ps2-questions.pdf - Introduction to Algorithms 6.006 Massachusetts Institute of Technology Instructors Jason Ku Julian Shun and Virginia Williams

ps2-questions.pdf - Introduction to Algorithms 6.006...

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Introduction to Algorithms: 6.006 Massachusetts Institute of Technology September 13, 2019 Instructors: Jason Ku, Julian Shun, and Virginia Williams Problem Set 2 Problem Set 2 All parts are due on September 20, 2019 at 6PM . Please write your solutions in the L A T E X and Python templates provided. Aim for concise solutions; convoluted and obtuse descriptions might receive low marks, even when they are correct. Solutions should be submitted on the course website, and any code should be submitted for automated checking on . Problem 2-1. [10 points] Famy k -sort Merge sort is a divide-and-conquer algorithm based on the idea that merging two sorted arrays into one larger sorted array can be done in linear time. Recall that merge sort divides unsorted input into two equally-sized subarrays, recursively sorts them, and then merges them together. Famy Owler is a 6.006 student this semester and is curious how modifications to merge sort would affect its running time. Famy has found a way to generalize the merge step of merge sort to combine k size- m sorted arrays into one sorted array of size km in Θ( k 2 m ) time, for any positive integer k . Famy k -sort is a generalization of merge sort which splits an input array into k equal chunks, recursively sorts them, and then combines them using Famy’s merge.
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