Let A And B Be Two Sorted Arrays, Each With N Elements. For The Purposes Of This Problem, Assume That All 2n Elements Are Distinct Integers, And Assumen= 2k + 1 For Some Integer K ≥ 1. In This Problem, We Wish To Compute Themedianof The 2nelements, Which Will Be The Average Of The Nth And (n+ 1)th Smallest Elements In The (combined) Array. For Example, Suppose A= [1,2,4,8,16,32,64,128,256] And B= [30,40,50,60,70,80,90,100,110]. If We Merge The Arrays And Sort It, We Get C= [1,2,4,8,16,30,32,40,50,60,64,70,80,90,100,110,128,256]. From This We See That The Middle Two Elements Are 50 And 60 And So The Median Is 55. Question: Consider The Following Algorithm: Merge The Two Arrays And Sort It To Produce A New Array C With 2n Elements. Then The Median Must Be (C[n] +C[n+ 1])/2. Determine Whether This Algorithm Is Linear Or Linearithmic. Clearly Justify Your Answer.

Let A and B be two sorted arrays, each with n elements. For the purposes of this problem, assume that all 2n elements are distinct integers, and assumen= 2k + 1 for some integer k ≥ 1. In this problem, we wish to compute themedianof the 2nelements, which will be the average of the nth and (n+ 1)th smallest elements in the (combined) array. For example, suppose A= [1,2,4,8,16,32,64,128,256] and B= [30,40,50,60,70,80,90,100,110]. If we merge the arrays and sort it, we get C= [1,2,4,8,16,30,32,40,50,60,64,70,80,90,100,110,128,256]. From this we see that the middle two elements are 50 and 60 and so the median is 55. Question: Consider the following algorithm: merge the two arrays and sort it to produce a new array C with 2n elements. Then the median must be (C[n] +C[n+ 1])/2. Determine whether this algorithm is linear or linearithmic. Clearly justify your answer.

- November 14, 2022 - Edwin Tunner

Let A and B be two sorted arrays, each with n elements. For the purposes of this problem, assume that all 2n elements are distinct integers, and assumen= 2^k + 1 for some integer k ≥ 1. In this problem, we wish to compute themedianof the 2nelements, which will be the average of the n^th and (n+ 1)^th smallest elements in the (combined) array.

For example, suppose A= [1,2,4,8,16,32,64,128,256] and B= [30,40,50,60,70,80,90,100,110]. If we merge the arrays and sort it, we get C= [1,2,4,8,16,30,32,40,50,60,64,70,80,90,100,110,128,256]. From this we see that the middle two elements are 50 and 60 and so the median is 55.

Question:

Consider the following algorithm: merge the two arrays and sort it to produce a new array C with 2n elements. Then the median must be (C[n] +C[n+ 1])/2. Determine whether this algorithm is linear or linearithmic. Clearly justify your answer.

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