5. Consider removing the "strict" restriction in our definition of strict majority element. That is, we define æ as a majority element of an array A if greater than or equal to half of the elements of A are equal to r. (In our more formal definition, we replace the > 4 by > 4.) The claim that A has at most one strict majority element is no longer true if we remove the “strict". That is, it might be the case that A has more than one majority element. (Can you think of an example? What restrictions on n must there be to have more than 1?) Since the claim is no longer true, our proof for the strict majority element can no longer work. Which line of the proof is the earliest line that is no longer true (i.e. it no longer follows from the previous line or from given assumptions). You should assume that we replace our contradiction assumption with “suppose that array A has at least two distinct majority elements a and y". a. The definitions of A and Ay b. That n 2 |Az|+ |Ay| c. That the previous line is > + d. That the previous line is = n.

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. Consider removing the "strict" restriction in our definition of strict majority element. That is,
we define r as a majority element of an array A if greater than or equal to half of the elements of
A are equal to r. (In our more formal definition, we replace the > by > .)
The claim that A has at most one strict majority element is no longer true if we remove the “strict".
That is, it might be the case that A has more than one majority element. (Can you think of an
example? What restrictions on n must there be to have more than 1?)
Since the claim is no longer true, our proof for the strict majority element can no longer work.
Which line of the proof is the earliest line that is no longer true (i.e. it no longer follows from the
previous line or from given assumptions). You should assume that we replace our contradiction
assumption with “suppose that array A has at least two distinct majority elements r and y".
a. The definitions of A, and Ay
b. That n 2 |Az|+ |Ay|
c. That the previous line is > +
d. That the previous line is = n.
Transcribed Image Text:5. Consider removing the "strict" restriction in our definition of strict majority element. That is, we define r as a majority element of an array A if greater than or equal to half of the elements of A are equal to r. (In our more formal definition, we replace the > by > .) The claim that A has at most one strict majority element is no longer true if we remove the “strict". That is, it might be the case that A has more than one majority element. (Can you think of an example? What restrictions on n must there be to have more than 1?) Since the claim is no longer true, our proof for the strict majority element can no longer work. Which line of the proof is the earliest line that is no longer true (i.e. it no longer follows from the previous line or from given assumptions). You should assume that we replace our contradiction assumption with “suppose that array A has at least two distinct majority elements r and y". a. The definitions of A, and Ay b. That n 2 |Az|+ |Ay| c. That the previous line is > + d. That the previous line is = n.
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