| Time Limit: 1 second |
| Memory Limit: 256 MB |
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| Overview |
| This is an INTERACTIVE PROBLEM. There are N kinds of minerals. For each kind there are exactly 2 slices, for a total of 2N slices numbered 1..2N. The judge fixes a hidden pairing: for each kind, the two slices of that kind form one pair. Your task is to determine all N pairs. |
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| You have access to a device. You may insert or extract slices from the device one at a time. After each operation, you learn how many DISTINCT kinds of minerals are currently present among the slices inside the device. |
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| Goal |
| Determine all N pairs while MINIMIZING the number of queries you use. You may use at most 1,000,000 queries. Any correct solution using ≤ 1,000,000 queries is accepted; fewer queries are considered better. |
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| Interaction Protocol (standard input/output) |
| 1) At the start, the judge outputs a single integer: |
| N |
| • 1 ≤ N ≤ 43,000. |
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| 2) You may then repeatedly perform queries. To toggle the presence of slice x in the device: |
| • Output a line: ? x |
| where 1 ≤ x ≤ 2N |
| • Flush stdout. |
| • Read a single integer r from stdin. |
| r is the number of DISTINCT kinds currently present among all slices inside the device after this toggle: |
| – If x was not in the device, it is now inserted. |
| – If x was already in the device, it is extracted. |
| – r counts how many mineral kinds appear at least once among the slices currently in the device. |
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| 3) When you have determined a pair (a, b), output exactly one line: |
| • Output: ! a b |
| where 1 ≤ a ≤ 2N and 1 ≤ b ≤ 2N. |
| Over the entire run you must output exactly N such lines, and together they must use each index 1..2N exactly once. |
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| 4) Order is flexible: |
| • You may interleave “? x” queries and “! a b” answers in any order. |
| • The judge terminates the interaction immediately after reading the N-th valid “! a b” line. Do not send any further output after that point. |
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| Important Rules and Constraints |
| • Only print lines of the form “? x” and “! a b”. |
| • Indices in queries and answers must satisfy their ranges. |
| • Exactly N answer lines must be printed and together cover each index 1..2N exactly once. |
| • A “query” is defined as one printed line “? x”. You may perform at most 1,000,000 queries. |
| • Flush stdout after every line you print (interactive). |
| • If you violate the protocol (bad format, invalid index, wrong pairings, too many queries, wrong number of answers), the judge will return a Wrong Answer verdict with a message. |
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| Device Behavior (for clarity) |
| • The device maintains a set S of slices currently inside. |
| • Query “? x” toggles membership of x in S: |
| – If x ∉ S, insert x. |
| – Else (x ∈ S), remove x. |
| • The judge replies with r = number of DISTINCT mineral kinds represented by S. If S is empty, r = 0. |
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| Scoring / Ratio (informative) |
| • Let Q be your total number of “? x” queries. |
| • The judge also knows an optimal_queries value for the instance. |
| • Your ratio is (1,000,000 − Q) / (1,000,000 − optimal_queries). |
| • The judge reports this ratio and scores only on Accepted submissions. |
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| Sample Communication |
| Judge → program: |
| 4 |
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| Program → judge: |
| ? 1 |
| Judge → program: |
| 1 |
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| Program → judge: |
| ? 2 |
| Judge → program: |
| 2 |
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| Program → judge: |
| ? 5 |
| Judge → program: |
| 2 |
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| Program → judge: |
| ? 2 |
| Judge → program: |
| 1 |
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| Program → judge: |
| ! 3 4 |
| Program → judge: |
| ! 5 1 |
| Program → judge: |
| ! 8 7 |
| Program → judge: |
| ! 2 6 |
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| (Here, the program used 4 queries total.) |
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