A linked list contains a cycle if, starting from some node p, following a sufficient number of next links brings us back to node p. p does not have to be the first node in the list. Assume that you are given a linked list that contains N nodes, however, the value of N is unknown.

a. Design an O(N) algorithm to determine if the list contains a cycle. You may use O(N) extra space.

b. Repeat part (a), but only use O(1) extra space. (hint. use two literators that are initially at the start of the list but advance at different speeds.)