Comparing 2 goblins with each other costs 1 "goblin comparison". Assume that more than half of the given n goblins are truth tellers. Design an O(n) goblin comparison algorithm that will identify 1 truth teller.

Computer Networking: A Top-Down Approach (7th Edition)
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ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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2. Honest Goblins are Easy to Find
At Hogwarts a new shipment of n goblins has arrived. To be of any use, a goblin must be completely truthful (never lies). Unfortunately, not all of the n
goblins in the shipment are truth tellers. Only some are truth-tellers, and some are deceivers. It is your task to design an algorithm to separate the truth-
teller goblins from the deceiver goblins. To do this, you have one tool available: You may combine any two goblins and have them state whether the other
goblin is a truth-teller or a deceiver. A truth-teller will always say correctly what the other goblin is, but a deceiver may lie (but also may sometimes tell the
truth to REALLY confuse you). For any two goblins that you test, the following can be concluded from the goblin responses:
Goblin A says
Goblin B says
Conclusion
B is a truth-teller
A is a truth-teller
both are truth-tellers or both are deceivers
B is a truth-teller
A is a deceiver
at least one is a deceiver
B is a deceiver
A is a truth-teller
at least one is a deceiver
B is a deceiver
A is a deceiver
at least one is a deceiver
Comparing 2 goblins with each other costs 1 "goblin comparison". Assume that more than half of the given n goblins are truth tellers. Design an O(n) goblin
comparison algorithm that will identify 1 truth teller.
Transcribed Image Text:2. Honest Goblins are Easy to Find At Hogwarts a new shipment of n goblins has arrived. To be of any use, a goblin must be completely truthful (never lies). Unfortunately, not all of the n goblins in the shipment are truth tellers. Only some are truth-tellers, and some are deceivers. It is your task to design an algorithm to separate the truth- teller goblins from the deceiver goblins. To do this, you have one tool available: You may combine any two goblins and have them state whether the other goblin is a truth-teller or a deceiver. A truth-teller will always say correctly what the other goblin is, but a deceiver may lie (but also may sometimes tell the truth to REALLY confuse you). For any two goblins that you test, the following can be concluded from the goblin responses: Goblin A says Goblin B says Conclusion B is a truth-teller A is a truth-teller both are truth-tellers or both are deceivers B is a truth-teller A is a deceiver at least one is a deceiver B is a deceiver A is a truth-teller at least one is a deceiver B is a deceiver A is a deceiver at least one is a deceiver Comparing 2 goblins with each other costs 1 "goblin comparison". Assume that more than half of the given n goblins are truth tellers. Design an O(n) goblin comparison algorithm that will identify 1 truth teller.
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