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# ps4 - Massachusetts Institute of Technology 6.046J/18.410J...

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Massachusetts Institute of Technology Handout 12 6.046J/18.410J: Introduction to Algorithms March 20, 2003 Professors Piotr Indyk and Bruce Tidor Problem Set 4 This problem set is due at the beginning of class on Thursday, April 3, 2003 . Each problem is to be done on a separate sheet (or sheets) of paper. Mark the top of each sheet with your name, 6.046J/18.410J, the problem number, your recitation section, the date, and the names of any students with whom you collaborated. Problem 4-1. Subsequences Consider a sequence of numbers stored in an array A [1 ..n ]. A subsequence of this array is just a subset of the elements of the array A [ i 1 ] , A [ i 2 ] , . . . , A [ i k ] where i 1 < i 2 < . . . < i k . Note that a subsequence does not have to be a contiguous block of elements. (a) A subsequence is called an increasing subsequence if A [ i 1 ] < A [ i 2 ] < . . . < A [ i k ]. Devise an algorithm for computing the longest increasing subsequence of an array — that is, an increasing subsequence consisting of the greatest possible number of array elements. The algorithm should run in O ( n 2

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