743. Network Delay Time

Medium

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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 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.)

class Solution:
    def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int:
        weights = {}
        d = defaultdict(list)
        for source, destination, weight in times:
            d[source].append((destination, weight))
        q = [(0,k)]
        heapq.heapify(q)
        while q:
            time, node = heapq.heappop(q)
            if node not in weights:
                weights[node] = time
                for adj, w in d[node]:
                    heapq.heappush(q, (time + w, adj))
        return max(weights.values()) if len(weights) == n else -1