Find max-score path in weighted DAG

Q: Find max-score path in weighted DAG

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Question

You are given a directed acyclic graph (DAG). Each node v has a score w(v). Each directed edge (u→v) has a nonnegative time cost t(u,v). There is a unique start node literally named "start" with w(start)=0. A terminal node is any node whose name begins with an underscore "_". You may traverse edges only in their given direction. For any path P from "start" to any terminal node, define its total score as Score(P) = (sum of w(v) over all nodes v on P) − (sum of t(u,v) over all edges on P). Compute the maximum Score(P) across all such paths and return both this maximum value and one corresponding optimal path (as an ordered list of node names). If no terminal is reachable from "start", indicate that no feasible path exists. Describe your algorithm and analyze its time and space complexity.

Find max-score path in weighted DAG

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