시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 128 MB73131125.581%

문제

시장은 새로운 TV 송신 시스템을 도입하기로 했다. 도시는 길이가 D인 선분 위에 여러 개의 빌딩이 놓여져 있는 형태이다. 빌딩의 너비는 무시할 수 있을만큼 작다. 일부 빌딩의 옥상에는 TV 송신기 있으며, 그 크기도 무시할 수 있다.

TV 송신기는 TV 신호를 모든 방향으로 전송한다. 신호는 직선으로 전송되며, 빌딩을 통과할 수 없다. 도시의 일부분은 기존에 설치된 송신기로 TV 신호를 수신할 수 있다.

TV 신호를 받을 수 있는 선분을 찾고 그 길이를 출력하는 프로그램을 작성하시오.

입력

첫째 줄에 빌딩의 수 N (1 ≤ N ≤ 3·105)과 도시의 길이 D(1 ≤ D ≤ 109)가 주어진다.

다음 N개 줄에는 i번째 빌딩의 정보를 나타내는 세 개의 정수가 주어진다.

  1. 빌딩의 옥상에 송신기가 설치된 경우에 첫 번째 정수는 1이고, 설치되지 않은 경우에는 0이다.
  2. 두 번째 정수는 빌딩이 도시의 왼쪽 끝으로부터 떨어진 거리 Xi (0 ≤ Xi ≤ D) 이다.
  3. 세 번째 정수는 빌딩의 높이 Hi (1 ≤ Hi ≤ 109) 이다.

빌딩은 왼쪽으로부터 떨어진 거리가 증가하는 순으로 주어진다. 두 빌딩이 같은 곳에 있는 경우는 없다.

출력

첫째 줄에 구한 정답을 출력한다. 오차는 최대 10-3까지 허용된다.

예제 입력 1

3 10
1 2 6
0 4 3
0 8 2

예제 출력 1

6.000000

예제 입력 2

5 15
0 4 3
1 5 5
1 6 6
0 9 2
0 10 3

예제 출력 2

8.500000

문제의 그림에서 X축이 굵은선으로 되어있는 부분은 TV 신호를 받을 수 없는 곳이다.

