| 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 “:)”. | |