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
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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-
Transcribed Image Text: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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