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문제

ACM 코더들은 보편적으로 사용하는 많은 알고리즘들에 대한 이해도가 폭넓게 높아야 한다. 그래서 일반적으로 ACM 대회를 개최할 땐 되도록이면 많은 알고리즘을 두루두루 사용하게끔 문제를 낸다.

하지만 어떤 대회에서, 문제 전체에서 단 한 번도 사용되지 않는 알고리즘이 하나라도 존재한다면 그건 문제 있는 문제 세트이다. 예를 들면 DP가 없거나, 그래프 이론과 관련된 알고리즘이 없는 문제 세트는 문제가 있다는 것이다.

이번 문제에서는 이번 대회를 위해 만든 문제 세트에 대하여, 문제들의 부분집합으로 이루어진 문제 세트들 중 문제 없는 문제 세트를 만들어볼 것이다. 세트 내에서 어떤 알고리즘이 너무 많이 사용되는 것은 상관없으나, 모든 알고리즘들을 반드시 한 번 이상 사용해야만 한다.

하지만 문제를 만드는 것은 매우 어려운 일이기 때문에 되도록이면 적은 문제로 이루어진 세트를 찾아야 한다. 그렇게 해야 남는 문제를 다음 대회에 사용할 수가 있다.

입력

첫 줄에 테스트 케이스의 수 K가 주어진다.

각 테스트 케이스의 첫 줄엔 두 정수 M과 N이 주어진다. (1 ≤ M, N ≤ 20)

M은 대회에서 사용할 알고리즘의 개수이며, N은 문제의 총 개수이다.

대회에서 사용해야 할 알고리즘은 1부터 M까지의 모든 자연수이며, 문제는 첫 번째 문제가 A, 두 번째 문제가 B, 세 번째 문제가 C.. 의 방식으로 이름을 붙인다.

이어서 N줄에 걸쳐 첫 번째 문제부터 N번째 문제까지 어떤 알고리즘들을 사용하는지가 공백으로 구분되어 주어진다.

출력

각 테스트 케이스마다 Data Set K: 를 출력한 뒤, 1부터 M까지의 모든 알고리즘을 포함할 수 있는 최소 크기의 문제 세트에 속한 문제들을 사전순으로 출력한다.

만일 답이 여러 가지라면 그 중 사전순으로 가장 앞선 것을 출력한다.

모든 테스트 케이스에서 답이 존재하지 않는 경우는 없다.

각 테스트 케이스의 사이엔 빈 줄을 하나 출력한다.

