| 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 |