1. Prof. Nigma at the Portland Institute of Technology (which still doesn't exist) was thrilled with your previous work and hired you again to analyze the algorithm given here in pseudocode! As usual, however, Prof. Nigma neglected to explain what the algorithm does. def Q(A[0..n-1]) // Input: Array A[0..n - 1] of n real numbers, for n ≥ 1 if n = 1 return A[0] else temp = Q(A[0..n - 2]) if temp A[n 1] return temp else return A[n - 1] (a) What does this algorithm compute? Give an English description of what value it returns on a given input array, along with a convincing explanation of your answer. (You do not need to give examples as part of your answer, but as always, you are welcome to include examples along with the English description, if it would make your answer clearer.) (b) What is the complexity class of this algorithm? To find it, first state a re- currence for the time complexity of the algorithm, then solve it using one of the methods presented in class for solving recurrences. Be sure to give a thorough ex- planation of what makes your recurrence correct, and show your work for solving the recurrence including showing a k'th step in your method if you use unwind-

1. Prof. Nigma at the Portland Institute of Technology (which still doesn't exist) was thrilled with your previous work and hired you again to analyze the algorithm given here in pseudocode! As usual, however, Prof. Nigma neglected to explain what the algorithm does. def Q(A[0..n-1]) // Input: Array A[0..n - 1] of n real numbers, for n ≥ 1 if n = 1 return A[0] else temp = Q(A[0..n - 2]) if temp A[n 1] return temp else return A[n - 1] (a) What does this algorithm compute? Give an English description of what value it returns on a given input array, along with a convincing explanation of your answer. (You do not need to give examples as part of your answer, but as always, you are welcome to include examples along with the English description, if it would make your answer clearer.) (b) What is the complexity class of this algorithm? To find it, first state a re- currence for the time complexity of the algorithm, then solve it using one of the methods presented in class for solving recurrences. Be sure to give a thorough ex- planation of what makes your recurrence correct, and show your work for solving the recurrence including showing a k'th step in your method if you use unwind-

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

1. Prof. Nigma at the Portland Institute of Technology (which still doesn't exist) was
thrilled with your previous work and hired you again to analyze the algorithm given
here in pseudocode! As usual, however, Prof. Nigma neglected to explain what the
algorithm does.
def Q(A[0..n - 1])
// Input: Array A[0..n-1] of n real numbers, for n ≥1
if n = 1 return A[0]
else temp = Q(A[0..n - 2])
if temp ≤ A[n 1] return temp
else return A[n - 1]
(a) What does this algorithm compute? Give an English description of what value
it returns on a given input array, along with a convincing explanation of your
answer. (You do not need to give examples as part of your answer, but as always,
you are welcome to include examples along with the English description, if it
would make your answer clearer.)
(b) What is the complexity class of this algorithm? To find it, first state a re-
currence for the time complexity of the algorithm, then solve it using one of the
methods presented in class for solving recurrences. Be sure to give a thorough ex-
planation of what makes your recurrence correct, and show your work for solving
the recurrence, including showing a k'th step in your method, if you use unwind-

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