예제 입력 1

2
2 3
1
2
1 2
4 5
1 2 3
1 2
2 4
1 3 4
2 3 4

예제 출력 1

Data Set 1: C

Data Set 2: A C
[{"problem_id":"5175","problem_lang":"0","title":"\ubb38\uc81c\uc5c6\ub294 \ubb38\uc81c","description":"<p>ACM \ucf54\ub354\ub4e4\uc740 \ubcf4\ud3b8\uc801\uc73c\ub85c \uc0ac\uc6a9\ud558\ub294 \ub9ce\uc740 \uc54c\uace0\ub9ac\uc998\ub4e4\uc5d0 \ub300\ud55c \uc774\ud574\ub3c4\uac00 \ud3ed\ub113\uac8c \ub192\uc544\uc57c \ud55c\ub2e4. \uadf8\ub798\uc11c \uc77c\ubc18\uc801\uc73c\ub85c ACM \ub300\ud68c\ub97c \uac1c\ucd5c\ud560 \ub550 \ub418\ub3c4\ub85d\uc774\uba74 \ub9ce\uc740 \uc54c\uace0\ub9ac\uc998\uc744 \ub450\ub8e8\ub450\ub8e8 \uc0ac\uc6a9\ud558\uac8c\ub054 \ubb38\uc81c\ub97c \ub0b8\ub2e4.<\/p>\r\n\r\n<p>\ud558\uc9c0\ub9cc \uc5b4\ub5a4 \ub300\ud68c\uc5d0\uc11c, \ubb38\uc81c \uc804\uccb4\uc5d0\uc11c \ub2e8 \ud55c \ubc88\ub3c4 \uc0ac\uc6a9\ub418\uc9c0 \uc54a\ub294 \uc54c\uace0\ub9ac\uc998\uc774 \ud558\ub098\ub77c\ub3c4 \uc874\uc7ac\ud55c\ub2e4\uba74 \uadf8\uac74 \ubb38\uc81c \uc788\ub294 \ubb38\uc81c \uc138\ud2b8\uc774\ub2e4. \uc608\ub97c \ub4e4\uba74 DP\uac00 \uc5c6\uac70\ub098, \uadf8\ub798\ud504 \uc774\ub860\uacfc \uad00\ub828\ub41c \uc54c\uace0\ub9ac\uc998\uc774 \uc5c6\ub294 \ubb38\uc81c \uc138\ud2b8\ub294 \ubb38\uc81c\uac00 \uc788\ub2e4\ub294 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc774\ubc88 \ubb38\uc81c\uc5d0\uc11c\ub294 \uc774\ubc88 \ub300\ud68c\ub97c \uc704\ud574 \ub9cc\ub4e0 \ubb38\uc81c \uc138\ud2b8\uc5d0 \ub300\ud558\uc5ec, \ubb38\uc81c\ub4e4\uc758 \ubd80\ubd84\uc9d1\ud569\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ubb38\uc81c \uc138\ud2b8\ub4e4 \uc911 \ubb38\uc81c \uc5c6\ub294 \ubb38\uc81c \uc138\ud2b8\ub97c \ub9cc\ub4e4\uc5b4\ubcfc \uac83\uc774\ub2e4. \uc138\ud2b8 \ub0b4\uc5d0\uc11c \uc5b4\ub5a4 \uc54c\uace0\ub9ac\uc998\uc774 \ub108\ubb34 \ub9ce\uc774 \uc0ac\uc6a9\ub418\ub294 \uac83\uc740 \uc0c1\uad00\uc5c6\uc73c\ub098, \ubaa8\ub4e0 \uc54c\uace0\ub9ac\uc998\ub4e4\uc744 \ubc18\ub4dc\uc2dc \ud55c \ubc88 \uc774\uc0c1 \uc0ac\uc6a9\ud574\uc57c\ub9cc \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ud558\uc9c0\ub9cc \ubb38\uc81c\ub97c \ub9cc\ub4dc\ub294 \uac83\uc740 \ub9e4\uc6b0 \uc5b4\ub824\uc6b4 \uc77c\uc774\uae30 \ub54c\ubb38\uc5d0 \ub418\ub3c4\ub85d\uc774\uba74 \uc801\uc740 \ubb38\uc81c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc138\ud2b8\ub97c \ucc3e\uc544\uc57c \ud55c\ub2e4. \uadf8\ub807\uac8c \ud574\uc57c \ub0a8\ub294 \ubb38\uc81c\ub97c \ub2e4\uc74c \ub300\ud68c\uc5d0 \uc0ac\uc6a9\ud560 \uc218\uac00 \uc788\ub2e4.<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc218 K\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab \uc904\uc5d4 \ub450 \uc815\uc218 M\uacfc N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; M, N &le; 20)<\/p>\r\n\r\n<p>M\uc740 \ub300\ud68c\uc5d0\uc11c \uc0ac\uc6a9\ud560 \uc54c\uace0\ub9ac\uc998\uc758 \uac1c\uc218\uc774\uba70, N\uc740 \ubb38\uc81c\uc758 \ucd1d \uac1c\uc218\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub300\ud68c\uc5d0\uc11c \uc0ac\uc6a9\ud574\uc57c \ud560 \uc54c\uace0\ub9ac\uc998\uc740 1\ubd80\ud130 M\uae4c\uc9c0\uc758 \ubaa8\ub4e0 \uc790\uc5f0\uc218\uc774\uba70, \ubb38\uc81c\ub294 \uccab \ubc88\uc9f8 \ubb38\uc81c\uac00 A, \ub450 \ubc88\uc9f8 \ubb38\uc81c\uac00 B, \uc138 \ubc88\uc9f8 \ubb38\uc81c\uac00 C.. \uc758 \ubc29\uc2dd\uc73c\ub85c \uc774\ub984\uc744 \ubd99\uc778\ub2e4.<\/p>\r\n\r\n<p>\uc774\uc5b4\uc11c N\uc904\uc5d0 \uac78\uccd0 \uccab \ubc88\uc9f8 \ubb38\uc81c\ubd80\ud130 N\ubc88\uc9f8 \ubb38\uc81c\uae4c\uc9c0 \uc5b4\ub5a4 \uc54c\uace0\ub9ac\uc998\ub4e4\uc744 \uc0ac\uc6a9\ud558\ub294\uc9c0\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 Data Set K: \ub97c \ucd9c\ub825\ud55c \ub4a4, 1\ubd80\ud130 M\uae4c\uc9c0\uc758 \ubaa8\ub4e0 \uc54c\uace0\ub9ac\uc998\uc744 \ud3ec\ud568\ud560 \uc218 \uc788\ub294 \ucd5c\uc18c \ud06c\uae30\uc758 \ubb38\uc81c \uc138\ud2b8\uc5d0 \uc18d\ud55c \ubb38\uc81c\ub4e4\uc744 \uc0ac\uc804\uc21c\uc73c\ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc77c \ub2f5\uc774 \uc5ec\ub7ec \uac00\uc9c0\ub77c\uba74 \uadf8 \uc911 \uc0ac\uc804\uc21c\uc73c\ub85c \uac00\uc7a5 \uc55e\uc120 \uac83\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0\uc11c \ub2f5\uc774 \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc0ac\uc774\uc5d4 \ube48 \uc904\uc744 \ud558\ub098 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"5175","problem_lang":"1","title":"Got problems?","description":"<p>In preparation for the contest, we came up with a number of algorithms and programming topics we want to check, such as graph algorithms, geometry, searching, sorting, string processing, etc.<\/p>\r\n\r\n<p>Also, we made up a number of problems (one of which you&rsquo;re looking at), and for each problem determined which categories it falls into. A problem will always belong to at least one category, but it can belong to several categories, potentially even all of them.<\/p>\r\n\r\n<p>Now we want to find a set of problems that will cover all categories. And as good problems are hard to make up and therefore precious, we want to use as few problems as possible. You are to write a program that will save us from doing this by hand.<\/p>\r\n","input":"<p>The first line will contain the number K of input data sets. This is followed by K data sets, each of the following form:<\/p>\r\n\r\n<p>The first line of a data set contains two numbers, M and N (1 &le; M, N &le; 20). M is the number of problem categories, and N is the number of available problems. Problem categories are denoted by 1, . . . , M, and problems by A, B, . . .. The following N lines each contain the numbers of the categories covered by a problem &mdash; the first line for problem A, the second one for B, and so on.<\/p>\r\n","output":"<p>The output file contains one line for each input, separated by an empty line. Each line contains first the number of the data set, and then the solution. The solution is the list of problems to be used, separated by whitespace, and sorted alphabetically.<\/p>\r\n\r\n<p>You may assume that there is always a solution, but it need not be unique. If there are several best solutions (i.e. of equal length), output the one which comes alphabetically first in the output format just described.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

University > The USC Programming Contest > Fall 2007 A번