Both pictures are the same question and can you answer parts A-D 21. (a) Suppose we are given two sorted arrays A[1 ..n] and B[1..n]. Describean algorithm to find the median element in thė union of A and B inƏ(log n) time. You can assume that the arrays contain no duplicateelements.UTF-8 4 spacePCg00000F4F5F6F7F8F9FIC&*4578.9YUFGHKLVNB (1) Question 1: Problem 21a of [Erickson], page 55. For simplicity, assume n is powerof 2 (which means that n/2 is always an integer) and define the median to be theone with rank n (i.e., nth smallest) in AU B. Note that AUB has 2n elements.The median must be larger than exactly n – 1 elements and smaller than n otherelements. The problem also assumes that all elements are distinct.Let C = A(1...n/2), D = A[n/2+1... n], E = B[1...n/2], F = B[n/2+1...n).You.may break the solutions into smaller parts by answering the following sub-questions.(a) Show that if A[n/2] < B[n/2], then the median of AUB must be in DUE.(b) Furthermore, show that the median of AUB must also be the median of DUE.(c) By symmetry, what can you say about the case A[n/2] > B[n/2]?(d) Design a divide-and-conquer algorithm based on the above observation. Showthat it runs in O(log n) time.000000F4F5F6E7F8F9$4%&5789RYUG |HKくoF.

#include<bits/stdc++.h>using namespace std;#define f(i,x,y) for(int i = (x);i <…

21. (a) Suppose we are given two sorted arrays A[1.n] and B[1..n]. Describe an algorithm to find the median element in thè union of A and B in O(logn) time. You can assume that the arrays contain no duplicate elements.

21. (a) Suppose we are given two sorted arrays A[1.n] and B[1..n]. Describe an algorithm to find the median element in thè union of A and B in O(logn) time. You can assume that the arrays contain no duplicate elements.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Both pictures are the same question and can you answer parts A-D

21. (a) Suppose we are given two sorted arrays A[1 ..n] and B[1..n]. Describe
an algorithm to find the median element in thė union of A and B in
Ə(log n) time. You can assume that the arrays contain no duplicate
elements.
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(1) Question 1: Problem 21a of [Erickson], page 55. For simplicity, assume n is power
of 2 (which means that n/2 is always an integer) and define the median to be the
one with rank n (i.e., nth smallest) in AU B. Note that AUB has 2n elements.
The median must be larger than exactly n – 1 elements and smaller than n other
elements. The problem also assumes that all elements are distinct.
Let C = A(1...n/2), D = A[n/2+1... n], E = B[1...n/2], F = B[n/2+1...n).
You.may break the solutions into smaller parts by answering the following sub-
questions.
(a) Show that if A[n/2] < B[n/2], then the median of AUB must be in DUE.
(b) Furthermore, show that the median of AUB must also be the median of DUE.
(c) By symmetry, what can you say about the case A[n/2] > B[n/2]?
(d) Design a divide-and-conquer algorithm based on the above observation. Show
that it runs in O(log n) time.
000
000
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F5
F6
E7
F8
F9
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4
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5
7
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