Took me a second to not just reach for Dijkstra out of habit.
Model the problem as a longest path in a directed graph with node weights and edge costs, which is NP-hard in general due to positive cycles. Clarify with the interviewer whether the graph is a DAG or if cycles are allowed; if a DAG, use dynamic programming with topological order; if cycles exist, discuss the implications and potential approaches like Bellman-Ford for longest paths with cycle detection or heuristics.
Pro tip: Always ask clarifying questions about graph properties (e.g., cycles, negative edges) before diving into a solution—this shows you understand the problem's complexity and can adapt your approach based on constraints.
Ask about graph size, whether it's a DAG, if cycles are allowed, and if rewards/costs can be negative. This determines the algorithmic approach.
Recognize that this is a longest path problem with node weights and edge costs. In general graphs, it's NP-hard if positive cycles exist; in DAGs, it's solvable in linear time.
For DAGs, use topological sort and DP to compute max score to each node. For general graphs, discuss Bellman-Ford for longest paths with cycle detection, or if cycles are positive, the answer may be infinite.
Define dp[v] as max score to reach v. Initialize dp[start] = reward[start]. For each edge u->v, dp[v] = max(dp[v], dp[u] + reward[v] - cost(u,v)). The answer is max dp[end] over all end nodes.
Discuss time/space complexity (O(V+E) for DAG, O(VE) for Bellman-Ford). Handle unreachable end nodes, negative scores, and cycles that may cause infinite scores.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.