Network Recovery Pathways

Given a directed acyclic graph with weighted edges and some offline nodes, find a path from 0 to n−1 whose intermediate nodes are all online and whose total edge cost ≤ k, and return the maximum possible path score defined as the minimum edge cost along the path (or −1 if no valid path exists). The core challenge is maximizing the path bottleneck (minimum edge weight) under a global cost budget on a DAG with node-availability constraints.