讲解：merge-sort、cs,java、median、Python/JavaSPSS|SPSS

Problem 12. (Difficulty 2) Bubblesort and oblivious merge-sort each give a sequence ofcompare-exchange operations which sorts any array A[0..3]. Write down both sequences.Problem 13. (Difficulty 4) For n distinct elements x1, x2, . . . , xn with positive weightsw1, w2, . . . , wn such that Pni=1 wi = 1, define the weighted median to be an index k satisfyingPi:xiwi ≤ 1/2 and Pi:xi>xkwi ≤ 1/2. Give an O(n) algorithm for finding theweighted median.Problem 14. (Difficulty 3) Suppose we are given k sorted lists, each consisting of n elements.The multimerge problem is to merge the k lists into a single sorted list of length nk. Design anefficient algorithm for the multimerge problem. Analyze the running time of your algorithm.The more efficient your algorithm is in terms of its worst-case running time, the more credityou will get.2 Homework 1Problem 15. (Difficulty 3) Return a list of the following functions separated by the symbol≡or �, where f ≡ g means f = Θ(g) and f � g means f = O(g). You do not needto justify your answer. For example, if the functions are log n, n, 5n, 2n a correct answer islog n � n ≡ 5n � 2n. All logarithms are in base 2. One point for each correct symbol.Problem 16. (Difficulty 3) Solve the following recurrences. Give both O(.) and (.).T(n) = 4T(n/3) + n,T(n) = 3T(n/4) + n,T(n) = 3T(n/4) + n2.5Problem 17. (Difficulty 2) Execute the Quick-Sort algorithm on the following array[5, 2, 6, 1, 3, 4, 7]using the last element of the array as a pivot element. Show the contents of the array aftereach pass of partition.Problem 18. (Difficulty 3) Give an algorithm running in time O(n) and space O(1) whichsorts an array of n elements in the range {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Note that you cannot useanother array of length n for the output because you are only allowed space O(1).Problem 19. (Difficulty 3) You are given as input an array A[1..n] containing integernumbers from 1 to n10. Give an O(n)-time algorithm to determine if there are two numberswhich sum to 0.转自：http://ass.3daixie.com/2019012368012078.html