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Network Delay Time

Detailed guide and Python implementation for the 'Network Delay Time' problem.

Problem Statement

Easy

You are given a network of n nodes, labeled from 1 to n. You are also given times, a list of travel times as directed edges times[i] = [ui, vi, wi], where ui is the source node, vi is the target node, and wi is the time it takes for a signal to travel from source to target.

We will send a signal from a given node k. Return the minimum time it takes for all the n nodes to receive the signal. If it is impossible for all the n nodes to receive the signal, return -1.

Write a function networkDelayTime(times: List[List[int]], n: int, k: int) -> int.

Constraints
  • 1 <= k <= n <= 100
  • 1 <= len(times) <= 6000
  • times[i].length == 3
  • 1 <= ui, vi <= n
  • ui != vi
  • 0 <= wi <= 100
  • All the pairs (ui, vi) are unique

Examples

Example 1
Input
times = [[2,1,1],[2,3,1],[3,4,1]], n = 4, k = 2
Output
2
Explanation

The signal starts at node 2. It reaches 1 and 3 in 1 unit of time, and 4 in 2 units of time.

Example 2
Input
times = [[1,2,1]], n = 2, k = 1
Output
1
Explanation

Signal reaches node 2 from node 1 in 1 unit of time.

Example 3
Input
times = [[1,2,1]], n = 2, k = 2
Output
-1
Explanation

Signal starts at node 2, but there is no path from node 2 to node 1. So node 1 never receives it.

Need a Hint?
Consider using Advanced Graphs-specific data structures like sets or heaps.
Edge Cases to Watch
  • Empty input structures
  • Single element inputs
  • Large numerical bounds

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