Clarify the problem constraints (e.g., n, number of edges, whether the graph is guaranteed to be undirected and connected components are defined as maximal connected subgraphs). Then propose an efficient algorithm like Union-Find (Disjoint Set Union) or BFS/DFS, explaining the trade-offs. Walk through a small example to demonstrate correctness and analyze time/space complexity.
Pro tip: At Amazon, interviewers value scalability and practical trade-offs. Mention that Union-Find with path compression and union by rank is often preferred for dynamic graphs or when edges are streamed, while BFS/DFS is simpler for static graphs and may be more memory-efficient for sparse graphs.
Ask about input format, constraints (n, number of edges), whether the graph is connected, and if there are any edge cases like self-loops or duplicate edges.
Decide between Union-Find and BFS/DFS based on constraints and trade-offs. Explain why your choice is optimal for the given scenario.
Describe the steps of your chosen algorithm clearly, including initialization, processing edges or nodes, and counting components.
State the time and space complexity. For Union-Find, mention near O(E α(n)) time; for BFS/DFS, O(V+E) time and O(V) space.
Walk through a small graph to verify the algorithm and handle edge cases like isolated nodes or multiple components.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.