1. Design an algorithm that reveals some secret integer number from the set {1, 2, .. , n} by guessing random numbers within the given range until the secret number has been guessed. Numbers should be replaced after being guessed such that it is possible to guess 2 and then 2 again, assuming 2 is in the given range. The algorithm should return both the secret number as well as the number of guesses taken. 2. If possible, calculate the tightest Big-O approximation for the average runtime complexity of the algorithm from part (a). If it is not possible, explain why not. Note: assume that choosing a random number takes O(1) time.
3. If possible, calculate the tightest Big-O approximation for the worst case runtime complexity of the algorithm from part (a). If it is not possible, explain why not. Note: assume that choosing a random number takes O(1) time.
4. In a single run, is it possible that of the algorithm from part (a) finds the secret number in fewer guesses than standard binary search algorithm? If so, please provide concrete example of one such situation