14.1.5. Question Number 10

Try these first

1. 1.

   Define a celebrity in the context of the party problem.

   Hint

   Recall the definition given in class.

2. 2.

   Can there be more than one celebrity in a party? Explain.

   Hint

   Think about the implications of mutual recognition.

3. 3.

   What is the definition of a celebrity?

   Hint

   Recall the characteristics discussed in class.

4. 4.

   How many unique questions are required to verify a celebrity among n guests?

   • n-1
   • 2n-2
   • 3n-1

   Hint

   Consider how each guest's relationship affects the total queries needed.

5. 5.

   Design an algorithm that takes a list of n guests and identifies any potential celebrities among them, ensuring it operates within the 3n-1 limit for questions.

   Hint

   Consider narrowing down your potential candidates significantly with each query.

6. 6.

   If three guests know each other, explain why no one among them can be identified as the celebrity following the proof's logic.

   Hint

   Evaluate their relationships critically against the definition provided.