시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
3 초 128 MB 677 116 74 14.800%

문제

도시의 북쪽에서 남쪽으로 흐르는 두 개의 강에 집이 그림처럼 각 강에 늘어서 있다. 여기에 양쪽의 각 집에 사는 사람들이 다른 곳으로 더 빨리 움직일 수 있게 하기 위해 다리를 놓을 생각이다.

왼쪽 강은 정확히 \(x = -1\)의 세로선이고, 오른쪽 강은 정확히 \(x=1\)의 세로선이다. 다리는 두 강의 각각의 지점을 연결하는 \(x\)-축에 평행한 선으로 표시되어 있다. 집의 위치가 세로선 위에 표시되어 있다.

다리의 최적 장소를 결정하기 위해 각각의 집이 \((-1, a_{i})\) 혹은 \((1, b_{j})\) (\(i=1,\cdots,n\), \(j=1,\cdots,m\))에 위치할 때,\[\sum_{\forall i,j}d(a_{i}, b_{j}) = \sum_{\forall i, j}\left(|a_{i}-h| + 2 + |h - b_{j}|\right)\]를 최소화하는 \(h\)에, 즉 (가능한) 왼쪽 집에서 오른쪽 집으로 가는 모든 거리의 합을 최소화하는 \(h\)에 다리를 놓는 것이 좋을 것이다. 이를 출력하는 프로그램을 작성하라.

입력

첫째 줄에 T가 주어진다. 이는 입력이 T개의 테스트 케이스로 구성된다는 의미이다. 각각의 테스트 케이스의 첫째 줄에 n과 m이 주어진다. (1 ≤ n, m ≤ 106) n은 왼쪽 강의 집 수를, m은 오른쪽 강의 집 수를 의미한다. 다음 n개의 줄에는 n개의 왼쪽 강의 집 위치인 ai가 주어지고, 그 다음 m개의 줄에는 m개의 오른쪽 강의 집 위치 bj가 주어진다. (|ai|, |bj| ≤ 107) 이 (n+m)개의 줄에 주어지는 집의 위치는 모두 다른 정수값이다.

출력

각각의 줄에 대해 문제의 조건을 만족하는 h를 소수점 한 자리까지 한 줄에 출력하라. 그런 h가 여러 개 존재한다면, 가장 작은 값을 출력하면 된다. 

예제 입력 1

2
3 4
30
-16
5
-5
25
-20
-10
4 7
18
-15
-3
2
8
20
12
-3
18
9
4

예제 출력 1

-5.0
4.0
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(|a<sub>i<\/sub>|, |b<sub>j<\/sub>| &le; 10<sup>7<\/sup>)&nbsp;\uc774 (n+m)\uac1c\uc758 \uc904\uc5d0 \uc8fc\uc5b4\uc9c0\ub294 \uc9d1\uc758 \uc704\uce58\ub294 \ubaa8\ub450 \ub2e4\ub978 \uc815\uc218\uac12\uc774\ub2e4.<\/p>\r\n","output":"<p>\uac01\uac01\uc758 \uc904\uc5d0 \ub300\ud574 \ubb38\uc81c\uc758 \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 h\ub97c \uc18c\uc218\uc810 \ud55c \uc790\ub9ac\uae4c\uc9c0&nbsp;\ud55c \uc904\uc5d0&nbsp;\ucd9c\ub825\ud558\ub77c. \uadf8\ub7f0 h\uac00 \uc5ec\ub7ec \uac1c \uc874\uc7ac\ud55c\ub2e4\uba74, \uac00\uc7a5 \uc791\uc740 \uac12\uc744 \ucd9c\ub825\ud558\uba74 \ub41c\ub2e4.&nbsp;<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9006","problem_lang":"1","title":"Bridge","description":"<p><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/9006\/1.png\" style=\"float:right; height:237px; width:178px\" \/>A river runs from north to south in a city. Houses are located along each side of the river as illustrated in Figure 1. The city plans to construct a horizontal bridge across the river so that people in both sides can reach quickly each other through the bridge.<\/p>\r\n\r\n<p>Precisely, the left side of the river is the vertical line with the x-coordinate of -1, and the right side of the river is the vertical line with the x-coordinate of +1. The vertical strip between two sides represents the river. The bridge is represented as a horizontal segment which connects two points on both sides. The positions of the houses are given on the vertical lines.<\/p>\r\n\r\n<p>To determine the optimal location of the bridge, the city want to minimize the sum of the distances between pairs (a, b) of houses where a is in the left side and b is in the right side. The distance between a and b is the sum of the distance from a to the end of the bridge, the length of the bridge, and the distance from the end of the bridge to b. Thus we want to construct the bridge so that the sum of all the distances between houses in both sides is minimized.<\/p>\r\n\r\n<p>More formally, let a<sub>i<\/sub> and b<sub>j<\/sub> be the positions of houses in the left and the right side, respectively, i = 1, ..., n and j = 1, ..., m and let h be the position of the bridge. Then the goal is to minimize the following quantity:<\/p>\r\n\r\n<p style=\"text-align:center\">&Sigma;<sub>i,j<\/sub>d(a<sub>i<\/sub>, b<sub>j<\/sub>) = &Sigma;<sub>&forall;i,j<\/sub>(|a<sub>i<\/sub>-h| + 2 + |h-b<sub>j<\/sub>|).<\/p>\r\n\r\n<p>the positions of houses are given as integers on the vertical lines with the x-coorinates of -1 or +1. you should find the position of the bridge, that is, the y-coordinate of the horizontal segment representing the bridge, minimizing the sum of all the distances between the houses in both sides.<\/p>\r\n","input":"<p>Your program is to read from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case starts with integer n and m, the number of houses of the left and the right side, respectively, where 1 &le; n, m &le; 1,000,000. Each of the following n lines contains an integer a, representing the y-coordinate of a house in the left side. Also each of the following m lines contains an integer b, representing the y-coordinate of a house in the right side. Note that all the y-coordinates of the houses on each side are distinct, and -10,000,000 &le; a, b &le; 10,000,000.<\/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 real value, the position of the bridge, that is, the y-coordinate of the horizontal segment minimizing the sum of all the distances between the houses of both sides; your output must contain the first digit after the decimal point, that is, simply ignore the ones from the 2nd digit after the decimal point. If there are multiple solutions, then print the smallest value of them.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]