| Bakery Survey |
|
|
| This is an interactive problem. |
|
|
| Your city has n bakeries (where n is a power of 2), and bakery i specializes in one type of cake a_i. |
|
|
| You want to determine d — the number of distinct cake types available in the city. |
|
|
| You don't know the values of a_1, ..., a_n. However, your friend can help you by tasting cakes. Your friend has a memory capacity of k (where k is also a power of 2), which works as follows: |
|
|
| Your friend's memory is a queue S. You can perform two types of operations: |
|
|
| 1. Query operation: Ask your friend to taste the cake from bakery c. This will: |
| - Tell you whether a_c is already in S (the last k cake types tasted) |
| - Add a_c to the end of S |
| - If |S| > k, remove the front element from S |
|
|
| 2. Reset operation: Clear your friend's memory, making S empty. |
|
|
| Your goal is to find d while minimizing the total cost of operations. |
|
|
| This problem is graded based on the total cost of operations. The cost is calculated as: |
| Total Cost = (number of resets) × n + (number of queries) + 1 |
|
|
| Your answer will be compared to a reference solution ref_cost. Your final score will be calculated as the average of 100 × min(ref_cost / your_cost, 1) across all test cases. |
|
|
| You must use at most 100,000 operations in total. |
|
|
| Input |
|
|
| The first line contains two integers n and k (1 ≤ k ≤ n ≤ 1024, both k and n are powers of 2). |
|
|
| Interaction |
|
|
| To perform an operation, output one line in one of the following formats: |
|
|
| ? c — Ask your friend to taste the cake from bakery c (1 ≤ c ≤ n). |
| R — Reset your friend's memory. |
|
|
| After a query operation, read a single character: |
| - Y (Yes) if a_c is in the memory S |
| - N (No) if a_c is not in the memory S |
|
|
| When you have found the answer, output: |
| ! d — where d is the number of distinct cake types. |
|
|
| After printing the answer, your program should terminate immediately. |
|
|
| To flush your output, use: |
| - fflush(stdout) or cout.flush() in C++ |
| - System.out.flush() in Java |
| - stdout.flush() in Python |
|
|
| Example |
|
|
| Input: |
| 4 2 |
| N |
| N |
| Y |
| N |
| N |
| N |
| N |
|
|
| Output: |
| ? 1 |
| ? 2 |
| ? 3 |
| ? 4 |
| R |
| ? 4 |
| ? 1 |
| ? 2 |
| ! 3 |
|
|
| Time limit: 4 seconds |
| Memory limit: 512 MB |
