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Unformatted text preview: 15750Midterm 1Page 1 of 915750:Practice Midterm 1Name:Email:InstructionsFill in the box above with your name, and your email address.Do it, now!This exam is open book: That is, you may use two books(Kozen and CLRS), any handoutsfrom class, and your notes.Clearly mark your answers in the allocated space. If need be, use the back of a page for scratchspace. If you have made a mess, cross out the invalid parts of your solution, and circle the onesthat should be graded.Scan the test first to make sure that none of the 9 pages are missing. The problems are ofvarying difficulty, you might wish to pick off the easy ones first.With each problem requiring you to present an algorithm make sure include the following threebullets: Algorithm: Correctness: and Timing:You have 80 minutes. Good luck.1302303309015750Midterm 1Page 2 of 9Problem 1:Finding the Closest Point to a Convex Body (30 pts)Suppose thatP={p1,...,pn}arenpoints on the plane that form a convex polygon andp1,...,pnis the counterclockwise order of the point onP. Further, letqis an arbitrary point on the plane.The goal of this problem is to find the closest point onPtoq. We assume that the polygonPisgiven in counterclockwise order. Observe that the closest point may be on a segment [pi,pi+1]....
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 Spring '09

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