Network Delay Time

Problem Statement

There are

network nodes, and they are labeled from to . You are given the following information:

• A list of
  m
  edges, where each edge is described by an array of three integers
  [source, destination, weight]
  . These edges represent the connections between the network nodes.
• You are also given an array
  time
  of length
  n
  , where
  time[i]
  represents the time taken to traverse from node
  i
  to all other nodes.

You need to calculate the minimum time it takes for all nodes to receive information. If the network is disconnected, return

.

Rules and Constraints

• The graph is represented as an adjacency list where each node has a weight (time) associated with it.
• The weight (time) associated with an edge is considered to be the weight of the edge instead of the edge's capacity.
• The input graph may contain self-loops and multiple edges between the same pair of nodes, but the weight will only be considered once.
• You must consider that the weight of the edges may not be symmetric.
• The network nodes are numbered from
  0
  to
  n-1
  .

Complexity Constraints

• The time complexity of your solution should be
  O(m + n log n)
  in the worst case.

Example

Input: {"input_data":[1,2,3]} Output: [1,2,3]