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해결한 사람
1
명
정답률
50.00
%
시간 제한
3000
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메모리 제한
2048
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문제 설명
국립 고고학 박물관은 볼리비아의 공룡 이주 패턴을 연구하고 있다. 고고학자들은 개의 서로 다른 장소에서 공룡 발자국을 발견하였다. 장소들은 오래된 것부터 시작해서 부터 까지 번호가 붙어 있다. 즉, 장소 이 가장 오래된 것이며 장소 이 가장 최근의 것이다.
각 장소의 공룡들은 (번 장소를 제외하고) 다른 더 오래된 장소에서 직접 이주해 왔다. 즉, 모든 장소 에 대해 () 장소 의 공룡들은 어떤 더 오래된 하나의 장소 에서 () 직접 이주해 왔다. 한 장소에서 다른 여러 장소로 직접 이주해 간 것은 가능하다.
고고학자들은 한 장소에서 다른 장소로 직접 이주해 간 관계를 무방향 간선으로 표현한다. 임의의 서로 다른 두 장소 와 에 대해 에서 로 하나 이상의 무방향 간선들을 이용하여 이동하는 것이 가능함을 알 수 있다. 두 장소 와 간의 거리는 에서 로 이동하며 거치는 최소 간선 개수로 정의된다.
예를 들어, 아래 그림은 개의 장소가 있고 , , , 인 상황을 보여 준다. 장소 에서 장소 로 이동하는데 개의 간선을 사용하면 가능하므로 두 장소 간의 거리는 이다.
박물관은 장소들 중 그 거리가 가장 먼 쌍을 알아내려고 한다.
답이 유일하지 않음에 주의하라. 위의 예에서 장소 쌍 과 장소 쌍 는 모두 그 거리가 전체에서 가장 큰 이다. 이러한 경우에 두 쌍 모두 정답으로 인정된다.
초기에 들의 값은 알려지지 않았다. 박물관은 연구팀을 각각의 장소에 보낸다. 보내는 순서는 장소 부터 장소 번호 순서대로, 즉, 장소 의 순서이다. 각 장소 ()에 도착하면 연구팀은 아래 두 작업을 진행한다.
- 장소 로 공룡들이 직접 이주한 다른 장소의 번호, 즉, 의 값을 알아낸다.
- 현재까지 수집된 정보들을 이용하여 박물관으로 하나의 메세지를 보낼 지 말지 결정한다.
메세지는 인공위성을 통해 전달되어 그 비용이 매우 비싸다. 그러한 이유로 각 메세지는 이상 이하의 정수 하나이다. 추가로, 연구팀이 전체 과정에서 보낼 수 있는 메세지는 최대 개 이다.
당신이 할 일은 아래 목표를 달성하는 전략을 구현하는 것이다.
- 연구팀은 장소들 중 어떤 곳에서 어떤 내용의 메세지를 보낼 지 결정한다.
- 박물관은 받은 메세지들만을 이용해서 어떤 쌍의 장소 간의 거리가 가장 먼지 파악할 수 있다. 박물관은 각 메세지가 어떤 장소에서 보내진 것인지 알 수 있다.
인공위성을 이용한 통신은 매우 비싸서, 당신의 해결책은 메세지들에 저장된 가장 큰 정수의 값과, 보낸 메세지의 총 개수에 따라 다른 점수를 받을 것이다.
구현 세부사항
두 개의 함수를 구현해야 한다. 하나는 연구팀을 위한 것이고, 다른 하나는 박물관을 위한 것이다.
연구팀을 위한 함수는 아래와 같다.
int send_message(int N, int i, int Pi)
- : 장소의 개수.
- : 현재 방문 중인 장소의 번호.
- :의 값.
- 이 함수는 각 테스트 케이스에 대해 번 호출된다. 의 순서로 호출된다.
이 함수는 이 장소에서 연구팀의 결과를 알려주는 를 리턴해야 한다.
- : 장소 에서 메세지를 보내지 않았다.
- : 연구팀은 장소 에서 를 메세지로 전송했다.
박물관을 위한 함수는 아래와 같다.
std::pair<int,int> longest_path(std::vector<int> S)
- : 길이 인 배열이고, 그 내용은 아래와 같다.
