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문제

선영이는 쓰레기를 편하게 버리기 위해서 빌딩에 쓰레기 슈트를 만들었다. 쓰레기 슈트는 빌딩에 설치할 수 있는 속이 빈 튜브다. 튜브로 쓰레기를 떨어뜨리면, 쓰레기는 지하실까지 떨어지게 된다.

쓰레기 슈트를 만드는 일은 매우 어려운 일이다. 사람들이 무엇을 버릴지 알 수 없기 때문에, 쓰레기 슈트에 들어가지 않는 쓰레기를 버린다면, 슈트가 막혀버릴 수 있기 때문이다. 쓰레기 슈트를 만드는데 드는 비용은 그 크기에 비례한다. 따라서, 최대한 작게 만드는 것이 효율적이다.

먼저, 쓰레기 슈트를 만드는 문제를 2차원으로 단순화 시켜보자. 슈트는 일정한 너비를 가지고 있고, 다각형으로 모델링된 물체를 이 곳의 상단에 넣을 수 있다.

물체를 넣기 전에, 슈트에 들어갈 수 있게 돌려야 할 수도 있다. 슈트에 던진 이후에는 일직선으로 아래로 떨어지고, 그 동안 물체는 회전하지 않는다.

아래 그림은 물체를 쓰레기 슈트에 들어갈 수 있게 회전시킨 다음 버리는 그림이다.

어떤 물체가 주어진다. 이 물체가 통과할 수 있는 가장 작은 슈트의 너비를 구하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스의 첫째 줄에는 물체(다각형)의 꼭지점의 개수 n이 주어진다. (3 ≤ n ≤ 100)

다음 n개 줄에는 꼭지점의 좌표 xi와 yi가 주어진다. (0 ≤ xi, yi ≤ 104) 꼭지점은 다각형을 이루는 순서대로 주어진다. 

입력으로 주어지는 다각형의 좌표는 모두 서로 다르며, 다각형의 변은 교차하지 않는다. 엄밀히 따지면, 인접한 변은 한 꼭지점을 공유한다는 예외가 하나 있다. 물론, 이 경우는 교차하는 것으로 생각하지 않는다.

마지막 테스트 케이스의 다음 줄에는 0이 하나 주어진다.

출력

각 테스트 케이스마다 케이스 번호와 가장 작은 쓰레기 슈트의 너비를 출력한다. 너비는 가장 가까운 0.01의 배수로 올림하여 소수점 둘째 자리까지 출력한다.

예제 입력 1

3
0 0
3 0
0 4
4
0 10
10 0
20 10
10 20
0

예제 출력 1

Case 1: 2.40
Case 2: 14.15
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(3 &le; n &le; 100)<\/p>\r\n\r\n<p>\ub2e4\uc74c n\uac1c \uc904\uc5d0\ub294 \uaf2d\uc9c0\uc810\uc758 \uc88c\ud45c x<sub>i<\/sub>\uc640 y<sub>i<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (0 &le; x<sub>i<\/sub>, y<sub>i<\/sub> &le; 10<sup>4<\/sup>) \uaf2d\uc9c0\uc810\uc740 \ub2e4\uac01\ud615\uc744 \uc774\ub8e8\ub294 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c0\ub294 \ub2e4\uac01\ud615\uc758 \uc88c\ud45c\ub294 \ubaa8\ub450 \uc11c\ub85c \ub2e4\ub974\uba70, \ub2e4\uac01\ud615\uc758 \ubcc0\uc740 \uad50\ucc28\ud558\uc9c0 \uc54a\ub294\ub2e4. \uc5c4\ubc00\ud788 \ub530\uc9c0\uba74, \uc778\uc811\ud55c \ubcc0\uc740 \ud55c \uaf2d\uc9c0\uc810\uc744 \uacf5\uc720\ud55c\ub2e4\ub294 \uc608\uc678\uac00 \ud558\ub098 \uc788\ub2e4. \ubb3c\ub860, \uc774 \uacbd\uc6b0\ub294 \uad50\ucc28\ud558\ub294 \uac83\uc73c\ub85c \uc0dd\uac01\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\ub9c8\uc9c0\ub9c9 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \ub2e4\uc74c \uc904\uc5d0\ub294 0\uc774 \ud558\ub098 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \ucf00\uc774\uc2a4 \ubc88\ud638\uc640 \uac00\uc7a5 \uc791\uc740 \uc4f0\ub808\uae30 \uc288\ud2b8\uc758 \ub108\ube44\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub108\ube44\ub294 \uac00\uc7a5 \uac00\uae4c\uc6b4 0.01\uc758 \ubc30\uc218\ub85c \uc62c\ub9bc\ud558\uc5ec \uc18c\uc218\uc810 \ub458\uc9f8 \uc790\ub9ac\uae4c\uc9c0 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"4225","problem_lang":"1","title":"Trash Removal","description":"<p>Allied Chute Manufacturers is a company that builds trash chutes. A trash chute is a hollow tube installed in buildings so that trash dropped in at the top will fall down and be collected in the basement. Designing trash chutes is actually highly nontrivial. Depending on what kind of trash people are expected to drop into them, the trash chute needs to have an appropriate size. And since the cost of manufacturing a trash chute is proportional to its size, the company always would like to build a chute that is as small as possible. Choosing the right size can be tough though.<\/p>\r\n\r\n<p>We will consider a 2-dimensional simplification of the chute design problem. A trash chute points straight down and has a constant width. Objects that will be dropped into the trash chute are modeled as polygons. Before an object is dropped into the chute it can be rotated so as to provide an optimal fit. Once dropped, it will travel on a straight path downwards and will not rotate in flight. The following figure shows how an object is first rotated so it fits into the trash chute.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/chute.png\" style=\"height:303px; opacity:0.9; width:387px\" \/><\/p>\r\n\r\n<p>Your task is to compute the smallest chute width that will allow a given polygon to pass through.<\/p>\r\n","input":"<p>The input contains several test cases. Each test case starts with a line containing an integer n (3 &le; n &le; 100), the number of points in the polygon that models the trash item.<\/p>\r\n\r\n<p>The next n lines then contain pairs of integers x<sub>i<\/sub> and y<sub>i<\/sub>&nbsp;(0 &le; x<sub>i<\/sub>, y<sub>i<\/sub>&nbsp;&le; 10<sup>4<\/sup>), giving the coordinates of the polygon vertices in order. All points in one test case are guaranteed to be mutually distinct and the polygon sides will never intersect. (Technically, there is one inevitable exception of two neighboring sides sharing their common vertex. Of course, this is not considered an intersection.)<\/p>\r\n\r\n<p>The last test case is followed by a line containing a single zero.<\/p>\r\n","output":"<p>For each test case, display its case number followed by the width of the smallest trash chute through which it can be dropped. Display the minimum width with exactly two digits to the right of the decimal point, rounding up to the nearest multiple of 1\/100. Answers within 1\/100 of the correct rounded answer will be accepted.<\/p>\r\n\r\n<p>Follow the format of the sample output.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > World Finals > 2011 World Finals K번

  • 문제를 번역한 사람: baekjoon
  • 빠진 조건을 찾은 사람: tae