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How to Solve Network Recovery Pathways Problem
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Hard#3620
LeetCode ProblemNetwork Recovery Pathways
You are given a directed acyclic graph of n nodes numbered from 0 to n − 1. This is represented by a 2D array edges of length m, where edges[i] = [ui, vi, costi] indicates a one‑way communication from node ui to node vi with a recovery cost of costi. Some nodes may be offline. You are given a boolean array online where online[i] = true means node i is online. Nodes 0 and n − 1 are always online. A path from 0 to n − 1 is valid if: For each valid path, define its score as the minimum edge‑cost along that path. Return the maximum path score (i.e., the largest minimum-edge cost) among all valid paths. If no valid path exists, return -1.
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Problem Breakdown
Understanding the Network Recovery Pathways Problem
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Problem Statement
You are given a directed acyclic graph of n nodes numbered from 0 to n − 1. This is represented by a 2D array edges of length m, where edges[i] = [ui, vi, costi] indicates a one‑way communication from node ui to node vi with a recovery cost of costi. Some nodes may be offline. You are given a boolean array online where online[i] = true means node i is online. Nodes 0 and n − 1 are always online. A path from 0 to n − 1 is valid if: For each valid path, define its score as the minimum edge‑cost along that path. Return the maximum path score (i.e., the largest minimum-edge cost) among all valid paths. If no valid path exists, return -1.
HardProblem #3620
LeetCodeNetwork Recovery Pathways
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Examples
# Example 1
Input
edges = [[0,1,5],[1,3,10],[0,2,3],[2,3,4]], online = [true,true,true,true], k = 10
Output
3
# Example 2
Input
edges = [[0,1,7],[1,4,5],[0,2,6],[2,3,6],[3,4,2],[2,4,6]], online = [true,true,true,false,true], k = 12
Output
6
Constraints
n == online.length
2 <= n <= 5 * 104
0 <= m == edges.length <= min(105, n * (n - 1) / 2)
edges[i] = [ui, vi, costi]
0 <= ui, vi < n
ui != vi
0 <= costi <= 109
0 <= k <= 5 * 1013
online[i] is either true or false, and both online[0] and online[n − 1] are true.
The given graph is a directed acyclic graph.
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Solve Network Recovery Pathways — You are given a directed acyclic graph of n nodes numbered from 0 to n − 1. This...
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