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743. Network Delay Time

Difficulty Topics

Description

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.

 

Example 1:

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

Example 2:

Input: times = [[1,2,1]], n = 2, k = 1
Output: 1

Example 3:

Input: times = [[1,2,1]], n = 2, k = 2
Output: -1

 

Constraints:

  • 1 <= k <= n <= 100
  • 1 <= times.length <= 6000
  • times[i].length == 3
  • 1 <= ui, vi <= n
  • ui != vi
  • 0 <= wi <= 100
  • All the pairs (ui, vi) are unique. (i.e., no multiple edges.)

Solution

network-delay-time.py
class Solution:
    def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int:
        weights = [float('inf')] * n
        weights[k - 1] = 0
        graph = defaultdict(list)

        for u, v, w in times:
            u -= 1
            v -= 1
            graph[u].append((v, w))

        pq = [(0, k - 1)]

        while pq:
            weight, node = heappop(pq)

            if weights[node] != weight: continue

            for nei, w in graph[node]:
                old = weights[nei]
                new = weight + w

                if new < old:
                    weights[nei] = new
                    heappush(pq, (new, nei))

        ans = max(weights)

        return -1 if ans == float('inf') else ans