File size: 3,401 Bytes
5fed0fc |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 |
Time limit per test: 1 second
Memory limit per test: 256 megabytes
Goal
-----
There is a hidden integer x with 1 ≤ x ≤ n that you must determine.
What you can do
----------------
1) Ask membership questions (up to 53 total):
- Choose any non-empty set S ⊆ {1, 2, …, n}.
- Ask whether x ∈ S.
- The judge replies “YES” if x ∈ S, otherwise “NO”.
2) Make guesses (up to 2 total):
- Output a single number as your guess for x.
- The reply is always truthful:
• “:)” if your guess equals x (you must terminate immediately).
• “:(” if your guess is wrong.
Noisy answers & guarantee
--------------------------
- Not all “YES”/“NO” answers are guaranteed to be truthful.
- However, for every pair of consecutive questions, at least one answer is correct.
- This remains true across guesses: if you ask a question, then make a guess, then ask another question, the “consecutive questions” rule applies to those two questions surrounding the guess.
- Guesses themselves are always judged correctly.
Adaptive x
----------
- The judge does not fix x in advance; it may change over time.
- Changes are constrained so that all previous responses remain valid and consistent with:
• the rule “for each two consecutive questions, at least one answer is correct,” and
• the correctness of guess judgments.
Input
-----
- A single integer n (1 ≤ n ≤ 100000), the maximum possible value of x.
Interactive protocol (I/O format)
----------------------------------
To ask a question about a set S:
- Print a line: “? k s1 s2 … sk”
• k = |S| (k ≥ 1)
• s1, s2, …, sk are distinct integers in [1, n]
- Flush output immediately.
- Read a single word reply: “YES” or “NO”.
To make a guess for x:
- Print a line: “! g” where g is your guess (1 ≤ g ≤ n).
- Flush output immediately.
- Read the judge’s reply:
• “:)” if correct — your program must terminate immediately.
• “:(” if incorrect — you may continue if you still have remaining queries/guesses.
Flushing
--------
After every printed line, flush the output to avoid idleness/timeout:
- C++: fflush(stdout) or cout.flush()
- Java: System.out.flush()
- Pascal: flush(output)
- Python: sys.stdout.flush()
- See language docs for others.
Limits
------
- Maximum questions: 53
- Maximum guesses: 2
- n up to 100000
Important notes
----------------
- Because at least one of every two consecutive question answers is correct, you can design strategies that compare adjacent answers to filter lies.
- Guesses are always reliable; use them sparingly (you only have 2).
- Note that this problem has a scoring system. You are graded based on the # of queries you use. The lower the # of queries you use, the higher the score you get.
Example
--------
Input
6
(Sequence of interactions as seen by the contestant)
? 5 1 2 5 4 3
NO
! 6
:(
? 4 1 2 3 4
NO
! 5
:)
Explanation
- If the first question’s “NO” had been truthful, x would have to be 6.
- The guess “! 6” receives “:(“, so 6 is not the answer. Therefore, the first answer must have been a lie.
- By the guarantee, the next question’s answer must then be truthful.
- From “? 4 1 2 3 4” with reply “NO”, we conclude x ∉ {1,2,3,4}; combined with “6 is wrong”, x must be 5.
- The final guess “! 5” is confirmed with “:)”.
|