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문제

국방 과학 연구소 (Korea Defense and Science Institute, KDSI) 에서는 최근 몇 년간 군인 개인이 착용할 새로운 장비를 꾸준히 개발하고 있고, 얼마 전에 N 종류의 장비를 출시했다.

KDSI는 새로 만든 모든 장비의 성능을 평가했고, 5가지 범주로 나눠서 평가를 해 점수로 나타냈다. 다섯 가지 범주는 공격 향상, 방어 향상, 시력 향상, 휴대성, 사용 편이성이다. 모든 점수는 0보다 크거나 같고, 10,000보다 작거나 같은 정수이다. 따라서, 모든 장비는 정수 다섯개로 나타낼 수 있다.

KDSI에서는 군인들의 능력의 평균과 비용 문제 때문에, 군인 한 명이 착용할 수 있는 장비의 개수를 K개로 제한했다. 만약, 한 군인이 장비를 하나만 착용한 경우에, 그 장비의 점수만큼 능력이 향상된다. 두 개 이상 착용한 경우에는 각 범주마다 독립적으로 능력이 향상되며, 착용한 장치의 점수의 최댓값만큼 능력이 향상된다. 예를 들어, 장비 a와 b의 시력 향상 점수가 10과 15일때, 두 장비를 착용하면 최댓값인 15만큼 시력이 향상된다. 이때, 최대 점수 15를 범주의 확장 점수라고 한다. 따라서, 이 예에서 {a, b}의 시력 향상 확장 점수는 15가 된다.

KDSI는 군인 한 명이 장비를 K개 착용했을 때, 가장 능력 향상이 많이 되는 조합을 찾으려고 한다. 특수 목적 군인의 경우에는 특정 범주의 점수가 훨씬 더 중요하다. 하지만, 범용성을 위해 각 범주의 확장 점수의 합이 최대가되는 조합을 찾으려고 한다. N개의 장비 중에서 확장 점수의 합이 최대가 되는 장비 K개 조합을 찾는 프로그램을 작성하시오.

장비가 N개를 {1, ..., N}로, 각 장비의 점수 Ri를 다섯 정수 Ri = (ri,1, ri,2, ri,3, ri,4, ri,5) (모든 i=1,...,N과 j=1,...,5에 대해서 0 ≤ ri,j ≤ 10,000)로 나타낼 수 있다. 이때, K (1 ≤ K ≤ N)가 주어졌을 때, 확장 점수의 합이 가장 큰 장비 K개를 찾아야 한다.

예를 들어, N=4, K=2이고, Ri가 다음과 같은 경우가 있다.

  • R1 = (30, 30, 30, 30, 0)
  • R2 = (50, 0, 0, 0, 0)
  • R3 = (0, 50, 0, 50, 10)
  • R4 = (0, 0, 50, 0, 20)

R1과 R3을 착용하면 향상 점수는 30+50+30+50+10 = 170이 되고, 이 점수가 가능한 값 중 가장 큰 값이다.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스의 첫째 줄에는 N과 K가 주어진다. (1 ≤ N ≤ 10,000, 1 ≤ K ≤ N) 다음 N개 줄에는 0보다 크거나 같고, 10,000보다 작거나 같은 정수 다섯개가 주어지며, 이 정수는 각 장비의 점수 ri,1, ri,2, ri,3, ri,4, ri,5를 나타낸다. 인접한 두 정수 사이에는 빈 칸이 하나 있다.

출력

각 테스트 케이스 마다, 장비 N개중 K개를 착용했을 때, 가장 큰 향상 점수의 합을 출력한다.

