5. For the version of quicksort given in this section: a. Are arrays made up of all equal elements the worst-case input, the best- case input, or neither? b. Are strictly decreasing arrays the worst-case input, the best-case input, or neither?

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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#5

ie, i =j, the value they are pointing to must be equal to p.
A Prove that when the scanning indices stop, j cannot point to an element
more than one position to the left of the one pointed to by i.
3 Give an example showing that quicksort is not a stable sorting algorithm.
4 Give an example of an array of n elements for which the sentinel mentioned
in the text is actually needed. What should be its value? Also explain why a
single sentinel suffices for any input.
5. For the version of quicksort given in this section:
a. Are arrays made up of all equal elements the worst-case input, the best-
case input, or neither?
b. Are strictly decreasing arrays the worst-case input, the best-case input, or
neither?
6. a. For quicksort with the median-of-three pivot selection, are strictly increas-
ing arrays the worst-case input, the best-case input, or neither?
b. Answer the same question for strictly decreasing arrays.
7. a. Estimate how many times faster quicksort will sort an array of one million
random numbers than insertion sort.
b. True or false: For every n > 1, there are n-element arrays that are sorted
faster by insertion sort than by quicksort?
0. Design an algorithm to rearrange elements of a given array of n real num-
Transcribed Image Text:ie, i =j, the value they are pointing to must be equal to p. A Prove that when the scanning indices stop, j cannot point to an element more than one position to the left of the one pointed to by i. 3 Give an example showing that quicksort is not a stable sorting algorithm. 4 Give an example of an array of n elements for which the sentinel mentioned in the text is actually needed. What should be its value? Also explain why a single sentinel suffices for any input. 5. For the version of quicksort given in this section: a. Are arrays made up of all equal elements the worst-case input, the best- case input, or neither? b. Are strictly decreasing arrays the worst-case input, the best-case input, or neither? 6. a. For quicksort with the median-of-three pivot selection, are strictly increas- ing arrays the worst-case input, the best-case input, or neither? b. Answer the same question for strictly decreasing arrays. 7. a. Estimate how many times faster quicksort will sort an array of one million random numbers than insertion sort. b. True or false: For every n > 1, there are n-element arrays that are sorted faster by insertion sort than by quicksort? 0. Design an algorithm to rearrange elements of a given array of n real num-
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Given :-For the version of quicksort given in this section:

a. Are arrays made up of all equal elements the worst-case input, the best-
case input, or neither?
b. Are strictly decreasing arrays the worst-case input, the best-case input, or
neither?

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