There are 2 options now:

1. Someone optimizes your code for you.
2. You generate test cases and profile your code.

Option 1 is unlikely given how messy the code is. Moreover, there is a possibility that you might have analyzed the time complexity of your code wrongly (then it would be a waste of time for others to try to study your code).

I recommend that you generate some large test cases and profile your code to see where the bottleneck in your code is.

You are using LinkedList for no reason instead of array/ArrayList for the goods variable.

Didn't look to carefully at your code, but the complexity is probably fine. To get AC you need to make sure the constant is low as well.

I got TLE in C++ because I used a multiset in the last loop instead of sorting. Also changing dist[n][k] to dist[k][n] almost halved the execution time (I assume here the cache misses really hurt the performance).

So look at other java solutions that get AC and keep tweaking your solution until you get AC (my guess is that you have to ditch the LinkedList altogether).

Re-read the original comment and then read this

            for(int i=0;i<n;i++){
                list.add(new ArrayList<>());
                int good = s.nextInt();
                good--;
                goods.get(good).add(i);
            }