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문제

아래 왼쪽 그림은 성냥개비 2×(3×4) = (24)개로 완전 3×3 그리드를 만든 것이다. 모든 성냥개비의 길이는 1이다. 그리드에는 다양한 크기의 정사각형이 있다. 정사각형의 크기는 변의 길이와 같다. 왼쪽 그림에 크기가 1인 정사각형은 9개, 2인 정사각형은 4개, 3인 정사각형은 1개가 있다.

완전 그리드에 있는 성냥개비에 아래 왼쪽 그림에 나와있는 것처럼 왼쪽부터 오른쪽, 위부터 아래 순서로 번호를 매길 수 있다. 완전 그리드에서 성냥개비 일부를 제거하면, 정사각형의 일부를 파괴할 수 있고, 완전하지 않은 그리드를 만들 수 있다. 오른쪽 그림은 완전하지 않은 3×3 그리드이며, 12, 17, 23번 성냥개비를 제거했을 때이다. 이 결과로 크기가 1인 정사각형 5개, 2인 정사각형 3개, 3인 정사각형 1개가 제거되고, 크기가 1인 정사각형이 3개, 2인 정사각형이 1개 남는다.

2n(n+1)개를 넘지 않는 성냥개비로 만든 완전 또는 완전하지 않은 n×n 그리드가 주어진다. (n ≤ 5) 이때, n×n 그리드의 모든 정사각형을 파괴하기 위해 제거해야 하는 성냥개비 개수의 최솟값을 구하는 프로그램을 작성하시오.

입력

입력은 T개의 테스트 케이스로 이루어져 있다. 첫째 줄에는 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스는 두 줄로 이루어져 있다.

첫째 줄에는 5를 넘지 않는 자연수 n이 주어진다. n은 그리드의 크기이다. 둘째 줄에는 음이 아닌 정수 k가 주어진다. k는 n×n 그리드에서 제거된 성냥개비의 개수이다. k의 다음에는 제거한 성냥개비의 번호가 주어진다. k가 0인 경우에는 입력으로 완전한 그리드가 주어진 것이고, 아닌 경우에는 완전하지 않는 그리드가 주어진 것이다.

출력

각 테스트 케이스에 대해서, 입력으로 주어진 그리드에서 모든 정사각형을 파괴하기 위해 제거해야 하는 성냥개비 개수의 최솟값을 출력한다.

