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2 초 128 MB 2 1 1 100.000%

문제

[0, 1]×[0, 1]의 정사각형과 그 안(정사각형의 테두리 및 꼭짓점 포함)에 N개의 점들 P[1], P[2], …, P[N]이 있다. 이 점들과 정사각형의 네 꼭짓점을 연결하여 임의의 두 점이 직접 혹은 간접적으로 연결되어 있게 하려 한다. 이와 같이 만든 그래프의 간선의 길이를 합한 것을 Len(P) 라고 정의하자.

N개의 점들의 위치를 임의로 바꾸면 Len(P)의 값도 이에 따라 변하게 된다. Len(P)가 최소가 되도록 하는 점들의 집합을 P'라고 하자. 즉, Len을 점들의 집합 P에 대한 함수로 생각했을 때, Len의 최솟값이 Len(P')가 되는 것이다.

N개의 점들을 잘 배치하여 Len이 최소가 되도록 할 때, 각각의 점들을 이동시킨 거리가 최소가 되도록 하는 프로그램을 작성하시오.

즉, Len(P'')=Len(P')를 만족하는 P''들 중에서, |P[1]-P''[1]|+|P[2]-P''[2]|+…+|P[N]-P''[N]|이 최소가 될 때, 그 최솟값을 구하는 것이다.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스의 첫째 줄에 N(1≤N≤100)이 주어진다. 다음 N개의 줄에는 각 점의 x, y 좌표가 주어진다. N이 0인 경우에 프로그램을 종료한다.

출력

각 테스트 케이스마다 답을 출력한다. 절대/상대 오차는 10-3까지 허용한다.

예제 입력 1

1
0.2 0.5
2
0 0.5
0.5 0.5
0

예제 출력 1

0.300
0.500

힌트

 

