I knew DFS was the right move but fumbled a bit on where to add memoization.
Clarify the problem and edge cases, then explain that the longest path in a DAG can be found using dynamic programming with topological sorting or DFS with memoization. Write clean Python code, analyze time and space complexity, and test with examples.
Pro tip: Mention that the graph is a DAG, so no cycles, and that topological order ensures we process nodes in dependency order. Also, note that the longest path can be computed in O(V+E) time, which is optimal.
Confirm that the adjacency list represents a DAG, that path length is the number of nodes, and that the graph may be disconnected. Ask about input size and edge cases.
Decide between topological sort with DP or DFS with memoization. Both are O(V+E). Explain the chosen method and why it works for DAGs.
Write Python code for the chosen approach. For topological sort, compute in-degrees, use a queue, and update distances. For DFS, use recursion with memoization to compute the longest path from each node.
State that time complexity is O(V+E) and space complexity is O(V+E) for storing the graph and auxiliary arrays. Mention that this is optimal for this problem.
Walk through a small example, including a disconnected graph, to verify correctness. Discuss potential pitfalls like recursion depth and handling of isolated nodes.
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