CodeForces 679A Bear and Prime 100

题目直通车 ：CodeForces 679A

知识要点：交互题 数学分析

（参考过网上一些资料，在这补充一些）

A. Bear and Prime 100

This is an interactive problem. In the output section below you will see the information about flushing the output.
Bear Limak thinks of some hidden number — an integer from interval [2, 100].
Your task is to say if the hidden number is prime or composite.
Integer x > 1 is called prime
if it has exactly two distinct divisors, 1 and x.
If integer x > 1 is not prime, it's called composite.
You can ask up to 20 queries about
divisors of the hidden number. In each query you should print an integer from interval [2, 100]. The system will answer "yes"
if your integer is a divisor of the hidden number. Otherwise, the answer will be "no".
For example, if the hidden number is 14 then
the system will answer "yes" only if you print 2, 7 or 14.
When you are done asking queries, print "prime" or "composite"
and terminate your program.
You will get the Wrong Answer verdict if
you ask more than 20 queries, or if you print an integer not from the range [2, 100].
Also, you will get the Wrong Answer verdict if the printed answer isn't correct.
You will get the Idleness Limit Exceeded verdict
if you don't print anything (but you should) or if you forget about flushing the output (more info below).

Input
After each query you should read one string from the input. It will be "yes"
if the printed integer is a divisor of the hidden number, and "no" otherwise.

Output
Up to 20 times you can ask a query —
print an integer from interval [2, 100] in one line. You have to both print the end-of-line character and flush the
output. After flushing you should read a response from the input.
In any moment you can print the answer "prime" or "composite"
(without the quotes). After that, flush the output and terminate your program.
To flush you can use (just after printing an integer and end-of-line):

fflush(stdout) in C++;

System.out.flush() in Java;

stdout.flush() in Python;

flush(output) in Pascal;

See the documentation for other languages.

Hacking. To hack someone, as the input you should print the hidden number — one integer from the interval [2, 100].
Of course, his/her solution won't be able to read the hidden number from the input.

Examples

input

yes
no
yes

output

2
80
5
composite

input

no
yes
no
no
no

output

58
59
78
78
2
prime

Note
The hidden number in the first query is 30. In a
table below you can see a better form of the provided example of the communication process.



The hidden number is divisible by both 2 and 5.
Thus, it must be composite. Note that it isn't necessary to know the exact value of the hidden number. In this test, the hidden number is 30.



59 is a divisor of the hidden number. In the interval [2, 100] there
is only one number with this divisor. The hidden number must be 59, which is prime. Note that the answer is known even after the
second query and you could print it then and terminate. Though, it isn't forbidden to ask unnecessary queries (unless you exceed the limit of 20 queries).

题目大意：
交互题，系统随机生成一个【2,100】的数，你通过询问一些数字是不是他的因子来判断这个数是什么质数还是合数（询问不超过20个）
每次输出一个数后，系统会输入 yes 或者 no。
解题思路：
如果一个数为合数，那么至少有三个因子 （1，因子，本身） 而因子中肯定包含质数，即合数肯定能整除一个质数。
列如 86 中因子 1,2,43,86. 每一个100以内的合数包含 质数*另一个质数 这对因子。特例 4,9,25,49 这些数是 质数*这个质数。
所以通过枚举 50 以内的质数 {2,3,5,7,9,11,13,17,19,23,29,31，37,41,43,47} + {4,9,25,49}。
对每一个 （2-100）的数中 如果包含上述两个上述的数 ，那么这个数为合数 反之为质数。
本题需要使用到 题目中所给的 fflush（sdout）

#include <iostream>
#include <cstdio>
#include <cmath>
#include <map>
#include <algorithm>
#include <cstring>
#include <string>
using namespace std;
int main()
{
int a[19] = {2,3,4,5,7,9,11,13,17,19,23,25,29,31,37,41,43,47,49};
char s[5];
int i,j,bj,sum=0;
for(i=0;i<19;i++)
{
printf("%d\n",a[i]);
fflush(stdout);
scanf("%s",s);
if (s[0] == 'y')
{
sum++;
}
}
if(sum>1)
{
printf("composite\n");
fflush(stdout);
}
else
{
printf("prime\n");
fflush(stdout);
}
return 0;
}