시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 26 8 6 33.333%

문제

창영제국의 황제 김상근이 세상을 떠났다. 사람들은 그가 가졌던 제국이 어떻게 자식들에게 나누어질 것인지 궁금해하기 시작했다. 제국은 직사각형 모양이고, N개의 도시가 있다.

땅은 K-1개의 선분으로 나누어야 한다. 선분은 지도의 축과 평행이어야 한다.

나누어진 지도에는 정확하게 K개의 직사각형이 있어야 하고, 모두 같은 높이(땅을 수직으로 나누었을 때)나 같은 너비(수평으로 나누었을 때)를 가지고 있어야 한다. 선분은 도시를 지나면 안 된다.

모든 상근이의 자식들은 K개의 나누어진 제국 하나를 임의로 받게 되고, 그 땅에 포함된 도시를 가질 수 있다.

모든 자식들에게 공평하게 땅을 나누어주기 위해서 각 자식들에게 N/K의 도시를 주려고 한다. 이 N/K를 기준값이라고 한다. 하지만, 기준값은 정수가 아닐수도 있기 때문에, 각각의 자식들은 최대한 기준값에 가깝게 도시를 얻기를 원한다.

각 자식의 불공평점수는 그 자식이 가진 도시의 수와 기준값과의 차이이다. 모든 자식의 불공평점수의 평균을 최소로 하려고 한다.

위의 예는 땅에 도시가 6개, 상근이의 자식이 3명 있을 때이다. (기준값 = 6/3 = 2.0) 왼쪽 그림은 제국의 지도이다. 가운데 그림처럼 나누었을 때, 가운데 영역에는 도시가 3개 있다. 이 땅을 받는 자식의 불공평점수는 |3-2| = 1이다. 왼쪽 영역은 2개의 도시가 있기 때문에 불공평점수는 0이고, 오른쪽 영역은 1개의 도시가 있기 때문에 불공평점수는 1이다. 따라서, 불공평점수의 평균은 2/3이 된다.

가장 오른쪽 그림은 모두 같은 수의 도시를 받게 되므로 불공평점수의 평균이 0이 된다.

땅과 도시의 위치가 주어졌을 때, 공평하게 땅을 나누어 불공평점수의 평균을 최소로 하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스는 N+1줄로 이루어져 있다.

테스트 케이스의 첫째 줄에는 도시의 수 N(N ≤ 100,000)과 자식의 수 K(K ≤ 10)가 주어진다. 항상 K ≤ N이다.

다음 N개의 줄에는 도시의 좌표 (x,y)가 주어진다. (0 ≤ x,y ≤ 100,000) x와 y는 정수이다. 원래 지도에 있는 도시의 좌표를 가까운 정수로 반올림해서 나타낸 것이기 때문에, 같은 위치에 하나보다 많은 도시가 있을 수도 있다. 모든 좌표를 포함하는 가상의 직사각형이 지도의 경계라고 생각하면 된다. 

나누는 선은 정수 좌표를 갖지 않아도 된다.

입력의 마지막 줄에는 0이 두 개 주어진다.

출력

각 테스트 케이스에 대해서, 테스트 케이스 번호와 불공평점수의 평균값의 최솟값을 출력한다. 불공평점수의 평균값은 A/B와 같은 형식으로 출력하고, 기약분수이어야 한다. 만약 평균이 정수일 경우에는 B=1로 출력해야 한다.

