Question: Our homework assignment asks us to prove that the Java `LinkedList` implementation is doubly-linked and not singly-linked. However, list operations such as adding elements, removing elements, and looking elements up seem to have the same complexity for both implementations, so there doesn't seem to be a way to use a performance argument to demonstrate the doubly-linked nature of Java's `LinkedList`. Anyone know of a better way to illustrate the difference between the two?

Answer: 
Look at iterating in forward or backward direction, removing the "before-last" element, and such.
The Java List interface doesn't have a method which allows you to remove an item without searching through a linked list. It has remove(int index), which would have to scan the list to find the indexed entry, and it also has remove(Object o), which has to scan the list as well. Since a linked list implementation can save the necessary previous-item entry context while scanning, remove has equivalent complexity for singly- and doubly-linked lists. This state can be saved in an iterator, as well, so Iterator.remove() doesn't change this. So I don't think you can tell from remove performance.

My guess is that the "right" answer to this is to create several lists of different sizes and time the performance of .indexOf() and .lastIndexOf() when searching for the first or last object. Presuming that the implementation is doubly-linked and searches from the beginning of the list for .indexOf() and searches from the end for .lastIndexOf(), the performance will be length-dependent or length-independent.