예제 입력 1

2
2
0
3
3 12 17 23

예제 출력 1

3
3
[{"problem_id":"7350","problem_lang":"0","title":"\uc815\uc0ac\uac01\ud615 \ubd80\uc218\uae30","description":"<p>\uc544\ub798 \uc67c\ucabd \uadf8\ub9bc\uc740 \uc131\ub0e5\uac1c\ube44 2&times;(3&times;4) = (24)\uac1c\ub85c \uc644\uc804 3&times;3 \uadf8\ub9ac\ub4dc\ub97c \ub9cc\ub4e0 \uac83\uc774\ub2e4. \ubaa8\ub4e0 \uc131\ub0e5\uac1c\ube44\uc758 \uae38\uc774\ub294 1\uc774\ub2e4. \uadf8\ub9ac\ub4dc\uc5d0\ub294 \ub2e4\uc591\ud55c \ud06c\uae30\uc758 \uc815\uc0ac\uac01\ud615\uc774 \uc788\ub2e4. \uc815\uc0ac\uac01\ud615\uc758 \ud06c\uae30\ub294 \ubcc0\uc758 \uae38\uc774\uc640 \uac19\ub2e4. \uc67c\ucabd \uadf8\ub9bc\uc5d0 \ud06c\uae30\uac00 1\uc778 \uc815\uc0ac\uac01\ud615\uc740 9\uac1c, 2\uc778 \uc815\uc0ac\uac01\ud615\uc740 4\uac1c, 3\uc778 \uc815\uc0ac\uac01\ud615\uc740 1\uac1c\uac00 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc644\uc804 \uadf8\ub9ac\ub4dc\uc5d0 \uc788\ub294 \uc131\ub0e5\uac1c\ube44\uc5d0 \uc544\ub798 \uc67c\ucabd \uadf8\ub9bc\uc5d0 \ub098\uc640\uc788\ub294 \uac83\ucc98\ub7fc \uc67c\ucabd\ubd80\ud130 \uc624\ub978\ucabd, \uc704\ubd80\ud130 \uc544\ub798 \uc21c\uc11c\ub85c \ubc88\ud638\ub97c \ub9e4\uae38 \uc218 \uc788\ub2e4. \uc644\uc804 \uadf8\ub9ac\ub4dc\uc5d0\uc11c \uc131\ub0e5\uac1c\ube44 \uc77c\ubd80\ub97c \uc81c\uac70\ud558\uba74, \uc815\uc0ac\uac01\ud615\uc758 \uc77c\ubd80\ub97c \ud30c\uad34\ud560 \uc218 \uc788\uace0, \uc644\uc804\ud558\uc9c0 \uc54a\uc740 \uadf8\ub9ac\ub4dc\ub97c \ub9cc\ub4e4 \uc218 \uc788\ub2e4. \uc624\ub978\ucabd \uadf8\ub9bc\uc740 \uc644\uc804\ud558\uc9c0 \uc54a\uc740 3&times;3 \uadf8\ub9ac\ub4dc\uc774\uba70, 12, 17, 23\ubc88 \uc131\ub0e5\uac1c\ube44\ub97c \uc81c\uac70\ud588\uc744 \ub54c\uc774\ub2e4. \uc774 \uacb0\uacfc\ub85c \ud06c\uae30\uac00 1\uc778 \uc815\uc0ac\uac01\ud615 5\uac1c, 2\uc778 \uc815\uc0ac\uac01\ud615 3\uac1c, 3\uc778 \uc815\uc0ac\uac01\ud615 1\uac1c\uac00 \uc81c\uac70\ub418\uace0, \ud06c\uae30\uac00 1\uc778 \uc815\uc0ac\uac01\ud615\uc774 3\uac1c, 2\uc778 \uc815\uc0ac\uac01\ud615\uc774 1\uac1c \ub0a8\ub294\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/matchsqaure(1).png\" style=\"height:318px; width:629px\" \/><\/p>\r\n\r\n<p>2n(n+1)\uac1c\ub97c \ub118\uc9c0 \uc54a\ub294 \uc131\ub0e5\uac1c\ube44\ub85c \ub9cc\ub4e0 \uc644\uc804 \ub610\ub294 \uc644\uc804\ud558\uc9c0 \uc54a\uc740 n&times;n \uadf8\ub9ac\ub4dc\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (n &le; 5) \uc774\ub54c, n&times;n \uadf8\ub9ac\ub4dc\uc758 \ubaa8\ub4e0 \uc815\uc0ac\uac01\ud615\uc744 \ud30c\uad34\ud558\uae30 \uc704\ud574 \uc81c\uac70\ud574\uc57c \ud558\ub294 \uc131\ub0e5\uac1c\ube44 \uac1c\uc218\uc758 \ucd5c\uc19f\uac12\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 T\uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uccab\uc9f8 \uc904\uc5d0\ub294 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ub450 \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uccab\uc9f8 \uc904\uc5d0\ub294 5\ub97c \ub118\uc9c0 \uc54a\ub294 \uc790\uc5f0\uc218 n\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. n\uc740 \uadf8\ub9ac\ub4dc\uc758 \ud06c\uae30\uc774\ub2e4. \ub458\uc9f8 \uc904\uc5d0\ub294 \uc74c\uc774 \uc544\ub2cc \uc815\uc218 k\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. k\ub294 n&times;n \uadf8\ub9ac\ub4dc\uc5d0\uc11c \uc81c\uac70\ub41c \uc131\ub0e5\uac1c\ube44\uc758 \uac1c\uc218\uc774\ub2e4. k\uc758 \ub2e4\uc74c\uc5d0\ub294 \uc81c\uac70\ud55c \uc131\ub0e5\uac1c\ube44\uc758 \ubc88\ud638\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. k\uac00 0\uc778 \uacbd\uc6b0\uc5d0\ub294 \uc785\ub825\uc73c\ub85c \uc644\uc804\ud55c \uadf8\ub9ac\ub4dc\uac00 \uc8fc\uc5b4\uc9c4 \uac83\uc774\uace0, \uc544\ub2cc \uacbd\uc6b0\uc5d0\ub294 \uc644\uc804\ud558\uc9c0 \uc54a\ub294 \uadf8\ub9ac\ub4dc\uac00 \uc8fc\uc5b4\uc9c4 \uac83\uc774\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \uadf8\ub9ac\ub4dc\uc5d0\uc11c \ubaa8\ub4e0 \uc815\uc0ac\uac01\ud615\uc744 \ud30c\uad34\ud558\uae30 \uc704\ud574 \uc81c\uac70\ud574\uc57c \ud558\ub294 \uc131\ub0e5\uac1c\ube44 \uac1c\uc218\uc758 \ucd5c\uc19f\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"7350","problem_lang":"1","title":"Square Destroyer","description":"<p>The left figure below shows a complete 3&times;3 grid made with 2&times;(3&times;4) (= 24) matchsticks. The lengths of all matchsticks are one. You can find many squares of different sizes in the grid. The size of a square is the length of its side. In the grid shown in the left figure, there are 9 squares of size one, 4 squares of size two, and 1 square of size three.<\/p>\r\n\r\n<p>Each matchstick of the complete grid is identified with a unique number which is assigned from left to right and from top to bottom as shown in the left figure. If you take some matchsticks out from the complete grid, then some squares in the grid will be destroyed, which results in an incomplete 3&times;3 grid. The right figure illustrates an incomplete 3&times;3 grid after removing three matchsticks numbered with 12, 17 and 23. This removal destroys 5 squares of size one, 3 squares of size two, and 1 square of size three. Consequently, the incomplete grid does not have squares of size three, but still has 4 squares of size one and 1 square of size two<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/matchsqaure(1).png\" style=\"height:318px; width:629px\" \/><\/p>\r\n\r\n<p>As input, you are given a (complete or incomplete) n &times; n grid made with no more than 2n(n +1) matchsticks for a natural number n &le; 5 . Your task is to compute the minimum number of matchsticks taken out to destroy all the squares existing in the input n &times; n grid.<\/p>\r\n","input":"<p>The input consists of T test cases. The number of test cases (T ) is given in the first line of the input file. Each test case consists of two lines: The first line contains a natural number n , not greater than 5, which implies you are given a (complete or incomplete) n &times; n grid as input, and the second line begins with a nonnegative integer k , the number of matchsticks that are missing from the complete n &times; n grid, followed by k numbers specifying the matchsticks. Note that if k is equal to zero, then the input grid is a complete n &times; n grid; otherwise, the input grid is an incomplete n &times; n grid such that the specified k matchsticks are missing from the complete n &times; n grid.<\/p>\r\n","output":"<p>Print exactly one line for each test case. The line should contain the minimum number of matchsticks that have to be taken out to destroy all the squares in the input grid.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > Asia > Korea > Asia Regional - Taejon 2001 H번

  • 문제를 번역한 사람: baekjoon
  • 문제의 오타를 찾은 사람: muckworm