Network Delay Time

DESCRIPTION (inspired by Leetcode.com)

A distributed system has n servers labeled 1 to n. The servers communicate through directed connections, where each connection [from, to, latency] means server from can send a message to server to with the given latency (in milliseconds).

When server k broadcasts an alert, it propagates through the network along all available paths. Return the minimum time required for every server to receive the alert. If some servers are unreachable from k, return -1.

Example 1:

Input:

connections = [[1,2,3], [1,3,5], [2,3,1]]
n = 3
k = 1

Output:

4

Explanation: There are two paths to server 3: the direct path 1→3 takes 5ms, but the path 1→2→3 takes only 3+1=4ms. The last server to receive the alert determines the answer.

Example 2:

Input:

connections = [[1,2,2], [3,2,1]]
n = 3
k = 1

Output:

-1

Explanation: The edge [3,2,1] points from server 3 to server 2, not the other way around. Server 1 can reach server 2, but there's no path from server 1 to server 3.