Network Delay Time
Difficulty: Medium
Category: DSA
Topics: Depth-First Search, Breadth-First Search, Graph, Heap (Priority Queue), Shortest Path
Asked at: Amazon
You are given a network of `n` nodes, labeled from `1` to `n`. You are also given `times`, a list of travel times as directed edges `times[i] = (ui, vi, wi)`, where `ui` is the source node, `vi` is the target node, and `wi` is the time it takes for a signal to travel from source to target.
We will send a signal from a given node `k`. Return _the **minimum** time it takes for all the_ `n` _nodes to receive the signal_. If it is impossible for all the `n` nodes to receive the signal, return `-1`.
**Example 1:**
**Input:** times = [[2,1,1],[2,3,1],[3,4,1]], n = 4, k = 2
**Output:** 2
```
**Example 2:**
**Input:** times = [[1,2,1]], n = 2, k = 1
**Output:** 1
```
**Example 3:**
**Input:** times = [[1,2,1]], n = 2, k = 2
**Output:** -1
```
**Constraints:**
- `1 <= k <= n <= 100`
- `1 <= times.length <= 6000`
- `times[i].length == 3`
- `1 <= ui, vi <= n`
- `ui != vi`
- `0 <= wi <= 100`
- All the pairs `(ui, vi)` are **unique**. (i.e., no multiple edges.)