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...

Question details

(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.