Question 3: Time and Space For this problem, we're going to be using big- notation. You can read about big-9 notation in section 0.3 of the textbook. We're using big-O notation for this question rather than big-C notation since big-0 is both an upper and a lower bound for the function it is applied to. (a) Can you think of an algorithm that takes a natural number of magnitude n as input, has a time complexity of (n2), and a has space complexity of (n)? If so, provide the pseudocode for the algorithm alongside a brief justification for its time and space complexity. It doesn't matter what your algorithm does, but a simpler algorithm is greatly preferred. If you cannot think of such an algorithm, explain why you were unable to do so. (b) Can you think of an algorithm that takes a natural number of magnitude n as input, has a time complexity of (n), and a has space complexity of (n2)? If so, provide the pseudocode for the algorithm alongside a brief justification for its time and space complexity. It doesn't matter what your algorithm does, but a simpler algorithm is greatly preferred. If you cannot think of such an algorithm, explain why you were unable to do so