A LinkedHashMap does use a HashMap (in fact it extends from it), so the hashCode is used to identify the right hash bucket in the array of hash buckets, just as for HashMap. put and get work just as for HashMap.

The reason insertion order is not kept by keeping an Array or ArrayList is that addition or removal in the middle of an ArrayList is an O(n) operation because you have to move all subsequent items along one place. You could do this with a LinkedList because addition and removal in the middle of a LinkedList is O(1) (all you have to do is break a few links and make a few new ones). However there's no point using a separate LinkedList because you may as well make the Map.Entry objects reference the previous and next Entry objects, which is exactly how LinkedHashMap works.

A LinkedHashMap does use a HashMap (in fact it extends from it), so the hashCode is used to identify the right hash bucket in the array of hash buckets, just as for HashMap. put and get work just as for HashMap (except that the before and after references for iterating over the entries are updated differently for the two implementations).

The reason insertion order is not kept by keeping an Array or ArrayList is that addition or removal in the middle of an ArrayList is an O(n) operation because you have to move all subsequent items along one place. You could do this with a LinkedList because addition and removal in the middle of a LinkedList is O(1) (all you have to do is break a few links and make a few new ones). However there's no point using a separate LinkedList because you may as well make the Map.Entry objects reference the previous and next Entry objects, which is exactly how LinkedHashMap works.