[{"problem_id":"2280","problem_lang":"0","title":"\uc815\uc0ac\uac01\ud615\uacfc \uc810","description":"<p>[0, 1]&times;[0, 1]\uc758 \uc815\uc0ac\uac01\ud615\uacfc \uadf8 \uc548(\uc815\uc0ac\uac01\ud615\uc758 \ud14c\ub450\ub9ac \ubc0f \uaf2d\uc9d3\uc810 \ud3ec\ud568)\uc5d0 N\uac1c\uc758 \uc810\ub4e4 P[1], P[2], &hellip;, P[N]\uc774 \uc788\ub2e4. \uc774 \uc810\ub4e4\uacfc \uc815\uc0ac\uac01\ud615\uc758 \ub124 \uaf2d\uc9d3\uc810\uc744 \uc5f0\uacb0\ud558\uc5ec \uc784\uc758\uc758 \ub450 \uc810\uc774 \uc9c1\uc811 \ud639\uc740 \uac04\uc811\uc801\uc73c\ub85c \uc5f0\uacb0\ub418\uc5b4 \uc788\uac8c \ud558\ub824 \ud55c\ub2e4. \uc774\uc640 \uac19\uc774 \ub9cc\ub4e0 \uadf8\ub798\ud504\uc758 \uac04\uc120\uc758 \uae38\uc774\ub97c \ud569\ud55c \uac83\uc744 Len(P) \ub77c\uace0 \uc815\uc758\ud558\uc790.<\/p>\r\n\r\n<p>N\uac1c\uc758 \uc810\ub4e4\uc758 \uc704\uce58\ub97c \uc784\uc758\ub85c \ubc14\uafb8\uba74 Len(P)\uc758 \uac12\ub3c4 \uc774\uc5d0 \ub530\ub77c \ubcc0\ud558\uac8c \ub41c\ub2e4. Len(P)\uac00 \ucd5c\uc18c\uac00 \ub418\ub3c4\ub85d \ud558\ub294 \uc810\ub4e4\uc758 \uc9d1\ud569\uc744 P&#39;\ub77c\uace0 \ud558\uc790. \uc989, Len\uc744 \uc810\ub4e4\uc758 \uc9d1\ud569 P\uc5d0 \ub300\ud55c \ud568\uc218\ub85c \uc0dd\uac01\ud588\uc744 \ub54c, Len\uc758 \ucd5c\uc19f\uac12\uc774 Len(P&#39;)\uac00 \ub418\ub294 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>N\uac1c\uc758 \uc810\ub4e4\uc744 \uc798 \ubc30\uce58\ud558\uc5ec Len\uc774 \ucd5c\uc18c\uac00 \ub418\ub3c4\ub85d \ud560 \ub54c, \uac01\uac01\uc758 \uc810\ub4e4\uc744 \uc774\ub3d9\uc2dc\ud0a8 \uac70\ub9ac\uac00 \ucd5c\uc18c\uac00 \ub418\ub3c4\ub85d \ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p>\uc989, Len(P&#39;&#39;)=Len(P&#39;)\ub97c \ub9cc\uc871\ud558\ub294 P&#39;&#39;\ub4e4 \uc911\uc5d0\uc11c, |P[1]-P&#39;&#39;[1]|+|P[2]-P&#39;&#39;[2]|+&hellip;+|P[N]-P&#39;&#39;[N]|\uc774 \ucd5c\uc18c\uac00 \ub420 \ub54c, \uadf8 \ucd5c\uc19f\uac12\uc744 \uad6c\ud558\ub294 \uac83\uc774\ub2e4.<\/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\uc758 \uccab\uc9f8 \uc904\uc5d0 N(1&le;N&le;100)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c N\uac1c\uc758 \uc904\uc5d0\ub294 \uac01 \uc810\uc758 x, y \uc88c\ud45c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. N\uc774 0\uc778 \uacbd\uc6b0\uc5d0 \ud504\ub85c\uadf8\ub7a8\uc744 \uc885\ub8cc\ud55c\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4&nbsp;\ub2f5\uc744 \ucd9c\ub825\ud55c\ub2e4. \uc808\ub300\/\uc0c1\ub300 \uc624\ucc28\ub294 10<sup>-3<\/sup>\uae4c\uc9c0 \ud5c8\uc6a9\ud55c\ub2e4.<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/JudgeOnline\/upload\/201008\/fig.PNG\" style=\"height:237px; width:485px\" \/><\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2280","problem_lang":"1","title":"Square","description":"<p>Given a square at [0, 1] * [0, 1] that has N points ( P<sub>1<\/sub>, P<sub>2<\/sub>, ..., P<sub>N<\/sub> ) in the square (you may assume that different points can be at the same position), we can connect the N points and the four corners of the square with some line segments so that through these segments any two of the N+4 points can reach each other (directly or indirectly). The graph length is defined as the total length of the line segments. When N points&#39; positions are fixed, there must exist a way of connecting them, such that it will make the shortest graph length. We can use LEN (P<sub>1<\/sub>, P<sub>2<\/sub>, ..., P<sub>N<\/sub>) to record the graph length using this way of connecting.&nbsp;<\/p>\r\n\r\n<p>In this situation, LEN (P<sub>1<\/sub>, P<sub>2<\/sub>, ..., P<sub>N<\/sub>) is a function of P<sub>1<\/sub>, P<sub>2<\/sub>, ..., P<sub>N<\/sub>. When P<sub>1<\/sub>, P<sub>2<\/sub>, ..., P<sub>N<\/sub> change their positions, LEN (P<sub>1<\/sub>, P<sub>2<\/sub>, ..., P<sub>N<\/sub>) also changes. It&#39;s easy to prove that there exist some P<sub>1<\/sub>&#39;, P<sub>2<\/sub>&#39;, ..., P<sub>N<\/sub>&#39; in the square such that LEN (P<sub>1<\/sub>&#39;, P<sub>2<\/sub>&#39;, ..., P<sub>N<\/sub>&#39;) is at its minimum.&nbsp;<\/p>\r\n\r\n<p>Given the initial positions of N points, your task is to find out N points P<sub>1<\/sub>&quot;, P<sub>2<\/sub>&quot;, ..., P<sub>N<\/sub>&quot; in the square such that |P<sub>1<\/sub>P<sub>1<\/sub>&quot;| + |P<sub>2<\/sub>P<sub>2<\/sub>&quot;| + ... + |P<sub>N<\/sub>P<sub>N<\/sub>&quot;| is minimum and LEN (P<sub>1<\/sub>&quot;, P<sub>2<\/sub>&quot;, ..., P<sub>N<\/sub>&quot;) = LEN (P<sub>1<\/sub>&#39;, P<sub>2<\/sub>&#39;, ..., P<sub>N<\/sub>&#39;) . You are requested to output the value of |P<sub>1<\/sub>P<sub>1<\/sub>&quot;| + |P<sub>2<\/sub>P<sub>2<\/sub>&quot;| + ... + |P<sub>N<\/sub>P<sub>N<\/sub>&quot;|, where |P<sub>i<\/sub>P<sub>i<\/sub>&quot;| is the distance between P<sub>i<\/sub> and P<sub>i<\/sub>&quot;.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/JudgeOnline\/upload\/201008\/fig.PNG\" style=\"height:237px; opacity:0.9; width:485px\" \/><\/p>\r\n\r\n<p>For example, Figure-1 gives the initial position of P<sub>1<\/sub> and the way of connecting to obtain LEN (P<sub>1<\/sub>). In Figure-2, it gives the position of P<sub>1<\/sub>&quot;, which is at the center of the square, and the way of connecting to obtain LEN (P<sub>1<\/sub>&quot;). It can be proved that LEN (P<sub>1<\/sub>&quot;) = LEN (P<sub>1<\/sub>&rsquo;); your job is to output the distance between P<sub>1<\/sub> and P<sub>1<\/sub>&quot;.<\/p>\r\n","input":"<p>The input consists of several test cases. For each test case, the first line consists of one integer N (1 &lt;= N &lt;= 100), the number of points, and N lines follow to give the coordinates for every point in the following format:&nbsp;<\/p>\r\n\r\n<p>x y&nbsp;<\/p>\r\n\r\n<p>Here, x and y are float numbers within the value [0, 1].&nbsp;<\/p>\r\n\r\n<p>A test case of N = 0 indicates the end of input, and should not be processed.&nbsp;<\/p>\r\n","output":"<p>For each test case, output the value of |P<sub>1<\/sub>P<sub>1<\/sub>&quot;| + |P<sub>2<\/sub>P<sub>2<\/sub>&quot;| + ... + |P<sub>N<\/sub>P<sub>N<\/sub>&quot;|. The value should be rounded to three digits after the decimal point.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]