Linear Time Median Algorithm Problem Set #1

Here we start a new series that on Tuesdays, Thursdays, and Saturdays, we will have "problem sets" for you to work on. I present several problems, and you solve them in the comments.

This problem set is about the linear time median algorithm video (link in the card), and some variants of the algorithm that I would like you to solve, or to show is impossible.

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I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.