I recognized it as a graph depth problem pretty quickly but the string IDs threw me off at first.
Model the dependencies as a directed graph and use DFS with memoization to compute the longest path from each node, detecting cycles to avoid infinite loops. Return the maximum depth found, ensuring O(V+E) time complexity.
Pro tip: Explicitly mention cycle detection and how you handle it (e.g., marking nodes as visiting/visited) to show robustness, and discuss trade-offs between DFS and BFS (topological sort) for depth calculation.
Ask clarifying questions about input format, cycle presence, and depth definition. Model the dependencies as a directed graph where edges point from a node to its dependencies.
Select DFS with memoization to compute the longest path from each node, or BFS with topological sort if the graph is a DAG. Discuss trade-offs.
Implement cycle detection using a recursion stack or visited states. If a cycle exists, decide whether to throw an error or treat depth as infinite.
For each node, recursively compute the maximum depth of its dependencies and add 1. Use memoization to avoid redundant calculations.
State that the time complexity is O(V+E) and space complexity is O(V) for the recursion stack and memoization table.
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