Express the following five loosely explained problems carefully in the form as used in the "Computers and Intractability". For every problem describe the best time and space complexity you are aware of for solving the problem (from scratch) along with the few words naming or explaining the method.

i) Determining the median of n = 2 k + 1 integers.

ii) Determining the 2 largest and 2 smallest of n integers.

iii) Finding that the graph is not a forest (not acyclic).

iv) Finding that the list of n numbers has no duplicates.

v) Finding that the maximum number of the edge disjoint paths between teh vertices v and w in a graph is less than k.