Skip to content

3112. Minimum Time to Visit Disappearing Nodes

Description

There is an undirected graph of n nodes. You are given a 2D array edges, where edges[i] = [ui, vi, lengthi] describes an edge between node ui and node vi with a traversal time of lengthi units.

Additionally, you are given an array disappear, where disappear[i] denotes the time when the node i disappears from the graph and you won't be able to visit it.

Note that the graph might be disconnected and might contain multiple edges.

Return the array answer, with answer[i] denoting the minimum units of time required to reach node i from node 0. If node i is unreachable from node 0 then answer[i] is -1.

 

Example 1:

Input: n = 3, edges = [[0,1,2],[1,2,1],[0,2,4]], disappear = [1,1,5]

Output: [0,-1,4]

Explanation:

We are starting our journey from node 0, and our goal is to find the minimum time required to reach each node before it disappears.

  • For node 0, we don't need any time as it is our starting point.
  • For node 1, we need at least 2 units of time to traverse edges[0]. Unfortunately, it disappears at that moment, so we won't be able to visit it.
  • For node 2, we need at least 4 units of time to traverse edges[2].

Example 2:

Input: n = 3, edges = [[0,1,2],[1,2,1],[0,2,4]], disappear = [1,3,5]

Output: [0,2,3]

Explanation:

We are starting our journey from node 0, and our goal is to find the minimum time required to reach each node before it disappears.

  • For node 0, we don't need any time as it is the starting point.
  • For node 1, we need at least 2 units of time to traverse edges[0].
  • For node 2, we need at least 3 units of time to traverse edges[0] and edges[1].

Example 3:

Input: n = 2, edges = [[0,1,1]], disappear = [1,1]

Output: [0,-1]

Explanation:

Exactly when we reach node 1, it disappears.

 

Constraints:

  • 1 <= n <= 5 * 104
  • 0 <= edges.length <= 105
  • edges[i] == [ui, vi, lengthi]
  • 0 <= ui, vi <= n - 1
  • 1 <= lengthi <= 105
  • disappear.length == n
  • 1 <= disappear[i] <= 105

Solutions

Solution 1: Heap-Optimized Dijkstra

First, we create an adjacency list $\textit{g}$ to store the edges of the graph. Then, we create an array $\textit{dist}$ to store the shortest distances from node $0$ to other nodes. Initialize $\textit{dist}[0] = 0$, and the distances for the rest of the nodes are initialized to infinity.

Next, we use the Dijkstra algorithm to calculate the shortest distances from node $0$ to other nodes. The specific steps are as follows:

  1. Create a priority queue $\textit{pq}$ to store the distances and node numbers. Initially, add node $0$ to the queue with a distance of $0$.
  2. Remove a node $u$ from the queue. If the distance $du$ of $u$ is greater than $\textit{dist}[u]$, it means $u$ has already been updated, so we skip it directly.
  3. Iterate through all neighbor nodes $v$ of node $u$. If $\textit{dist}[v] > \textit{dist}[u] + w$ and $\textit{dist}[u] + w < \textit{disappear}[v]$, then update $\textit{dist}[v] = \textit{dist}[u] + w$ and add node $v$ to the queue.
  4. Repeat steps 2 and 3 until the queue is empty.

Finally, we iterate through the $\textit{dist}$ array. If $\textit{dist}[i] < \textit{disappear}[i]$, then $\textit{answer}[i] = \textit{dist}[i]$; otherwise, $\textit{answer}[i] = -1$.

