F. Coffee Varieties
time limit per test1 second
memory limit per test256 megabytes
This is the easy version of the problem. You can find the hard version in the Div. 1 contest. Both versions only differ in the number of times you can ask your friend to taste coffee.
This is an interactive problem.
You're considering moving to another city, where one of your friends already lives. There are n cafés in this city, where n is a power of two. The i-th café produces a single variety of coffee ai.
As you're a coffee-lover, before deciding to move or not, you want to know the number d of distinct varieties of coffees produced in this city.
You don't know the values a1,…,an. Fortunately, your friend has a memory of size k, where k is a power of two.
Once per day, you can ask him to taste a cup of coffee produced by the café c, and he will tell you if he tasted a similar coffee during the last k days.
You can also ask him to take a medication that will reset his memory. He will forget all previous cups of coffee tasted. You can reset his memory at most 30 000 times.
More formally, the memory of your friend is a queue S. Doing a query on café c will:
Tell you if ac is in S;
Add ac at the back of S;
If |S|>k, pop the front element of S.
Doing a reset request will pop all elements out of S.
Your friend can taste at most 2n2k cups of coffee in total. Find the diversity d (number of distinct values in the array a).
Note that asking your friend to reset his memory does not count towards the number of times you ask your friend to taste a cup of coffee.
In some test cases the behavior of the interactor is adaptive. It means that the array a may be not fixed before the start of the interaction and may depend on your queries. It is guaranteed that at any moment of the interaction, there is at least one array a consistent with all the answers given so far.
Input
The first line contains two integers n and k (1≤k≤n≤1024, k and n are powers of two).
It is guaranteed that 2n2k≤20 000.
Interaction
You begin the interaction by reading n and k.
To ask your friend to taste a cup of coffee produced by the café c, in a separate line output
? c
Where c must satisfy 1≤c≤n. Don't forget to flush, to get the answer.
In response, you will receive a single letter Y (yes) or N (no), telling you if variety ac is one of the last k varieties of coffee in his memory.
To reset the memory of your friend, in a separate line output the single letter R in upper case. You can do this operation at most 30 000 times.
When you determine the number d of different coffee varieties, output
! d
In case your query is invalid, you asked more than 2n2k queries of type ? or you asked more than 30 000 queries of type R, the program will print the letter E and will finish interaction. You will receive a Wrong Answer verdict. Make sure to exit immediately to avoid getting other verdicts.
After printing a query do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:
fflush(stdout) or cout.flush() in C++;
System.out.flush() in Java;
flush(output) in Pascal;
stdout.flush() in Python;
see documentation for other languages.
Hack format
The first line should contain the word fixed
The second line should contain two integers n and k, separated by space (1≤k≤n≤1024, k and n are powers of two).
It must hold that 2n2k≤20 000.
The third line should contain n integers a1,a2,…,an, separated by spaces (1≤ai≤n).
Examples
input
4 2
N
N
Y
N
N
N
N
output
? 1
? 2
? 3
? 4
R
? 4
? 1
? 2
! 3
input
8 8
N
N
N
N
Y
Y
output
? 2
? 6
? 4
? 5
? 2
? 5
! 6
Note
In the first example, the array is a=[1,4,1,3]. The city produces 3 different varieties of coffee (1, 3 and 4).
The successive varieties of coffee tasted by your friend are 1,4,1,3,3,1,4 (bold answers correspond to Y answers). Note that between the two ? 4 asks, there is a reset memory request R, so the answer to the second ? 4 ask is N. Had there been no reset memory request, the answer to the second ? 4 ask is Y.
In the second example, the array is a=[1,2,3,4,5,6,6,6]. The city produces 6 different varieties of coffee.
The successive varieties of coffee tasted by your friend are 2,6,4,5,2,5.
題意
你來到一個城市，這個城市有n個咖啡館，每個咖啡館都銷售一種咖啡，你現在想知道這個城市一共有多少種咖啡在賣。
你可以讓你的朋友去第i個咖啡館喝咖啡，你的朋友會告訴你這咖啡時候和他喝過的前k個咖啡的味道存在相同。
easy版本你可以問2n^2/k次，hard版本只能問3n^2/2k次。
題解
視頻題解：https://www.bilibili.com/video/av86529667/
考慮最暴力的做法，你依次讓朋友去咖啡館1，咖啡館2，這時候你就知道咖啡館2和1是否相同了，然后這時候你清理一下記憶；然后你讓朋友去13，去14，然后去23，24，34。這樣你就能知道前4家咖啡館兩兩之間的關系了，但是這肯定詢問次數很多。
div2的easy版本，你按照大小k/2來進行分塊，一共可以分成n/(k/2)塊，然后你依次詢問第一塊，第二塊；第一塊，第三塊；第一塊，第四塊；第二塊，第三塊；第二塊，第四塊；第三塊，第四塊。由於你每次都詢問兩塊，每塊的大小是k/2，加在一起恰好是k，所以你每一對你都能知道全部的信息，這樣詢問的話，你一共詢問次數是(2n^2-kn)/(k)，恰好是滿足easy版本的。
div1的hard版本，我們考慮問完第一塊，第二塊之后，我們緊接着問第三塊，我們會發現第三塊的記憶覆蓋了第一塊，實際上我們相當於問了12和23。 所以我只要連續的去問就可以了，這樣的詢問次數恰好是放縮到3n^2/2k。
代碼
#include<bits/stdc++.h>
using namespace std;
const int maxn = 30006;
int n,k;
int good[maxn];
void reset(){
cout<<"R"<<endl;
}
bool query(int x){
cout<<"? "<<x+1<<endl;
string s;cin>>s;
if(s[0]=='Y')return true;
return false;
}
int main(){
cin>>n>>k;
for(int i=0;i<n;i++)
good[i]=1;
if(k==1){
for(int i=0;i<n;i++){
for(int j=i+1;j<n;j++){
reset();
query(i);
if(query(j)){
good[j]=false;
}
}
}
}else{
int block=k/2;
int m=n/block;
for(int jump=1;jump<m;jump++){
for(int start=0;start<jump&&start+jump<m;start++){
reset();
for(int i=start;i<m;i+=jump){
for(int x=i*block;x<(i+1)*block;x++){
if(query(x)){
good[x]=false;
}
}
}
}
}
}
int ans = 0;
for(int i=0;i<n;i++){
if(good[i])ans++;
}
cout<<"! "<<ans<<endl;
}