Please answer questions 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 the union of A and B inO(logn) time. You can assume that the arrays contain no duplicateelements.(b) Suppose we are given two sorted arrays A[1..m] and B[1..n] and aninteger k. Describe an algorithm to find the kth smallest element inAUB in O(log(m + n)) time. For example, if k = 1, your algorithmshould return the smallest element of AUB.) [Hint: Use your solutionto part (a).]"(c) Now suppose we are given three sorted arrays A[1..n], B[1..n], andC[1..n], and an integer k. Describe an algorithm to find the kth smallestelement in AUBUC in O(logn) time.55RECURSION(d) Finally, suppose we are given a two dimensional array A[1.. m, 1..n] inwhich every row A[i, ] is sorted, and an integer k. Describe an algorithmto find the kth smallest element in A as quickly as possible. How doesthe running time of your algorithm depend on m? [Hint: Solve problem16 first.]W

If n is 1, return the average of both arrays' elements. If n is 2, return the average of the first…

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

Suppose we are given two sorted arrays A[1..n] and B[1..n]. Describe an algorithm to find the median element in the union of A and B in O(log n) 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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Concept explainers

Counting sort

The counting sort algorithm sorts an array’s contents by counting the repetition of each element that occurs in the array. A counting sort algorithm is a stable algorithm that works the best when the range of elements in the array is small, say for example from 0 to 9. The count which is the number of repetitions of an element in the array is mapped to an index of an auxiliary array, which is then saved in an auxiliary array. The counting sort algorithm has a stable time complexity of the order of O(size of array + size of auxiliary array). Let’s discuss the algorithm in detail as follows.

Question

Please answer questions 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 the union of A and B in
O(logn) time. You can assume that the arrays contain no duplicate
elements.
(b) Suppose we are given two sorted arrays A[1..m] and B[1..n] and an
integer k. Describe an algorithm to find the kth smallest element in
AUB in O(log(m + n)) time. For example, if k = 1, your algorithm
should return the smallest element of AUB.) [Hint: Use your solution
to part (a).]
"(c) Now suppose we are given three sorted arrays A[1..n], B[1..n], and
C[1..n], and an integer k. Describe an algorithm to find the kth smallest
element in AUBUC in O(logn) time.
55
RECURSION
(d) Finally, suppose we are given a two dimensional array A[1.. m, 1..n] in
which every row A[i, ] is sorted, and an integer k. Describe an algorithm
to find the kth smallest element in A as quickly as possible. How does
the running time of your algorithm depend on m? [Hint: Solve problem
16 first.]
W

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