예제 입력 1

2
4 2
30 30 30 30 0
50 0 0 0 0
0 50 0 50 10
0 0 50 0 20
5 1
10 20 60 0 0
0 0 20 50 30
30 50 20 20 0
10 10 10 20 30
30 0 20 10 20

예제 출력 1

170
120
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N\uac1c\uc758 \uc7a5\ube44 \uc911\uc5d0\uc11c \ud655\uc7a5 \uc810\uc218\uc758 \ud569\uc774 \ucd5c\ub300\uac00 \ub418\ub294 \uc7a5\ube44 K\uac1c \uc870\ud569\uc744 \ucc3e\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p>\uc7a5\ube44\uac00 N\uac1c\ub97c {1, ..., N}\ub85c, \uac01 \uc7a5\ube44\uc758 \uc810\uc218 R<sub>i<\/sub>\ub97c \ub2e4\uc12f \uc815\uc218 R<sub>i<\/sub> = (r<sub>i,1<\/sub>, r<sub>i,2<\/sub>, r<sub>i,3<\/sub>, r<sub>i,4<\/sub>, r<sub>i,5<\/sub>) (\ubaa8\ub4e0 i=1,...,N\uacfc j=1,...,5\uc5d0 \ub300\ud574\uc11c 0 &le; r<sub>i,j<\/sub> &le; 10,000)\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \uc774\ub54c, K (1 &le; K &le; N)\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ud655\uc7a5 \uc810\uc218\uc758 \ud569\uc774 \uac00\uc7a5 \ud070 \uc7a5\ube44 K\uac1c\ub97c \ucc3e\uc544\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, N=4, K=2\uc774\uace0, Ri\uac00 \ub2e4\uc74c\uacfc \uac19\uc740 \uacbd\uc6b0\uac00 \uc788\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>R<sub>1<\/sub> = (30, 30, 30, 30, 0)<\/li>\r\n\t<li>R<sub>2<\/sub> = (50, 0, 0, 0, 0)<\/li>\r\n\t<li>R<sub>3<\/sub> = (0, 50, 0, 50, 10)<\/li>\r\n\t<li>R<sub>4<\/sub> = (0, 0, 50, 0, 20)<\/li>\r\n<\/ul>\r\n\r\n<p>R<sub>1<\/sub>\uacfc R<sub>3<\/sub>\uc744 \ucc29\uc6a9\ud558\uba74 \ud5a5\uc0c1 \uc810\uc218\ub294 30+50+30+50+10 = 170\uc774 \ub418\uace0, \uc774 \uc810\uc218\uac00 \uac00\ub2a5\ud55c \uac12 \uc911 \uac00\uc7a5 \ud070 \uac12\uc774\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 N\uacfc K\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; N &le; 10,000, 1 &le; K &le; N) \ub2e4\uc74c N\uac1c \uc904\uc5d0\ub294 0\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uace0, 10,000\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uc815\uc218 \ub2e4\uc12f\uac1c\uac00 \uc8fc\uc5b4\uc9c0\uba70, \uc774 \uc815\uc218\ub294 \uac01 \uc7a5\ube44\uc758 \uc810\uc218 r<sub>i,1<\/sub>, r<sub>i,2<\/sub>, r<sub>i,3<\/sub>, r<sub>i,4<\/sub>, r<sub>i,5<\/sub>\ub97c \ub098\ud0c0\ub0b8\ub2e4. \uc778\uc811\ud55c \ub450 \uc815\uc218 \uc0ac\uc774\uc5d0\ub294 \ube48 \uce78\uc774 \ud558\ub098 \uc788\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ub9c8\ub2e4, \uc7a5\ube44 N\uac1c\uc911 K\uac1c\ub97c \ucc29\uc6a9\ud588\uc744 \ub54c, \uac00\uc7a5 \ud070 \ud5a5\uc0c1 \uc810\uc218\uc758 \ud569\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"8903","problem_lang":"1","title":"Equipment","description":"<p>The Korea Defense and Science Institute, shortly KDSI, has been putting constant effort into new equipment for individual soldiers for recent years, and at last released N new types of equipment. KDSI has already done evaluation of each of the N types of equipment, finally resulting in scores in five categories: attack improvement, defense improvement, vision improvement, portability, and easiness of usage. The score in each category is quantified as an integer in the range 0 to 10,000, and the rating of each type of equipment is thus represented as a sequence of five integers.&nbsp;<\/p>\r\n\r\n<p>In consideration of costs and capability of average individual soldiers, KDSI also reported that each soldier will be able to install at most K types of equipment on his body to extend his ability. If a single type is installed on a soldier, then his ability in each category is extended by the specified score of that type. Moreover, if a soldier installs more than one type of equipment, then his ability in each category is extended by the maximum score of the chosen types in that category. For example, if the vision improvement scores of type a and type b are 10 and 15, respectively, then installing a combination of two types a and b will result in a vision improvement by their maximum score 15. We call the maximum score 15 the extension score of a category; so, the extension score of vision improvement for combination {a, b} is 15 in this example.