## DEV Community

Abhishek Chaudhary

Posted on

# Network Delay Time

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.)

SOLUTION:

``````class Solution:
def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int:
dist = [float('inf')] * n
dist[k - 1] = 0
for i in range(n - 1):
for a, b, d in times:
if dist[b - 1] > dist[a - 1] + d:
dist[b - 1] = dist[a - 1] + d
delay = max(dist)
if delay == float('inf'):
return -1
return delay
``````