Prоblem 1: Sоlving Recurrences (6 pоints) Derive solutions to the following recurrences. (а) (T(n) = 9T!left(tfrаc{n}{3}right) + n^2 lg n) (b) (T(n) = 2T!left(tfrаc{n}{2}right) + n^2) Problem 2: Asymptotic Notations (4 points) A GPU team implements a blocked algorithm to compute many large dense matrix products in a graphics pipeline. Their algorithm splits an (n times n) matrix pair into 8 independent subproblems of size (n/3) each (work on different tiles in parallel). Unfortunately, the tile-assembly and synchronization needed in the combine step are expensive, costing (Theta(n^{2.9})) time per level. Let (T(n)) be the runtime (ignoring constant-factor parallel speedups). Does this tiled algorithm run asymptotically faster than Strassen’s algorithm (which runs in (Theta(n^{lg 7}) approx Theta(n^{2.81})))? Congratulations, you are almost done with Quiz 3. DO NOT end the Honorlock session until you have submitted your work to Gradescope. When you have answered all questions: Use your smartphone to scan your answer sheet and save the scan as a PDF. Make sure your scan is clear and legible. Submit your PDF to Gradescope as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.). Click this link to go to Gradescope to submit your work: Quiz 3 Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam. End the Honorlock session.
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