II. Read each problem carefully and present an algorithm with the required running-time to solve eachproblem.2. Let A be a sorted array of n integers. You want to implement two functions:update (i, x) - which takes as input an index i in A and sets A[i] = x. For example, callingupdate (3,10) will set A[3] = 10. Note that array A might not be completely sorted after anupdate.is Sorted (i) - returns true if the subarray A[0... i] is sorted, otherwise it returns false.A straightforward implementation of the two operations using only the given array can be doneas follows:update operation can directly change the value of A[i] to x.is Sorted will scan A[0] up to A[i] while checking if elements are non-decreasing.With the above implementations, update takes O(1) time but is Sorted takes O(n) time.a. Give another implementation where update takes O(n) time while isSorted takes O(1) time.

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Answered: a. Give another implementation where…

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a. Give another implementation where update takes O(n) time while isSorted takes 0(1) time.

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

Randomized Select Algorithm

A randomized algorithm is defined as one that uses a certain amount of randomization in its logic or operation. It is said to be an algorithm that depends on the random number to perform its operation. It is used for reducing the overall time complexity, space complexity in the standard algorithm. The randomized algorithm uses the concept of random numbers to find the solutions to the different kinds of problems and also to improve the problem solutions.

Question

II. Read each problem carefully and present an algorithm with the required running-time to solve each
problem.
2. Let A be a sorted array of n integers. You want to implement two functions:
update (i, x) - which takes as input an index i in A and sets A[i] = x. For example, calling
update (3,10) will set A[3] = 10. Note that array A might not be completely sorted after an
update.
is Sorted (i) - returns true if the subarray A[0... i] is sorted, otherwise it returns false.
A straightforward implementation of the two operations using only the given array can be done
as follows:
update operation can directly change the value of A[i] to x.
is Sorted will scan A[0] up to A[i] while checking if elements are non-decreasing.
With the above implementations, update takes O(1) time but is Sorted takes O(n) time.
a. Give another implementation where update takes O(n) time while isSorted takes O(1) time.

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