- .
- 각 ()에 대해 는
send_message(N, i, Pi)가 리턴한 값이다.
- 이 함수는 각 테스트 케이스에 대해 정확히 한 번 호출된다..
이 함수는 거리가 가장 먼 장소의 쌍 를 리턴해야 한다.
실제 채점 과정에서 위 두 함수를 호출하는 프로그램은 정확히 두 번 실행된다.
- 첫번째 실행에서는,
send_message가 정확히 번 호출된다.- 당신이 작성한 프로그램은 연속한 함수 호출이 진행되는 동안 정보를 저장하고 활용하는 것이 가능하다.
- 리턴된 값들(배열 )이 채점 시스템에 저장된다.
- 그레이더는 적응적으로 행동할 수 있다. 즉,
send_message함수 호출의 인자의 값이 이전 호출의 행동에 따라 달라질 수 있다.
- 두번째 실행에서는:
longest_path함수가 정확히 한 번 호출된다.longest_path함수가 사용할 수 있는 정보는, 첫번째 실행에서 저장된 배열 뿐이다.
제약 조건
- ().
서브태스크와 점수
| Subtask | Score | Additional Constraints |
|---|---|---|
| 1 | 장소 과, 다른 어떤 장소 간의 거리가 가장 큰 거리이다. | |
| 2 | 추가적인 제한이 없다. |
는 배열 에 등장하는 가장 큰 정수의 값이고 은 전체 메세지의 개수라고 하자.
각 테스트 케이스에서 아래 조건들 중 하나라도 사실이면 점수는 점이 된다. (CMS에서는 Output isn't correct로 결과가 나온다.):
- 의 원소 중 하나라도 규칙을 어겼다.
- 혹은 .
longest_path함수의 리턴 값이 정답이 아니다.
그렇지 않은 경우, subtask 에 대한 점수는 아래와 같이 계산된다.
| Condition | Score |
|---|---|
Subtask 에 대한 점수는 아래와 같이 계산된다.
| Condition | Score |
|---|---|
| , | |
| and | |
| and | |
| and |
예제
이고 , , , 이며 ()인 경우를 생각하자.
연구팀의 작전이, send_message 호출에 의해 알려진 최대 거리가 더 커지게 만드는
장소 쌍 를 알게 될
때마다 메세지 를 보내는 것이라고 하자.
초기에 연구팀이 알고 있는 최대 거리인 장소 쌍은 이다. 채점 서버에서 프로그램을 첫번째로 돌릴 때 아래와 같은 일이 일어난다.
| 함수 호출 | 리턴 값 () | |
|---|---|---|
send_message(10000, 1, 0) | ||
send_message(10000, 2, 1) | ||
send_message(10000, 3, 2) | ||
send_message(10000, 4, 2) |
이후의 모든 호출에서 이라는 것에 주의하라. 즉, 이후에는 최대 거리를 만드는 장소 쌍이 바뀌지 않으므로 연구팀은 메세지를 더이상 보내지 않는다.
이제, 프로그램의 두번째 실행에서 다음 호출이 일어난다.
longest_path([0, 10, 20, 30, 0, ...])
박물관은 연구팀이 보낸 마지막 메세지인 을 읽고 이 최대 거리를 만드는 장소 쌍임을 알 수 있다. 이 호출은 을 리턴한다.
이 방법으로 모든 경우에 정답을 찾지는 못함에 주의하라.
입력 형식
N
P[1] P[2] ... P[N-1]
출력 형식
S[1] S[2] ... S[N-1]
U V
Sample grader를 사용하기 위해 지정하는 의 값은 임의의 값이 가능함에 주의하라.
예제
예제 입력 1
10000
0 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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0 3
참고
Sample grader는 send_message와 longest_path를 한번의 실행에서 모두 호출한다. 이 동작은 채점 서버에서의 동작과 다르다.
출처 및 라이선스
International Olympiad in Informatics (IOI) 2025, official task package and official Korean translation.
Reporch에서 한국어 번역, 수식 표기, 이미지 호스팅 및 형식을 수정했습니다.
로그인 상태를 확인하는 중입니다.