We know that lookup on a singly linked list is O(n) given a head pointer. Let us say I maintain a pointer at half the linked list at all times. Would I be improving any lookup times?
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Nice thought, but this still does not improve the search operation. No matter how many pointers you have at different portions of the list, you still have to analyze each element in the list. However, you -could- two threads to search each half of the list making the operation twice as fast in theory.