시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

상근이와 정인이는 숫자 맞추기 게임을 하고 있다.

먼저, 정인이는 1보다 크거나 같고, n보다 작거나 같은 자연수 하나를 생각한다.

상근이는 1보다 크거나 같고, n보다 작거나 같은 자연수 x를 정해 정인이에게 생각한 숫자가 x인지 물어볼 수 있다. 이때 정인이는 자신이 생각한 숫자와 x의 최대공약수가 몇 인지 말해준다.

다음은 n=6일 때 가능한 상근이와 정인이의 대화이다.

  • 상근: 3이야?
  • 정인: 3이랑 내가 생각한 숫자의 최대공약수는 1이야.
  • 상근: (음... 그럼 3이랑 6은 아니네? 근데 1,2,4,5는 될 수 있어!) 그럼 2야?
  • 정인: 2랑 내가 생각한 숫자의 최대공약수는 2야.
  • 상근: (오!? 그럼 1, 5는 아니겠네?) 너가 생각한 숫자는 4야 맞지?
  • 정인: 4랑 내가 생각한 숫자의 최대공약수는 2야.
  • 상근: 그럼 니가 생각한 숫자는 2네 ㅋㅋㅋ

위의 예에서 상근이는 정인이가 생각한 숫자를 맞추기 위해서 질문을 총 3번 했다. 하지만, n=6인 경우에 항상 2번의 질문으로 정인이가 생각한 숫자를 맞출 수 있다.

제일 먼저 상근이는 6을 물어보면 된다. 만약 정인이가 1이라고 대답했다면, 정인이가 생각한 숫자는 1과 5중 하나이기 때문에, 2번 질문으로 맞출 수 있다. 정인이의 대답이 2라면, 정인이가 생각한 숫자는 2와 4중 하나이다. 만약, 정인이가 3이라고 대답했다면, 정답은 3이고, 6이라고 대답했다면 6이다.

따라서, 상근이는 최대 2번의 질문으로 정인이가 생각한 숫자를 맞출 수 있다.

n이 주어졌을 때, 상근이가 최적의 방법으로 질문했을 때, 최대 몇 번 만에 정인이가 생각한 숫자를 맞출 수 있는지 구하는 프로그램을 작성하시오.

입력

첫째 줄에 n이 주어진다. 2 ≤ n ≤ 10,000

출력

첫째 줄에 상근이가 최적의 방법으로 질문했을 때, 최대 몇 번의 질문으로 정인이가 생각한 숫자를 맞출 수 있는지 출력한다.

예제 입력 1

6

예제 출력 1

2
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Andrew knew that Paul&rsquo;s age is an integer between 1 and n, inclusive. Andrew can guess any number x between 1 and n, and Paul will tell him what is the greatest common divisor of x and his age.<\/p>\r\n\r\n<p>Here&rsquo;s a possible course of the game for n = 6. Andrew starts with guessing 3, and Paul replies that the greatest common divisor of 3 and his age is 1. That means that Paul&rsquo;s age can&rsquo;t be 3 or 6, but can still be 1, 2, 4 or 5. Andrew continues with guessing 2, and Paul replies 2. That means that Paul&rsquo;s age can&rsquo;t be 1 or 5, and the only two remaining choices are 2 and 4. Finally, Andrew guesses 4, and Paul replies 2. That means that Paul&rsquo;s age is 2, and the game is over.<\/p>\r\n\r\n<p>Andrew needed three guesses in the above example, but it&rsquo;s possible to always determine Paul&rsquo;s age in at most two guesses for n = 6. The optimal strategy for Andrew is: at the \ufb01rst step, guess 6. If Paul says 1, then its 1 or 5 and he can check which one by guessing 5. If Paul says 2, then its 2 or 4, and he can check by guesing 4 as we&rsquo;ve seen above. If Paul says 3, then we already know the answer is 3. Finally, if Paul says 6, the answer is 6.<\/p>\r\n\r\n<p>What is the number of guesses required in the worst case if Andrew guesses optimally for the given n?<\/p>\r\n","input":"<p>The input \ufb01le contains one integer n, 2 &le; n &le; 10 000.<\/p>\r\n","output":"<p>Output one integer &mdash; the number of guesses Andrew will need to make in the worst case.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ICPC > Regionals > Northern Eurasia > Northern Eurasia Finals > NEERC 2011 G번