743. Network Delay Time

743. Network Delay Time (Medium)

There are N network nodes, labelled 1 to N.

Given times, a list of travel times as directed edges times[i] = (u, v, w), where u is the source node, v is the target node, and w is the time it takes for a signal to travel from source to target.

Now, we send a signal from a certain node K. How long will it take for all nodes to receive the signal? If it is impossible, return -1.

 

Example 1:

Input: times = [[2,1,1],[2,3,1],[3,4,1]], N = 4, K = 2
Output: 2

 

Note:

1. N will be in the range [1, 100].
2. K will be in the range [1, N].
3. The length of times will be in the range [1, 6000].
4. All edges times[i] = (u, v, w) will have 1 <= u, v <= N and 0 <= w <= 100.

Related Topics:
Heap, Depth-first Search, Breadth-first Search, Graph

Solution 1. Dijkstra

// OJ: https://leetcode.com/problems/network-delay-time/
// Author: github.com/lzl124631x
// Time: O(E + VlogV)
// Space: O(E)
class Solution {
    typedef pair<int, int> iPair;
    typedef unordered_map<int, vector<iPair>> Graph;
    vector<int> dijkstra(Graph &graph, int N, int source) {
        priority_queue<iPair, vector<iPair>, greater<>> pq;
        vector<int> dist(N, INT_MAX);
        pq.emplace(0, source);
        dist[source] = 0;
        while (pq.size()) {
            auto [w, u] = pq.top();
            pq.pop();
            if (w > dist[u]) continue;
            for (auto &[v, c] : graph[u]) {
                if (dist[v] > w + c) {
                    dist[v] = w + c;
                    pq.emplace(dist[v], v);
                }
            }
        }
        return dist;
    }
public:
    int networkDelayTime(vector<vector<int>>& times, int N, int K) {
        Graph graph;
        for (auto e : times) graph[e[0] - 1].emplace_back(e[1] - 1, e[2]);
        auto dist = dijkstra(graph, N, K - 1);
        int mx = *max_element(begin(dist), end(dist)); 
        return mx == INT_MAX ? -1 : mx;
    }
};

Solution 2. Bellman-Ford

// OJ: https://leetcode.com/problems/network-delay-time/
// Author: github.com/lzl124631x
// Time: O(VE)
// Space: O(V)
class Solution {
    vector<int> bellmanFord(vector<vector<int>>& edges, int V, int src) {
        vector<int> dist(V, INT_MAX);
        dist[src - 1] = 0;
        for (int i = 1; i < V; ++i) {
            for (auto &e : edges) {
                int u = e[0] - 1, v = e[1] - 1, w = e[2];
                if (dist[u] == INT_MAX) continue;
                dist[v] = min(dist[v], dist[u] + w);
            }
        }
        return dist;
    }
public:
    int networkDelayTime(vector<vector<int>>& times, int N, int K) {
        auto dist = bellmanFord(times, N, K);
        int ans = *max_element(dist.begin(), dist.end());
        return ans == INT_MAX ? -1 : ans;
    }
};