1. Engineering
  2. Chemical Engineering
  3. b 12 points suppose the ministry knows that strictly more...

Question: b 12 points suppose the ministry knows that strictly more...

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3. (30 pts total) The Dementors have captured n prisoners, of dubious morals and dubious reliability. The Ministry of Magic n

(b) (12 points) Suppose the Ministry knows that strictly more than n/2 of the prisoners are truthful, but not which ones. Prove that bn/2c pairwise tests are sufficient to reduce the problem to one of nearly half the size.

(c) (8 points) Now, under the same assumptions as part (3b), prove that all of the truthful prisoners can be identified with Θ(n) pairwise tests. Give and solve the recurrence (as always, in O or Θ notation) that describes the number of tests.

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