin, visits all required nodes at least once, and returns to the origin.

Algorithms & Data Structures

Author's notes

The second I saw 'visit all required nodes and return to start' I knew it was TSP-flavored but blanked on the exact DP formulation for a bit.

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AI HintsAI Generated

Suggested Approach

This is a variant of the Traveling Salesman Problem with optional intermediate nodes. The optimal strategy is to compute all-pairs shortest paths between the origin and required nodes, then solve the TSP on the reduced metric graph using dynamic programming (Held-Karp algorithm).

Pro tip: Mention that the problem is NP-hard, so for large inputs you'd need approximation or heuristic approaches, but for typical interview constraints the DP solution is expected. Also, clarify edge cases like unreachable required nodes.

1. Clarify problem constraints

Ask about graph size, whether edges are directed or undirected, if weights are non-negative, and if all required nodes are reachable. This shows attention to detail.

2. Reduce to metric TSP

Compute shortest paths from origin to all required nodes and between all pairs of required nodes using Dijkstra's algorithm (or Floyd-Warshall for dense graphs). This creates a complete graph on the required nodes plus origin with metric distances.

3. Apply dynamic programming (Held-Karp)

Use bitmask DP where state is (current node, set of visited required nodes). Transition by adding an unvisited required node, and finally return to origin. This gives optimal tour in O(2^k * k^2) time where k is number of required nodes.

4. Analyze complexity and alternatives

Discuss time and space complexity, and mention that for large k, approximation algorithms like Christofides or heuristics (nearest neighbor, 2-opt) may be needed.

5. Handle edge cases

Consider cases where a required node is unreachable, or when there are no required nodes (return 0). Also, if multiple required nodes are the same, deduplicate.

Key Points to Mention

All-pairs shortest paths (Dijkstra/Floyd-Warshall) to reduce graph
Held-Karp dynamic programming with bitmasking
Time complexity O(2^k * k^2) and space O(2^k * k)
NP-hardness of TSP and implications for large inputs
Approximation algorithms (e.g., Christofides) for large instances
Edge cases: unreachable nodes, no required nodes, duplicate required nodes

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