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Algorithm, Computer Science: (if you need more information, please mention what kind of information you need, thank you.)


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Screen Shot 2020-08-16 at 10.20.09 AM.png
Design a strategy that minimizes the expected number of questions you will ask in the fol-
lowing game. You have a deck of cards that consists of one one, two twos, three threes, and
so on up to nine nines for a total of 45 cards. Someone draws a card from the shuffled deck
and looks at its value (hiding it from you). The goal is to determine the value of the card
through asking a series of questions, each of which must be answerable with "yes" or "no"
(such as "Is the card a nine?").
To answer this question, you should express your strategy as a decision tree. You may either
explicitly draw the decision tree or describe its construction in sufficient detail so that I could
draw it from your description. If you draw the tree instead of describing its construction, give
a brief (1-2 sentences) description of how you came up with it.
Furthermore, briefly explain why this minimizes the expected number of questions you will
ask in this game. You are not required to give a formal proof.
Hint: The first question to ask in the optimal decision tree is "Is the card one of {4,5,9}?"
Equivalently, the question can be "Is the card one of {1, 2, 3, 6, 7, 8 }?"

Step-by-step answer

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