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743. Network Delay Time 👍

  • Time: $O((|V| + |E|)\log |V|)$
  • Space: $O(|V| + |E|)$
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class Solution {
 public:
  int networkDelayTime(vector<vector<int>>& times, int n, int k) {
    vector<vector<pair<int, int>>> graph(n);

    for (const vector<int>& time : times) {
      const int u = time[0] - 1;
      const int v = time[1] - 1;
      const int w = time[2];
      graph[u].emplace_back(v, w);
    }

    return dijkstra(graph, k - 1);
  }

 private:
  int dijkstra(const vector<vector<pair<int, int>>>& graph, int src) {
    vector<int> dist(graph.size(), INT_MAX);

    dist[src] = 0;
    using P = pair<int, int>;  // (d, u)
    priority_queue<P, vector<P>, greater<>> minHeap;
    minHeap.emplace(dist[src], src);

    while (!minHeap.empty()) {
      const auto [d, u] = minHeap.top();
      minHeap.pop();
      if (d > dist[u])
        continue;
      for (const auto& [v, w] : graph[u])
        if (d + w < dist[v]) {
          dist[v] = d + w;
          minHeap.emplace(dist[v], v);
        }
    }

    const int maxDist = ranges::max(dist);
    return maxDist == INT_MAX ? -1 : maxDist;
  }
};

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class Solution {
  public int networkDelayTime(int[][] times, int n, int k) {
    List<Pair<Integer, Integer>>[] graph = new List[n];

    for (int i = 0; i < n; i++)
      graph[i] = new ArrayList<>();

    for (int[] time : times) {
      final int u = time[0] - 1;
      final int v = time[1] - 1;
      final int w = time[2];
      graph[u].add(new Pair<>(v, w));
    }

    return dijkstra(graph, k - 1);
  }

  private int dijkstra(List<Pair<Integer, Integer>>[] graph, int src) {
    int[] dist = new int[graph.length];
    Arrays.fill(dist, Integer.MAX_VALUE);

    dist[src] = 0;
    Queue<Pair<Integer, Integer>> minHeap =
        new PriorityQueue<>(Comparator.comparing(Pair::getKey)) {
          { offer(new Pair<>(dist[src], src)); } // (d, u)
        };

    while (!minHeap.isEmpty()) {
      final int d = minHeap.peek().getKey();
      final int u = minHeap.poll().getValue();
      if (d > dist[u])
        continue;
      for (Pair<Integer, Integer> pair : graph[u]) {
        final int v = pair.getKey();
        final int w = pair.getValue();
        if (d + w < dist[v]) {
          dist[v] = d + w;
          minHeap.offer(new Pair<>(dist[v], v));
        }
      }
    }

    final int maxDist = Arrays.stream(dist).max().getAsInt();
    return maxDist == Integer.MAX_VALUE ? -1 : maxDist;
  }
}

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class Solution:
  def networkDelayTime(self, times: list[list[int]], n: int, k: int) -> int:
    graph = [[] for _ in range(n)]

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

    return self._dijkstra(graph, k - 1)

  def _dijkstra(self, graph: list[list[tuple[int, int]]], src: int) -> int:
    dist = [math.inf] * len(graph)

    dist[src] = 0
    minHeap = [(dist[src], src)]  # (d, u)

    while minHeap:
      d, u = heapq.heappop(minHeap)
      if d > dist[u]:
        continue
      for v, w in graph[u]:
        if d + w < dist[v]:
          dist[v] = d + w
          heapq.heappush(minHeap, (dist[v], v))

    maxDist = max(dist)
    return maxDist if maxDist != math.inf else -1