예제 입력 1

6 3
0 4
1 3
2 3
3 1
4 4
5 0
4 3
0 0
0 1
1 1
1 0
0 0

예제 출력 1

1. 0/1
2. 8/9
[{"problem_id":"4896","problem_lang":"0","title":"\ub545 \ub098\ub204\uae30","description":"<p>\ucc3d\uc601\uc81c\uad6d\uc758 \ud669\uc81c \uae40\uc0c1\uadfc\uc774 \uc138\uc0c1\uc744 \ub5a0\ub0ac\ub2e4. \uc0ac\ub78c\ub4e4\uc740 \uadf8\uac00 \uac00\uc84c\ub358 \uc81c\uad6d\uc774 \uc5b4\ub5bb\uac8c \uc790\uc2dd\ub4e4\uc5d0\uac8c \ub098\ub204\uc5b4\uc9c8 \uac83\uc778\uc9c0 \uad81\uae08\ud574\ud558\uae30 \uc2dc\uc791\ud588\ub2e4. \uc81c\uad6d\uc740 \uc9c1\uc0ac\uac01\ud615 \ubaa8\uc591\uc774\uace0, N\uac1c\uc758 \ub3c4\uc2dc\uac00 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ub545\uc740 K-1\uac1c\uc758 \uc120\ubd84\uc73c\ub85c \ub098\ub204\uc5b4\uc57c \ud55c\ub2e4. \uc120\ubd84\uc740 \uc9c0\ub3c4\uc758 \ucd95\uacfc \ud3c9\ud589\uc774\uc5b4\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub098\ub204\uc5b4\uc9c4 \uc9c0\ub3c4\uc5d0\ub294 \uc815\ud655\ud558\uac8c K\uac1c\uc758 \uc9c1\uc0ac\uac01\ud615\uc774 \uc788\uc5b4\uc57c \ud558\uace0, \ubaa8\ub450 \uac19\uc740 \ub192\uc774(\ub545\uc744 \uc218\uc9c1\uc73c\ub85c \ub098\ub204\uc5c8\uc744 \ub54c)\ub098 \uac19\uc740 \ub108\ube44(\uc218\ud3c9\uc73c\ub85c \ub098\ub204\uc5c8\uc744 \ub54c)\ub97c \uac00\uc9c0\uace0 \uc788\uc5b4\uc57c \ud55c\ub2e4. \uc120\ubd84\uc740 \ub3c4\uc2dc\ub97c \uc9c0\ub098\uba74 \uc548 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \uc0c1\uadfc\uc774\uc758 \uc790\uc2dd\ub4e4\uc740 K\uac1c\uc758 \ub098\ub204\uc5b4\uc9c4 \uc81c\uad6d \ud558\ub098\ub97c \uc784\uc758\ub85c \ubc1b\uac8c \ub418\uace0, \uadf8 \ub545\uc5d0 \ud3ec\ud568\ub41c \ub3c4\uc2dc\ub97c \uac00\uc9c8 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \uc790\uc2dd\ub4e4\uc5d0\uac8c \uacf5\ud3c9\ud558\uac8c \ub545\uc744 \ub098\ub204\uc5b4\uc8fc\uae30 \uc704\ud574\uc11c \uac01 \uc790\uc2dd\ub4e4\uc5d0\uac8c N\/K\uc758 \ub3c4\uc2dc\ub97c \uc8fc\ub824\uace0 \ud55c\ub2e4. \uc774 N\/K\ub97c \uae30\uc900\uac12\uc774\ub77c\uace0 \ud55c\ub2e4. \ud558\uc9c0\ub9cc, \uae30\uc900\uac12\uc740 \uc815\uc218\uac00 \uc544\ub2d0\uc218\ub3c4 \uc788\uae30 \ub54c\ubb38\uc5d0, \uac01\uac01\uc758 \uc790\uc2dd\ub4e4\uc740 \ucd5c\ub300\ud55c \uae30\uc900\uac12\uc5d0 \uac00\uae5d\uac8c \ub3c4\uc2dc\ub97c \uc5bb\uae30\ub97c \uc6d0\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uac01 \uc790\uc2dd\uc758 \ubd88\uacf5\ud3c9\uc810\uc218\ub294 \uadf8 \uc790\uc2dd\uc774 \uac00\uc9c4 \ub3c4\uc2dc\uc758 \uc218\uc640 \uae30\uc900\uac12\uacfc\uc758 \ucc28\uc774\uc774\ub2e4. \ubaa8\ub4e0 \uc790\uc2dd\uc758 \ubd88\uacf5\ud3c9\uc810\uc218\uc758 \ud3c9\uade0\uc744 \ucd5c\uc18c\ub85c \ud558\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/land.png\" style=\"height:123px; width:629px\" \/><\/p>\r\n\r\n<p>\uc704\uc758 \uc608\ub294 \ub545\uc5d0 \ub3c4\uc2dc\uac00 6\uac1c, \uc0c1\uadfc\uc774\uc758 \uc790\uc2dd\uc774 3\uba85 \uc788\uc744 \ub54c\uc774\ub2e4. (\uae30\uc900\uac12 = 6\/3 = 2.0) \uc67c\ucabd \uadf8\ub9bc\uc740 \uc81c\uad6d\uc758 \uc9c0\ub3c4\uc774\ub2e4. \uac00\uc6b4\ub370 \uadf8\ub9bc\ucc98\ub7fc \ub098\ub204\uc5c8\uc744 \ub54c, \uac00\uc6b4\ub370 \uc601\uc5ed\uc5d0\ub294 \ub3c4\uc2dc\uac00 3\uac1c \uc788\ub2e4. \uc774 \ub545\uc744 \ubc1b\ub294 \uc790\uc2dd\uc758 \ubd88\uacf5\ud3c9\uc810\uc218\ub294 |3-2| = 1\uc774\ub2e4. \uc67c\ucabd \uc601\uc5ed\uc740 2\uac1c\uc758 \ub3c4\uc2dc\uac00 \uc788\uae30 \ub54c\ubb38\uc5d0 \ubd88\uacf5\ud3c9\uc810\uc218\ub294 0\uc774\uace0, \uc624\ub978\ucabd \uc601\uc5ed\uc740 1\uac1c\uc758 \ub3c4\uc2dc\uac00 \uc788\uae30 \ub54c\ubb38\uc5d0 \ubd88\uacf5\ud3c9\uc810\uc218\ub294 1\uc774\ub2e4. \ub530\ub77c\uc11c, \ubd88\uacf5\ud3c9\uc810\uc218\uc758 \ud3c9\uade0\uc740 2\/3\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uac00\uc7a5 \uc624\ub978\ucabd \uadf8\ub9bc\uc740 \ubaa8\ub450 \uac19\uc740 \uc218\uc758 \ub3c4\uc2dc\ub97c \ubc1b\uac8c \ub418\ubbc0\ub85c \ubd88\uacf5\ud3c9\uc810\uc218\uc758 \ud3c9\uade0\uc774 0\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\ub545\uacfc \ub3c4\uc2dc\uc758 \uc704\uce58\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uacf5\ud3c9\ud558\uac8c \ub545\uc744 \ub098\ub204\uc5b4 \ubd88\uacf5\ud3c9\uc810\uc218\uc758 \ud3c9\uade0\uc744 \ucd5c\uc18c\ub85c \ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 N+1\uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \ub3c4\uc2dc\uc758 \uc218 N(N &le; 100,000)\uacfc \uc790\uc2dd\uc758 \uc218 K(K &le; 10)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ud56d\uc0c1 K &le; N\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c N\uac1c\uc758 \uc904\uc5d0\ub294 \ub3c4\uc2dc\uc758 \uc88c\ud45c (x,y)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (0 &le; x,y &le; 100,000) x\uc640 y\ub294 \uc815\uc218\uc774\ub2e4. \uc6d0\ub798 \uc9c0\ub3c4\uc5d0 \uc788\ub294 \ub3c4\uc2dc\uc758 \uc88c\ud45c\ub97c \uac00\uae4c\uc6b4 \uc815\uc218\ub85c \ubc18\uc62c\ub9bc\ud574\uc11c \ub098\ud0c0\ub0b8 \uac83\uc774\uae30 \ub54c\ubb38\uc5d0, \uac19\uc740 \uc704\uce58\uc5d0 \ud558\ub098\ubcf4\ub2e4 \ub9ce\uc740 \ub3c4\uc2dc\uac00 \uc788\uc744 \uc218\ub3c4 \uc788\ub2e4. \ubaa8\ub4e0 \uc88c\ud45c\ub97c \ud3ec\ud568\ud558\ub294 \uac00\uc0c1\uc758 \uc9c1\uc0ac\uac01\ud615\uc774 \uc9c0\ub3c4\uc758 \uacbd\uacc4\ub77c\uace0 \uc0dd\uac01\ud558\uba74 \ub41c\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\ub098\ub204\ub294 \uc120\uc740 \uc815\uc218 \uc88c\ud45c\ub97c \uac16\uc9c0 \uc54a\uc544\ub3c4 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \ub450 \uac1c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ubc88\ud638\uc640 \ubd88\uacf5\ud3c9\uc810\uc218\uc758 \ud3c9\uade0\uac12\uc758 \ucd5c\uc19f\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4. \ubd88\uacf5\ud3c9\uc810\uc218\uc758 \ud3c9\uade0\uac12\uc740 A\/B\uc640 \uac19\uc740 \ud615\uc2dd\uc73c\ub85c \ucd9c\ub825\ud558\uace0, \uae30\uc57d\ubd84\uc218\uc774\uc5b4\uc57c \ud55c\ub2e4. \ub9cc\uc57d \ud3c9\uade0\uc774 \uc815\uc218\uc77c \uacbd\uc6b0\uc5d0\ub294 B=1\ub85c \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"4896","problem_lang":"1","title":"Land Division","description":"<p>The king of the Far, Far Away Kingdom has passed-away and the kingdom must be split amongst his K sons. The kingdom, which can be drawn on a rectangular map, consists of N cities. To