Question

In this problem, your goal is to identify who among a group of people has a certain disease. You collect a blood sample from each of the people in the group, and label them 1 through n. Suppose that you know in advance that exactly one person is infected with the disease, and you must identify who that person is by performing blood tests. In a single blood test, you can specify any subset of the samples, combine a drop of blood from each of these samples, and then get a result. If any sample in the subset is infected, the test will come up positive, otherwise it will come up negative. Your goal is to find the infected person with as few blood tests as possible. This idea of testing multiple samples at a time has been used in history at times when it was impractical or expensive to perform blood tests, for example, to find out which soldiers in World War II were carrying diseases. In those situations, the problem was even harder because there could be any number of infected people in the group. Later, we will encounter this same problem in more generality. Give an algorithm that finds the infected sample in a set of n blood samples, using as few tests as you can. Write pseudocode and a high-level English description of how your algorithm works. You don't need to prove the correctness of your algorithm.