Considering the problem of performing rapid COVID test among a large group of people. Assuming there are exactly 1 positive case among N people, and you are asked to find the positive case with the least number tests. 1. A straight forward approach is to test every single person, which requires N tests in total. Can you design a testing framework that works better than the greedy one under, even under the worst-case scenario? Write the pseudo code for your approach and briefly explain the time complexity of your approach. 2. Based on your framework, if there are 1,000 people, what are the maximum number of tests that need to be performed in order to identify the positive case (number of tests required in the worst case)?

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