← Early-stage Startup Interview Insights
My first instinct was greedy: pick the node with the highest degree, mark it and its neighbors as covered, repeat.
Recognize this as the minimum dominating set problem on a graph, which is NP-hard in general. For an interview, discuss the NP-hardness and then propose a solution for special cases (e.g., trees) or a greedy approximation, while clarifying constraints with the interviewer.
Pro tip: Always clarify the graph's properties (e.g., is it a tree, planar, or general?) and the expected input size. This shows you understand that the approach depends on constraints and avoids over-engineering.
Ask about graph size, structure (tree, general graph), and whether an exact or approximate solution is needed. This determines the algorithmic approach.
Explain that a mail room covers itself and neighbors, so we need a minimum dominating set. Mention that this is NP-hard for general graphs.
If the graph is a tree, use dynamic programming or greedy algorithm. For general graphs, discuss approximation algorithms or exponential exact algorithms if small.
State the time and space complexity of your chosen approach. Discuss trade-offs between optimality and efficiency.
Walk through a simple example (e.g., a path or star graph) to verify the solution. Consider edge cases like disconnected graphs or isolated vertices.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.