The time complexity is $O(m \times \log m)$, and the space complexity is $O(m)$. Here, $m$ is the number of edges.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
class Solution:
    def minimumTime(
        self, n: int, edges: List[List[int]], disappear: List[int]
    ) -> List[int]:
        g = defaultdict(list)
        for u, v, w in edges:
            g[u].append((v, w))
            g[v].append((u, w))
        dist = [inf] * n
        dist[0] = 0
        pq = [(0, 0)]
        while pq:
            du, u = heappop(pq)
            if du > dist[u]:
                continue
            for v, w in g[u]:
                if dist[v] > dist[u] + w and dist[u] + w < disappear[v]:
                    dist[v] = dist[u] + w
                    heappush(pq, (dist[v], v))
        return [a if a < b else -1 for a, b in zip(dist, disappear)]
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
class Solution {
    public int[] minimumTime(int n, int[][] edges, int[] disappear) {
        List<int[]>[] g = new List[n];
        Arrays.setAll(g, k -> new ArrayList<>());
        for (var e : edges) {
            int u = e[0], v = e[1], w = e[2];
            g[u].add(new int[] {v, w});
            g[v].add(new int[] {u, w});
        }
        int[] dist = new int[n];
        Arrays.fill(dist, 1 << 30);
        dist[0] = 0;
        PriorityQueue<int[]> pq = new PriorityQueue<>((a, b) -> a[0] - b[0]);
        pq.offer(new int[] {0, 0});
        while (!pq.isEmpty()) {
            var e = pq.poll();
            int du = e[0], u = e[1];
            if (du > dist[u]) {
                continue;
            }
            for (var nxt : g[u]) {
                int v = nxt[0], w = nxt[1];
                if (dist[v] > dist[u] + w && dist[u] + w < disappear[v]) {
                    dist[v] = dist[u] + w;
                    pq.offer(new int[] {dist[v], v});
                }
            }
        }
        int[] ans = new int[n];
        for (int i = 0; i < n; ++i) {
            ans[i] = dist[i] < disappear[i] ? dist[i] : -1;
        }
        return ans;
    }
}
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
class Solution {
public:
    vector<int> minimumTime(int n, vector<vector<int>>& edges, vector<int>& disappear) {
        vector<vector<pair<int, int>>> g(n);
        for (const auto& e : edges) {
            int u = e[0], v = e[1], w = e[2];
            g[u].push_back({v, w});
            g[v].push_back({u, w});
        }

        vector<int> dist(n, 1 << 30);
        dist[0] = 0;

        using pii = pair<int, int>;
        priority_queue<pii, vector<pii>, greater<pii>> pq;
        pq.push({0, 0});

        while (!pq.empty()) {
            auto [du, u] = pq.top();
            pq.pop();

            if (du > dist[u]) {
                continue;
            }

            for (auto [v, w] : g[u]) {
                if (dist[v] > dist[u] + w && dist[u] + w < disappear[v]) {
                    dist[v] = dist[u] + w;
                    pq.push({dist[v], v});
                }
            }
        }

        vector<int> ans(n);
        for (int i = 0; i < n; ++i) {
            ans[i] = dist[i] < disappear[i] ? dist[i] : -1;
        }

        return ans;
    }
};
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
func minimumTime(n int, edges [][]int, disappear []int) []int {
    g := make([][]pair, n)
    for _, e := range edges {
        u, v, w := e[0], e[1], e[2]
        g[u] = append(g[u], pair{v, w})
        g[v] = append(g[v], pair{u, w})
    }

    dist := make([]int, n)
    for i := range dist {
        dist[i] = 1 << 30
    }
    dist[0] = 0

    pq := hp{{0, 0}}

    for len(pq) > 0 {
        du, u := pq[0].dis, pq[0].u
        heap.Pop(&pq)

        if du > dist[u] {
            continue
        }

        for _, nxt := range g[u] {
            v, w := nxt.dis, nxt.u
            if dist[v] > dist[u]+w && dist[u]+w < disappear[v] {
                dist[v] = dist[u] + w
                heap.Push(&pq, pair{dist[v], v})
            }
        }
    }

    ans := make([]int, n)
    for i := 0; i < n; i++ {
        if dist[i] < disappear[i] {
            ans[i] = dist[i]
        } else {
            ans[i] = -1
        }
    }

    return ans
}

type pair struct{ dis, u int }
type hp []pair

func (h hp) Len() int           { return len(h) }
func (h hp) Less(i, j int) bool { return h[i].dis < h[j].dis }
func (h hp) Swap(i, j int)      { h[i], h[j] = h[j], h[i] }
func (h *hp) Push(v any)        { *h = append(*h, v.(pair)) }
func (h *hp) Pop() any          { a := *h; v := a[len(a)-1]; *h = a[:len(a)-1]; return v }
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
function minimumTime(n: number, edges: number[][], disappear: number[]): number[] {
    const g: [number, number][][] = Array.from({ length: n }, () => []);
    for (const [u, v, w] of edges) {
        g[u].push([v, w]);
        g[v].push([u, w]);
    }
    const dist = Array.from({ length: n }, () => Infinity);
    dist[0] = 0;
    const pq = new PriorityQueue({
        compare: (a, b) => (a[0] === b[0] ? a[1] - b[1] : a[0] - b[0]),
    });
    pq.enqueue([0, 0]);
    while (pq.size() > 0) {
        const [du, u] = pq.dequeue()!;
        if (du > dist[u]) {
            continue;
        }
        for (const [v, w] of g[u]) {
            if (dist[v] > dist[u] + w && dist[u] + w < disappear[v]) {
                dist[v] = dist[u] + w;
                pq.enqueue([dist[v], v]);
            }
        }
    }
    return dist.map((a, i) => (a < disappear[i] ? a : -1));
}

Comments