2.a. Given a sequential file that contains at most 4 billion 32-bit integers in random order (one
billion = $10^9$). Find a 32-bit integer that is not present in the file.
[6 Marks]
Note: It is obvious to observe that multiple numbers will be missing. Assume you could create
temporary files but you have only a few hundred bytes of main memory to use.
2.b. An editor of The History of the 20$^{th}$ Century World Science wants to efficiently find out
the year of 20$^{th}$ century when the most number of prominent scientists were alive. The prominent
scientists are, by definition, the people mentioned in the book with the dates of their birth and
death. (No living scientists are included in the book.) Devise an algorithm for this task. The
entries in the index are names of scientists sorted alphabetically and each entry has the scientist's
birth and death years. If person A died the same year person B was born, assume that the death
event happened before the birth. Assume that you are given the book's index as input and that
you can only traverse the list of scientists only once.
[6 Marks]
