> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/graphs-bfs-and-dfs/network-delay-time.md).

# Network Delay Time

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:**

![](https://assets.leetcode.com/uploads/2019/05/23/931_example_1.png)

```
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`.

```java
class Solution {
    public int networkDelayTime(int[][] times, int N, int K) {
        // Creating Adjacency List
        ArrayList<int[]>[] graph = new ArrayList[N];
        for (int i = 0; i < N; i++)
            graph[i] = new ArrayList<>();
        for (int[] edge : times)
            graph[edge[0] - 1].add(new int[] { edge[1] - 1, edge[2] });

        // (distance, node) into pq
        PriorityQueue<int[]> pq = new PriorityQueue<>((a, b) -> (a[0] - b[0]));
        pq.add(new int[] { 0, K - 1 });

        boolean[] visited = new boolean[N];
        int res = 0, coveredNodes = 0;
        while (!pq.isEmpty()) {
            // Picking the Node at shortest Distance
            int[] cur = pq.remove();
            int curDist = cur[0];
            int curNode = cur[1];
            if (visited[curNode])
                continue;
            visited[curNode] = true;
            // The last node in the PQ will have the largest distance already
            res = curDist;
            coveredNodes++;
            for (int[] node : graph[curNode])
                pq.add(new int[] { curDist + node[1], node[0] });
        }
        return coveredNodes == N ? res : -1;
    }
}
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://mayanktyagi3111.gitbook.io/interview-prep/graphs-bfs-and-dfs/network-delay-time.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.