Let's revisit our first problem, where we want to set up a series of chess matches so we can rank six players in our class. As we did before, we will assume that everyone keeps their chess rating a private secret; however, when two players have a chess match, the person with the higher rating wins 100% of the time. But this time, we are only interested in identifying the BEST of these six players and the WORST of these six players. (We don't care about the relative ordering or ranking of the middle four players.) Your goal is to devise a comparison-based algorithm that is guaranteed to identify the player with the highest rating and the player with the lowest rating. Because you are very strong at Algorithm Design, you know how to do this in the most efficient way. Here are five statements. A. There exists an algorithm to solve this problem using 6 matches, but there does not exist an algorithm using only 5 matches. B. There exists an algorithm to solve this problem using 7 matches, but there does not exist an algorithm using only 6 matches. C. There exists an algorithm to solve this problem using 8 matches, but there does not exist an algorithm using only 7 matches. D. There exists an algorithm to solve this problem using 9 matches, but there does not exist an algorithm using only 8 matches. E. There exists an algorithm to solve this problem using 10 matches, but there does not exist an algorithm using only 9 matches. Determine which of these five statements is correct. Answer either A, B, C, D, or E.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter17: Markov Chains

Section: Chapter Questions

Problem 12RP

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Let's revisit our first problem, where we want to set up a series of chess matches so
we can rank six players in our class.
As we did before, we will assume that everyone keeps their chess rating a private
secret; however, when two players have a chess match, the person with the higher
rating wins 100% of the time.
But this time, we are only interested in identifying the BEST of these six players and
the WORST of these six players. (We don't care about the relative ordering or
ranking of the middle four players.)
Your goal is to devise a comparison-based algorithm that is guaranteed to identify
the player with the highest rating and the player with the lowest rating.
Because you are very strong at Algorithm Design, you know how to do this in the
most efficient way.
Here are five statements.
A. There exists an algorithm to solve this problem using 6 matches, but there does
not exist an algorithm using only 5 matches.
B. There exists an algorithm to solve this problem using 7 matches, but there does
not exist an algorithm using only 6 matches.
C. There exists an algorithm to solve this problem using 8 matches, but there does
not exist an algorithm using only 7 matches.
D. There exists an algorithm to solve this problem using 9 matches, but there does
not exist an algorithm using only 8 matches.
E. There exists an algorithm to solve this problem using 10 matches, but there
does not exist an algorithm using only 9 matches.
Determine which of these five statements is correct. Answer either A, B, C, D, or E.

Expert Solution

Step 1

We have 6 players. To find best players among them, first we are organizing 3 chess game where 6 players participates

In the three game, 3 players will win and 3 will lose,

we have to make 2 games among each winners group and losers group. so we need minimum 7 games.

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