[{"problem_id":"9630","problem_lang":"0","title":"TV \uc1a1\uc2e0\uae30","description":"<p>\uc2dc\uc7a5\uc740 \uc0c8\ub85c\uc6b4 TV \uc1a1\uc2e0 \uc2dc\uc2a4\ud15c\uc744 \ub3c4\uc785\ud558\uae30\ub85c \ud588\ub2e4. \ub3c4\uc2dc\ub294 \uae38\uc774\uac00 D\uc778 \uc120\ubd84 \uc704\uc5d0 \uc5ec\ub7ec \uac1c\uc758 \ube4c\ub529\uc774 \ub193\uc5ec\uc838 \uc788\ub294 \ud615\ud0dc\uc774\ub2e4. \ube4c\ub529\uc758 \ub108\ube44\ub294 \ubb34\uc2dc\ud560 \uc218 \uc788\uc744\ub9cc\ud07c \uc791\ub2e4. \uc77c\ubd80 \ube4c\ub529\uc758 \uc625\uc0c1\uc5d0\ub294 TV \uc1a1\uc2e0\uae30 \uc788\uc73c\uba70, \uadf8 \ud06c\uae30\ub3c4 \ubb34\uc2dc\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>TV \uc1a1\uc2e0\uae30\ub294 TV \uc2e0\ud638\ub97c \ubaa8\ub4e0 \ubc29\ud5a5\uc73c\ub85c \uc804\uc1a1\ud55c\ub2e4. \uc2e0\ud638\ub294 \uc9c1\uc120\uc73c\ub85c \uc804\uc1a1\ub418\uba70, \ube4c\ub529\uc744 \ud1b5\uacfc\ud560 \uc218 \uc5c6\ub2e4. \ub3c4\uc2dc\uc758 \uc77c\ubd80\ubd84\uc740 \uae30\uc874\uc5d0 \uc124\uce58\ub41c \uc1a1\uc2e0\uae30\ub85c TV \uc2e0\ud638\ub97c \uc218\uc2e0\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/69ffbe8c-ce04-4aea-b63e-9d28606310fb\/-\/preview\/\" style=\"width: 627px; height: 320px;\" \/><\/p>\r\n\r\n<p>TV \uc2e0\ud638\ub97c \ubc1b\uc744 \uc218 \uc788\ub294 \uc120\ubd84\uc744 \ucc3e\uace0 \uadf8 \uae38\uc774\ub97c \ucd9c\ub825\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ube4c\ub529\uc758 \uc218 N (1 &le; N &le; 3&middot;10<sup>5<\/sup>)\uacfc \ub3c4\uc2dc\uc758 \uae38\uc774 D(1 &le; D &le; 10<sup>9<\/sup>)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c N\uac1c \uc904\uc5d0\ub294 i\ubc88\uc9f8 \ube4c\ub529\uc758 \uc815\ubcf4\ub97c \ub098\ud0c0\ub0b4\ub294 \uc138 \uac1c\uc758 \uc815\uc218\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>\ube4c\ub529\uc758 \uc625\uc0c1\uc5d0 \uc1a1\uc2e0\uae30\uac00 \uc124\uce58\ub41c \uacbd\uc6b0\uc5d0 \uccab \ubc88\uc9f8 \uc815\uc218\ub294 1\uc774\uace0, \uc124\uce58\ub418\uc9c0 \uc54a\uc740 \uacbd\uc6b0\uc5d0\ub294 0\uc774\ub2e4.<\/li>\r\n\t<li>\ub450 \ubc88\uc9f8 \uc815\uc218\ub294 \ube4c\ub529\uc774 \ub3c4\uc2dc\uc758 \uc67c\ucabd \ub05d\uc73c\ub85c\ubd80\ud130 \ub5a8\uc5b4\uc9c4 \uac70\ub9ac X<sub>i<\/sub> (0 &le; X<sub>i<\/sub> &le; D) \uc774\ub2e4.<\/li>\r\n\t<li>\uc138 \ubc88\uc9f8 \uc815\uc218\ub294 \ube4c\ub529\uc758 \ub192\uc774 H<sub>i<\/sub> (1 &le; H<sub>i<\/sub> &le; 10<sup>9<\/sup>) \uc774\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\ube4c\ub529\uc740 \uc67c\ucabd\uc73c\ub85c\ubd80\ud130 \ub5a8\uc5b4\uc9c4 \uac70\ub9ac\uac00 \uc99d\uac00\ud558\ub294 \uc21c\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \ub450 \ube4c\ub529\uc774 \uac19\uc740 \uacf3\uc5d0 \uc788\ub294 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uad6c\ud55c \uc815\ub2f5\uc744 \ucd9c\ub825\ud55c\ub2e4. \uc624\ucc28\ub294 \ucd5c\ub300 10<sup>-3<\/sup>\uae4c\uc9c0 \ud5c8\uc6a9\ub41c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean","sample_explain_2":"<p>\ubb38\uc81c\uc758 \uadf8\ub9bc\uc5d0\uc11c X\ucd95\uc774 \uad75\uc740\uc120\uc73c\ub85c \ub418\uc5b4\uc788\ub294 \ubd80\ubd84\uc740 TV \uc2e0\ud638\ub97c \ubc1b\uc744 \uc218 \uc5c6\ub294 \uacf3\uc774\ub2e4.<\/p>\r\n"},{"problem_id":"9630","problem_lang":"1","title":"ODA\u0160ILJA\u010cI","description":"<p>The mayor has decided that it is high time to implement a new system of television transmitters. The city can be represented as a segment of the length D on which there are buildings of different heights. The width of a building is negligible. On top of some buildings, television transmitters are set, their dimensions are also negligible.&nbsp;<\/p>\r\n\r\n<p>Television transmitters emit a television signal in all directions around them. The signal is spread through space in straight lines and cannot pass through buildings. A certain point in the city is considered covered if it is reached by a signal from an existing transmitter.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/city.png\" style=\"height:338px; width:654px\" \/><\/p>\r\n\r\n<p>Find the segment of the city covered by television signal and output its length.&nbsp;<\/p>\r\n","input":"<p>The first line of input contains the integer N (1 &le; N &le; 3&middot;10<sup>5<\/sup>), the number of buildings, and the integer D (1 &le; D &le; 10<sup>9<\/sup>), the city length.&nbsp;<\/p>\r\n\r\n<p>Each of the following N lines contains three numbers which describe the i<sup>th<\/sup> building:&nbsp;<\/p>\r\n\r\n<ol>\r\n\t<li>a number which determines whether there is a transmitter on top of the building: 0 (no) or 1 (yes)&nbsp;<\/li>\r\n\t<li>an integer X<sub>i<\/sub> (0 &le; X<sub>i<\/sub> &le; D), the distance between the building and the left end of the city&nbsp;<\/li>\r\n\t<li>an integer H<sub>i<\/sub> (1 &le; H<sub>i<\/sub> &le; 10<sup>9<\/sup>), the building height&nbsp;<\/li>\r\n<\/ol>\r\n\r\n<p>The buildings are sorted in ascending order by the distance from the left end of the city. No two buildings will be located on the same distance from the left end of the city.&nbsp;<\/p>\r\n","output":"<p>The first and only line of output must contain the required length from the text.&nbsp;<\/p>\r\n\r\n<p>Note: the maximum permissible deviation from the official solution is 10<sup>-3<\/sup>.&nbsp;<\/p>\r\n","hint":"<p>This example corresponds to the image from the text. The image depicts the city. The buildings are marked with vertical lines, and the transmitters with circles on the tops of the buildings. The bold lines on the x-axis represent the segment of the city not covered by television signal.<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English","sample_explain_2":"<p>This example corresponds to the image from the text. The image depicts the city. The buildings are marked with vertical lines, and the transmitters with circles on the tops of the buildings. The bold lines on the x-axis represent the segment of the city not covered by television signal.<\/p>\r\n"}]

출처

Contest > Croatian Open Competition in Informatics > COCI 2013/2014 > Contest #3 6번