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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Consider an unsorted array of elements {25, 17, 36, 2, 3, 100, 1, 19, 7}:i) Show how to get the first four sorted numbers when applying Selection sort and Insertion sort.ii) Show how to get the first two partitions for the above array when Quicksort is applied.iii) Show the steps to search for 25 in the above sequence using binary search algorithm.iv) Write a C++ program to search for 17 in the above sequence using linear searching algorithm.
Problem 4: Divide and conquer.(i) Let A be an array containing n different integers. Elements in A are sorted inincreasing order. Given an integer x describe an algorithm which in time O(log n)finds an index i of x in A, that is, A[i] = x, where the length n of A is unknown(you may assume that the implementation of an array is such that for A[i], wherei > n, a special character ∞ is returned).(ii) Let A be an array containing n different integers. Elements in A are not necessarysorted. Given an integer x describe an algorithm which in time O(n log n) testswhether there exist two elements u and v in A such that their sum is equal to x, thatis, u + v = x. The length n of A is known.
Problem 6: Suppose you are given an unsorted array A of all integers in the range 0 ton except for one integer, called the missing number. Assume n = 2k − 1. Using the divideand conquer strategy design an O(n)-algorithm to find the missing number.
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