시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

승현의 방은 출입 보안이 철저하다. 승현의 방에 들어가려면 많은 센서가 부착된 복도를 지나가야 한다. 센서는 일정 범위에 사람이나 물체가 감지되면 경보를 울린다.

현석은 매우 민첩한 스파이다. 그는 승현의 방에 있는 어떤 기밀문서를 훔쳐와 달라는 의뢰를 받았고, 실행하기에 앞서 현석은 복도 설계도를 입수했다. 현석은 이 설계도를 보고 자신이 직접 들어갈지, 그게 안 된다면 어느 정도의 로봇을 들여보낼 지 결정해야 한다.

현석은 복도를 2차원적으로 해석하기로 했다. 복도의 좌우 벽은 직선으로, 센서와 센서의 범위는 각각 원의 중심과 그 내부로 대응시켰다. 센서는 복도의 벽에 붙어있거나 복도 중간에 위치해 있으며 그 범위는 복도 양 끝 사이에 적절히 위치해 있다. 현석은 또한 센서 사이를 지나가는 물체를 원으로 가정했다.

센서들의 배치도가 주어져 있을 때, 이 원(현석 혹은 로봇)이 센서에 걸리지 않고 복도를 지나갈 수 있게 하기 위한 원의 최대 반지름을 구하자.

예제 입력을 시각화한 것이다.

입력

첫째 줄에는 테스트 케이스의 개수 T가 주어진다. (1 ≤ T ≤ 100) 그리고,

  • 그 다음 줄에 복도의 너비, 정수 w가 주어진다. (1 ≤ w ≤ 100 000) 복도의 양 벽은 직선 x = 0 과 x = w 로 해석한다.
  • 그 다음 줄에 센서의 개수, 정수 n이 주어진다. (0 ≤ n ≤ 1 000)
  • 그 다음 각 n개의 줄에 센서의 위치, 반지름을 나타내는 정수 x, y, r 이 주어진다. (0 ≤ x ≤ w, -100 000 ≤ y ≤ 100 000 and 1 ≤ r ≤ 100 000)

복도의 양 끝은 y = -∞, y = ∞ 이다. 쉽게 말해 센서들의 범위에서 한참 벗어나있다.

출력

각 테스트 케이스마다 센서에 감지되지 않고 복도를 지나갈 수 있는 원형 물체의 최대 반지름을 부동소수점 실수로 한 줄에 출력한다. 물체는 매우 정밀하게 움직일 수 있다고 가정한다. 만약 들키지 않고 지나가는 게 불가능하다면 0을 출력한다. 답은 소수점 아래 6번째 자리까지 정확해야 한다.