&nbsp;<\/p>\r\n\r\n<p>KDSI now started devising a way of finding an optimal combination of K types of equipment for best performance of individual soldiers. While a force can sometimes be of a special purpose so that a certain category would be more important than the others, every single category is, however, regarded equally important in general. For this general purpose, KDSI defined the objective score of a combination of equipment to be the sum of the extension scores of the five categories for the combination. KDSI thus wants to find a best combination of K types of equipment such that its objective score is maximized among all possible combinations of K types. You are asked by KDSI to devise and write a computer program that finds the objective score of a best combination of K types of equipment, that is, the maximum possible objective score for all possible combinations of K types among the given N types of equipment.&nbsp;<\/p>\r\n\r\n<p>Put differently, you are given N types of equipment {1, ..., N} and their ratings R<sub>i<\/sub> represented by five integers R<sub>i<\/sub> = (r<sub>i,1<\/sub>, r<sub>i,2<\/sub>, r<sub>i,3<\/sub>, r<sub>i,4<\/sub>, r<sub>i,5<\/sub>) with 0 &le; r<sub>i,j<\/sub> &le; 10,000 for each i, ..., N and j = 1, ..., 5. Given another natural number K (1 &le; K &le; N), your program has to compute the objective score of a best combination of K types of equipment.&nbsp;<\/p>\r\n\r\n<p>For example, consider an input instance in which N = 4, K = 2, and each R<sub>i<\/sub> is given as below:&nbsp;<\/p>\r\n\r\n<p>R<sub>1<\/sub> = (30, 30, 30, 30, 0)&nbsp;<br \/>\r\nR<sub>2<\/sub> = (50, 0, 0, 0, 0)&nbsp;<br \/>\r\nR<sub>3<\/sub> = (0, 50, 0, 50, 10)&nbsp;<br \/>\r\nR<sub>4<\/sub> = (0, 0, 50, 0, 20).&nbsp;<\/p>\r\n\r\n<p>Then, choosing R<sub>1<\/sub> and R<sub>3<\/sub> forms a best combination of two types {1, 3} and yields the objective score 30+50+30+50+10 = 170, which will be the answer of a correct program.&nbsp;<\/p>\r\n","input":"<p>Your program is to read from standard input. The input consists of T test cases. The number T of test cases is given in the first line of the input. From the second line, each test case is given in order, consisting of the following: a test case contains two integers N (1 &le; N &le; 10,000) and K (1 &le; K &le; N) in its first line, and is followed by N lines each of which consists of five integers inclusively between 0 and 10,000, representing the five scores r<sub>i,1<\/sub>, r<sub>i,2<\/sub>, r<sub>i,3<\/sub>, r<sub>i,4<\/sub>, and r<sub>i,5<\/sub> of each type i of equipment for i = 1, ..., N in order. Two consecutive integers in one line are separated by a single space and there is no empty line between two consecutive test cases.&nbsp;<\/p>\r\n","output":"<p>Your program is to write to standard output. Print exactly one line for each test case. The line should contain a single integer that is the objective score of a best combination of K types of equipment; the maximum possible objective score for all possible combinations of K types among the given N types of equipment for the corresponding test case.&nbsp;<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > Regionals > Asia Pacific > Korea > Asia Regional - Daejeon 2011 D번

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