divide the land, they will draw K &minus; 1 straight segments on the map, all of them parallel to either the vertical or the horizontal axis of the map. This divides the map into exactly K rectangles, all having equal heights (if the dividing lines where vertical), or equal widths (if the dividing lines where horizontal). No segment should pass through any of the cities. Each son will then be assigned one random region out of the K regions and the cities inside that region will be his share.<\/p>\r\n\r\n<p>Of course, they want the division to be as fair as possible: theoretically, in the fairest division, each son should get N\/K cities (we&rsquo;ll call this value the baseline), but since the baseline isn&rsquo;t always a whole number, each of the sons wants to be as close as possible to the baseline. We will calculate the unfairness of each son as the absolute di\ufb00erence between the number of cities assigned to him and the baseline. The fairest division is the one that minimizes the average unfairness of all the sons.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/land(1).png\" style=\"height:166px; width:641px\" \/><\/p>\r\n\r\n<p>Consider the example above with 3 sons and 6 cities (so the baseline is 6\/3 = 2.0) Figure (a) is the original map. Figure (b) shows a non-optimal division (the dashed lines are the 2 dividing lines.) In this case, the middle region contains 3 cities (unfairness of |3 &minus; 2| = 1), the left region contains 1 city (unfairness of |1 &minus; 2| = 1), while the right region contains 2 cities (perfectly fair, unfairness of 0), so the average unfairness is 2\/3.<\/p>\r\n\r\n<p>Figure (c) on the right shows the optimal division since all three regions contain the same number of cities for an average unfairness of 0.<\/p>\r\n\r\n<p>Write a program to determine the fairest land division for a given kingdom.<\/p>\r\n","input":"<p>Your program will be tested on one or more test cases. Each test case is described on N + 1 lines. The \ufb01rst line of each test case speci\ufb01es two positive integers: (N &le; 100, 000) and (K &le; 10) where N is the number of cities and K is number of children. Note that K &le; N.<\/p>\r\n\r\n<p>N lines follows, each describing the coordinates of a city by specifying two integers (x, y) where 0 &le; x, y &le; 100, 000. Since coordinates are rounded to the nearest integer, more than one city could have the exact same coordinate on the map. You may assume that the map of the kingdom is any rectangle that contains all of the given points (although such information is not needed by the program.) Note also that while all cities lie on integer coordinates, the dividing lines need not be.<\/p>\r\n\r\n<p>The last line of the input \ufb01le contains two zeros.<\/p>\r\n","output":"<p>For each test case, print the following line:<\/p>\r\n\r\n<pre>k. A\/B<\/pre>\r\n\r\n<p>Where k is the test case number (starting at one,) and A\/B is the minimum average that could be obtained. A\/B should be an irreducible fraction. Let B=1 when the result is a whole number.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]