신성 문자
시간 제한1초메모리 제한192 MB
16진수 비트맵을 해독한 뒤 각 검은 연결 성분 내부에 완전히 둘러싸인 흰 영역(구멍)의 개수를 세어 구멍 수에 대응하는 상형문자 부호를 알아낸다.
문제
고고학자는 초기 문명을 이해하기 위해 고대 언어로 쓰인 글을 연구하기도 한다. 약 3000년 전, 이집트에서는 동물, 사물, 신체의 모습을 본뜬 고대 문자인 '신성 문자'를 사용했다.
이 문제에서는 다음 여섯 개의 신성 문자를 인식하는 프로그램을 작성한다. 각 신성 문자는 검은 픽셀이 이어져 만들어진 하나의 도형이며, 여섯 문자는 서로 다른 개수의 '구멍'(도형으로 완전히 둘러싸인 흰색 영역)을 가진다는 점으로 구별된다. 즉, 구멍의 개수만으로 어떤 문자인지 알 수 있다.
| 신성 문자 | 코드 | 구멍 개수 |
|---|---|---|
| Ankh | A | 1 |
| Wedjat | J | 3 |
| Djed | D | 5 |
| Scarab | S | 4 |
| Was | W | 2 |
| Akhet | K | 0 |
주어진 그림에 들어 있는 모든 신성 문자를 알아내어라.
입력
입력은 여러 개의 테스트 케이스로 이루어진다. 각 테스트 케이스는 하나 이상의 신성 문자를 담은 하나의 그림이다. 그림은 0과 1로 이루어지며, 1은 검은 픽셀, 0은 흰 픽셀을 나타낸다.
그림의 각 줄은 16진수로 인코딩되어 있다. 예를 들어 여덟 개의 픽셀 10011100은 9c로 인코딩된다. 16진수 인코딩에는 문자 0–9와 a–f를 사용한다.
각 테스트 케이스의 첫 줄에는 두 정수 H와 W가 주어진다. H (0<H≤200)는 그림의 줄 수, W (0<W≤50)는 각 줄에 있는 16진수 문자의 개수이며, 따라서 그림의 가로 픽셀 수는 4W이다. 이어지는 H개의 줄에 그림이 주어진다.
입력으로 주어지는 그림은 다음 규칙을 만족한다.
- 그림에는 위에서 설명한 여섯 개의 신성 문자만 나타난다.
- 모든 그림에는 올바른 신성 문자가 적어도 하나 있다.
- 모든 검은 픽셀은 어떤 올바른 신성 문자의 일부이다.
- 하나의 신성 문자는 검은 픽셀이 이어진 형태이다. 즉, 모든 검은 픽셀은 위, 아래, 왼쪽, 오른쪽 중 적어도 한 방향에서 다른 검은 픽셀과 맞닿아 있다.
- 서로 다른 신성 문자는 맞닿지 않으며, 한 문자가 다른 문자를 안에 포함하지도 않는다.
- 두 검은 픽셀이 대각선으로 맞닿아 있으면, 그 두 픽셀 모두와 상하좌우로 맞닿은 검은 픽셀이 반드시 존재한다.
- 신성 문자는 다소 비뚤어져 있을 수 있으나, 그 구멍의 개수는 항상 위 표와 같다.
마지막 테스트 케이스 다음 줄에는 0 두 개가 주어진다.
출력
각 테스트 케이스마다 Case x: 코드들 형식으로 한 줄에 출력한다. 여기서 x는 1부터 시작하는 테스트 케이스 번호이고, 코드들은 그림에 있는 신성 문자들의 코드를 알파벳 순서(사전순)로 정렬해 이어 붙인 문자열이다.
예제2
예제 1
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00000f8000000000003e00000 00000f8000000000001e00000 00000f8000000000001f00000 00000fc000000000001f00000 00000fc000000000001f00000 00000fc000000000001f00000 00000fc000000000000f00000 00001fc000000000000f80000 00001fc000000000000f80000 00001fc000000000000f80000 00001fc000000000000f80000 00001fe000000000000f80000 00001fe000000000000780000 00001fe0000000000007c0000 00001fe0000000000007c0000 00003fe0000000000007c0000 00003fe0000000000007c0000 00003fe0000000000007c0000 00003fe0000c00000003c0000 00000000003ff0000003c0000 00000000007ff8000003e0000 0000000001fffc000003e0000 0000000003e03f000003e0000 0000000007c00f000003e0000 000000000f0003800003f0000 000000000e0001c00003fc000 000000001c0001e00007fe000 000000003c0000e0000fff000 000000073c000070000fdf000 0000001ff8000070001f0f800 0000001ff8000070001e07800 0000003cf0000078001e03800 0000003870000033001e03800 000000307800003fc01e03800 000000703800007fe00e03800 000000703800007ce00e03800 000000703c000078700703800 000000701e0000f0700701000 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예상 출력Case 1: AKW Case 2: AAAAA
예제 2
입력15 5 00000 00000 00000 1ff00 1ff00 1ff00 1cf00 1cf00 1ff00 1ff00 1ff00 1ff00 00000 00000 00000 0 0
예상 출력Case 1: A