Express the following five loosely described problems carefully in { Instance, problem } form as utilized in "Computers and Intractability". For each problem discuss the best time and space complexity you are aware of for solving the problem (from scratch) along with a few words naming or describing the method.
(i) Finding the median of n = 2 k + 1 integers.
(ii) Finding the 2 largest and 2 smallest of n integers.
(iii) Determining that a graph is not a forest (not acyclic).
(iv) Determining that a list of n numbers has no duplicates.
(v) Determining that the maximum number of edge disjoint paths between vertices v and w in a graph is less than k.