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2737. Find the Closest Marked Node 👍

  • Time: $O((|V| + |E|)\log |V|)$
  • Space: $O(|E| + |V|)$
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class Solution {
 public:
  int minimumDistance(int n, vector<vector<int>>& edges, int s,
                      vector<int>& marked) {
    int ans = INT_MAX;
    vector<vector<pair<int, int>>> graph(n);

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

    const vector<int> dist = dijkstra(graph, s);

    for (const int u : marked)
      ans = min(ans, dist[u]);

    return ans == INT_MAX ? -1 : ans;
  }

 private:
  vector<int> dijkstra(const vector<vector<pair<int, int>>>& graph, int src) {
    vector<int> dist(graph.size(), INT_MAX);
    using P = pair<int, int>;  // (d, u)
    priority_queue<P, vector<P>, greater<>> minHeap;

    dist[src] = 0;
    minHeap.emplace(dist[src], src);

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

    return dist;
  }
};

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class Solution {
  public int minimumDistance(int n, List<List<Integer>> edges, int s, int[] marked) {
    int ans = Integer.MAX_VALUE;
    List<Pair<Integer, Integer>>[] graph = new List[n];

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

    for (List<Integer> edge : edges) {
      final int u = edge.get(0);
      final int v = edge.get(1);
      final int w = edge.get(2);
      graph[u].add(new Pair<>(v, w));
    }

    int[] dist = dijkstra(graph, s);

    for (final int u : marked)
      ans = Math.min(ans, dist[u]);

    return ans == Integer.MAX_VALUE ? -1 : ans;
  }

  private int[] dijkstra(List<Pair<Integer, Integer>>[] graph, int src) {
    int[] dist = new int[graph.length];
    Arrays.fill(dist, Integer.MAX_VALUE);
    // (d, u)
    Queue<Pair<Integer, Integer>> minHeap = new PriorityQueue<>(Comparator.comparing(Pair::getKey));

    dist[src] = 0;
    minHeap.offer(new Pair<>(dist[src], src));

    while (!minHeap.isEmpty()) {
      Pair<Integer, Integer> p = minHeap.poll();
      final int d = p.getKey();
      final int u = p.getValue();
      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));
        }
      }
    }

    return dist;
  }
}

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class Solution:
  def minimumDistance(self, n: int, edges: List[List[int]], s: int, marked: List[int]) -> int:
    graph = [[] for _ in range(n)]

    for u, v, w in edges:
      graph[u].append((v, w))

    dist = self._dijkstra(graph, s)
    ans = min(dist[u] for u in marked)
    return -1 if ans == math.inf else ans

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

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

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

    return dist