예제 입력 1

3
10
2
2 0 3
7 12 4
10
2
2 0 3
7 8 4
10
2
2 0 3
7 4 4

예제 출력 1

1.5
1.216991
0
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(1 &le; T &le; 100) \uadf8\ub9ac\uace0,<\/p>\r\n\r\n<ul>\r\n\t<li>\uadf8 \ub2e4\uc74c \uc904\uc5d0 \ubcf5\ub3c4\uc758 \ub108\ube44, \uc815\uc218 w\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;(1 &le; w &le; 100 000) \ubcf5\ub3c4\uc758 \uc591 \ubcbd\uc740 \uc9c1\uc120 x = 0 \uacfc x = w \ub85c \ud574\uc11d\ud55c\ub2e4.<\/li>\r\n\t<li>\uadf8 \ub2e4\uc74c \uc904\uc5d0 \uc13c\uc11c\uc758 \uac1c\uc218, \uc815\uc218 n\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;(0 &le; n &le; 1 000)<\/li>\r\n\t<li>\uadf8 \ub2e4\uc74c \uac01 n\uac1c\uc758 \uc904\uc5d0&nbsp;\uc13c\uc11c\uc758 \uc704\uce58, \ubc18\uc9c0\ub984\uc744 \ub098\ud0c0\ub0b4\ub294 \uc815\uc218&nbsp;x, y, r \uc774 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;(0 &le; x &le; w, -100 000 &le; y &le; 100 000 and 1 &le; r &le; 100 000)<\/li>\r\n<\/ul>\r\n\r\n<p>\ubcf5\ub3c4\uc758&nbsp;\uc591 \ub05d\uc740 y = -&infin;, y = &infin; \uc774\ub2e4. \uc27d\uac8c \ub9d0\ud574 \uc13c\uc11c\ub4e4\uc758 \ubc94\uc704\uc5d0\uc11c \ud55c\ucc38 \ubc97\uc5b4\ub098\uc788\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4&nbsp;\uc13c\uc11c\uc5d0 \uac10\uc9c0\ub418\uc9c0 \uc54a\uace0 \ubcf5\ub3c4\ub97c \uc9c0\ub098\uac08 \uc218 \uc788\ub294 \uc6d0\ud615 \ubb3c\uccb4\uc758 \ucd5c\ub300 \ubc18\uc9c0\ub984\uc744&nbsp;\ubd80\ub3d9\uc18c\uc218\uc810 \uc2e4\uc218\ub85c&nbsp;\ud55c \uc904\uc5d0 \ucd9c\ub825\ud55c\ub2e4. \ubb3c\uccb4\ub294 \ub9e4\uc6b0 \uc815\ubc00\ud558\uac8c \uc6c0\uc9c1\uc77c \uc218 \uc788\ub2e4\uace0 \uac00\uc815\ud55c\ub2e4. \ub9cc\uc57d \ub4e4\ud0a4\uc9c0 \uc54a\uace0 \uc9c0\ub098\uac00\ub294&nbsp;\uac8c \ubd88\uac00\ub2a5\ud558\ub2e4\uba74 0\uc744 \ucd9c\ub825\ud55c\ub2e4. \ub2f5\uc740 \uc18c\uc218\uc810&nbsp;\uc544\ub798 6\ubc88\uc9f8&nbsp;\uc790\ub9ac\uae4c\uc9c0 \uc815\ud655\ud574\uc57c&nbsp;\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9373","problem_lang":"1","title":"Getting Through","description":"<p>A long and straight corridor is \ufb01tted with a number of sensors. Each sensor has a certain range within which it can detect objects or persons. If a part of an object is within the sensor&rsquo;s range, an alarm will go off. Otherwise, nothing will happen.<\/p>\r\n\r\n<p>Ethan needs to traverse this corridor in order to do some spy stuff at the other end. The question is, can he pass through the corridor without being detected? Can he \ufb01t so easily that he can bring some equipment along, or does he have to wear some tight clothing? Or can he perhaps sent a robot through instead?<\/p>\r\n\r\n<p>We model the corridor as being two-dimensional (we ignore the height), bounded by two straight lines. Each sensor is located inside the corridor or on a wall. Their scopes are well in between the two ends of the corridor. We model the person or robot going through as a circle. Given the layout, what is the maximum radius this circle can have so that it is possible to negotiate the corridor without being detected?<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/through.png\" style=\"height:247px; width:418px\" \/><\/p>\r\n\r\n<p>A visual representation of the samples.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","input":"<p>On the \ufb01rst line one positive number: the number of test cases, at most 100. After that per test case:<\/p>\r\n\r\n<ul>\r\n\t<li>one line with a single integer w (1 &le; w &le; 100 000): the width of the corridor. The two walls are given by the lines x = 0 and x = w.<\/li>\r\n\t<li>one line with a single integer n (0 &le; n &le; 1 000): the number of sensors in the corridor.<\/li>\r\n\t<li>n lines with three space-separated integers x, y and r (0 &le; x &le; w, -100 000 &le; y &le; 100 000 and 1 &le; r &le; 100 000): the location and the range of each sensor, respectively.<\/li>\r\n<\/ul>\r\n\r\n<p>The two ends of the corridor are at y = -&infin; and y = +&infin;, or in less technical terms, they are far beyond the scope of all the sensors.<\/p>\r\n","output":"<p>Per test case:<\/p>\r\n\r\n<ul>\r\n\t<li>one line with one \ufb02oating point number: the radius of the largest circular object (or person) that could pass through the corridor without being detected, assuming the object can (be) move(d) with absolute precision. If nothing could possibly get through, the output should be zero. The number should be accurate up to 10<sup>-6<\/sup> absolute precision.<\/li>\r\n<\/ul>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]