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problemthis problem deals with modification of the quick-select algorithm to make it deterministic yet still run in on
problembob has a set a of n nuts and a set b of n bolts such that each nut in a has a unique matching bolt in b
problem1 let a and b be two sequences of n integers each given an integer m describe an on log n -time algorithm for
problemlet s be a sequence of n elements on which a total order relation is defined recall that an inversion in s is a
problem1 given a sequence s of n elements on which a total order relation is defined describe an efficient method for
problemsuppose we are given two sequences a and b of n elements possibly containing duplicates on which a total order
problem1 show that any comparison-based sorting algorithm can be made to be stable without affecting its asymptotic
problemdescribe a nonrecursive in-place version of the quick-sort algorithm the algorithm should still be based on the
problemanother way to analyze randomized quick-sort is to use a recurrence equation in this case we let tn denote the
problemconsider a version of deterministic quick-sort where we pick as our pivot the median of the d last elements in
problemconsider sets whose elements are integers in the range 0n - 1 a popular scheme for representing a set a of this
problem1 suppose that we represent sets with balanced search trees describe and analyze algorithms for each of the
problemlinda claims to have an algorithm that takes an input sequence s and produces an output sequence t that is a
problem1 describe an in-place version of the quick-select algorithm in pseudo-code2 show that the worst-case running
problem1 give an example input list that requires merge-sort and heapsort to take onlogn time to sort but
problemdescribe a radix-sort method for lexicographically sorting a sequence s of triplets klm where k l and m are
problem1 show that the probability that any given input element x belongs to more than 2logn subproblems in size group
problem1 show that the best-case running time of quick-sort on a sequence of size n with distinct elements is onlogn2
problemsuppose we modify the deterministic version of the quick-sort algorithm so that instead of selecting the last
problem1 show that x - a x - b x - a cap b for any three sets x a and b2 consider again the modification of the
problem1 give a complete pseudo-code description of the recursive merge-sort algorithm that takes an array as its input
problem1 suppose s is a list of n bits that is n 0s and 1s how long will it take to sort s with the merge-sort
problem1 write a function that takes a picture as input and make the top half of the picture black2 the function copy
problemwrite a function to create a lightened gray scale image by use make lighter first lighten the image by using the
problem1 write a function to mirror an image vertically2 write a function to create a lightened gray scale image first