<P> Some hybrid solutions try to combine the advantages of the two representations . Unrolled linked lists store several elements in each list node, increasing cache performance while decreasing memory overhead for references . CDR coding does both these as well, by replacing references with the actual data referenced, which extends off the end of the referencing record . </P> <P> A good example that highlights the pros and cons of using dynamic arrays vs. linked lists is by implementing a program that resolves the Josephus problem . The Josephus problem is an election method that works by having a group of people stand in a circle . Starting at a predetermined person, you count around the circle n times . Once you reach the nth person, take them out of the circle and have the members close the circle . Then count around the circle the same n times and repeat the process, until only one person is left . That person wins the election . This shows the strengths and weaknesses of a linked list vs. a dynamic array, because if you view the people as connected nodes in a circular linked list then it shows how easily the linked list is able to delete nodes (as it only has to rearrange the links to the different nodes). However, the linked list will be poor at finding the next person to remove and will need to search through the list until it finds that person . A dynamic array, on the other hand, will be poor at deleting nodes (or elements) as it cannot remove one node without individually shifting all the elements up the list by one . However, it is exceptionally easy to find the nth person in the circle by directly referencing them by their position in the array . </P> <P> The list ranking problem concerns the efficient conversion of a linked list representation into an array . Although trivial for a conventional computer, solving this problem by a parallel algorithm is complicated and has been the subject of much research . </P> <P> A balanced tree has similar memory access patterns and space overhead to a linked list while permitting much more efficient indexing, taking O (log n) time instead of O (n) for a random access . However, insertion and deletion operations are more expensive due to the overhead of tree manipulations to maintain balance . Schemes exist for trees to automatically maintain themselves in a balanced state: AVL trees or red - black trees . </P>

(i) write the all types of linked lists