문제
좌표평면에 $N$개의 점이 주어진다. $i$번째 점의 좌표는 $(x_i, y_i)$이다. 모든 점들은 위치가 서로 다르며, 한 직선 위에 세 점이 놓이게 되는 경우는 없다.
당신의 목표는 점들의 쌍들 중 일부를 빨간색, 또는 파란색 선분으로 연결하여 다음 조건들을 모두 만족하도록 하는 것이다.
빨간색 선분만을 고려할 때, 모든 점들은 연결되어있다. 즉, 아무 서로다른 두 점을 잡아도 해당 두 점을 양 끝 점으로 가지는 빨간색 선분으로 이루어진 경로가 존재한다. 파란색 선분만을 고려할 때에도 성립한다.
임의의 두 선분이 두 선분의 끝점을 제외한 곳에서 교점을 가지지 않는다.
선분의 색상과 상관없이, 선분은 최대 2ドルN-2$개까지 존재한다.
조건을 모두 만족하도록 선분을 그릴 수 있는지 판별하고, 만약 가능하다면 답을 출력하라.
출력
만약 조건을 모두 만족하도록 점들을 연결하는 것이 불가능하다면, 첫 줄에 -1
그렇지 않을 경우, 답을 출력한다. 첫 줄에는 답에 사용된 선분의 개수 $m$을 출력한다.
다음 $m$개의 줄 중 $i$번째 줄에는 두 정수 $a_i$와 $b_i,ドル 한 문자 $c_i$를 공백을 사이에 두고 출력한다. 이는 답에 사용된 $i$번째 선분이 $a_i$번째, $b_i$번째 점을 끝점으로 하는 선분임을 의미하며, $c_i$가 RB
제한
3ドル \le N \le 2,000円$
모든 1ドル \le i \le N$에 대하여 $|x_i|, |y_i| \le 1,000円,000円,000円$
모든 1ドル \le i<j \le N$에 대하여 $(x_i, y_i) \ne (x_j, y_j)$
주어진 $N$개의 점 중 세 점이 한 직선 위에 놓이게 되는 경우는 없다.
서브태스크 번호 배점 제한 1 11 $N \le 5$
2 31 $N \le 100$
3 58 추가적인 제약 조건이 없다.
예제 출력 1
복사
6
1 3 R
1 4 R
1 2 B
4 3 B
2 3 B
2 4 R
예제 출력 2
복사
8
1 5 R
1 3 R
1 4 B
3 5 B
4 5 B
4 3 R
1 2 R
2 5 B
[{"problem_id":"33805","problem_lang":"0","title":"Red and Blue","description":"<p>\uc88c\ud45c\ud3c9\uba74\uc5d0 $N$\uac1c\uc758 \uc810\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. $i$\ubc88\uc9f8 \uc810\uc758 \uc88c\ud45c\ub294 $(x_i, y_i)$\uc774\ub2e4. \ubaa8\ub4e0 \uc810\ub4e4\uc740 \uc704\uce58\uac00 \uc11c\ub85c \ub2e4\ub974\uba70, \ud55c \uc9c1\uc120 \uc704\uc5d0 \uc138 \uc810\uc774 \ub193\uc774\uac8c \ub418\ub294 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\ub2f9\uc2e0\uc758 \ubaa9\ud45c\ub294 \uc810\ub4e4\uc758 \uc30d\ub4e4 \uc911 \uc77c\ubd80\ub97c \ube68\uac04\uc0c9, \ub610\ub294 \ud30c\ub780\uc0c9 \uc120\ubd84\uc73c\ub85c \uc5f0\uacb0\ud558\uc5ec \ub2e4\uc74c \uc870\uac74\ub4e4\uc744 \ubaa8\ub450 \ub9cc\uc871\ud558\ub3c4\ub85d \ud558\ub294 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ube68\uac04\uc0c9 \uc120\ubd84\ub9cc\uc744 \uace0\ub824\ud560 \ub54c, \ubaa8\ub4e0 \uc810\ub4e4\uc740 \uc5f0\uacb0\ub418\uc5b4\uc788\ub2e4. \uc989, \uc544\ubb34 \uc11c\ub85c\ub2e4\ub978 \ub450 \uc810\uc744 \uc7a1\uc544\ub3c4 \ud574\ub2f9 \ub450 \uc810\uc744 \uc591 \ub05d \uc810\uc73c\ub85c \uac00\uc9c0\ub294 \ube68\uac04\uc0c9 \uc120\ubd84\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uacbd\ub85c\uac00 \uc874\uc7ac\ud55c\ub2e4.  \ud30c\ub780\uc0c9 \uc120\ubd84\ub9cc\uc744 \uace0\ub824\ud560 \ub54c\uc5d0\ub3c4 \uc131\ub9bd\ud55c\ub2e4.<\/li>\r\n\t<li>\uc784\uc758\uc758 \ub450 \uc120\ubd84\uc774 \ub450 \uc120\ubd84\uc758 \ub05d\uc810\uc744 \uc81c\uc678\ud55c \uacf3\uc5d0\uc11c \uad50\uc810\uc744 \uac00\uc9c0\uc9c0 \uc54a\ub294\ub2e4.<\/li>\r\n\t<li>\uc120\ubd84\uc758 \uc0c9\uc0c1\uacfc \uc0c1\uad00\uc5c6\uc774, \uc120\ubd84\uc740 \ucd5c\ub300 $2N-2$\uac1c\uae4c\uc9c0 \uc874\uc7ac\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc870\uac74\uc744 \ubaa8\ub450 \ub9cc\uc871\ud558\ub3c4\ub85d \uc120\ubd84\uc744 \uadf8\ub9b4 \uc218 \uc788\ub294\uc9c0 \ud310\ubcc4\ud558\uace0, \ub9cc\uc57d \uac00\ub2a5\ud558\ub2e4\uba74 \ub2f5\uc744 \ucd9c\ub825\ud558\ub77c.<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0 \uc810\uc758 \uc218 $N$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c $N$\uac1c\uc758 \uc904 \uc911 $i$\ubc88\uc9f8 \uc904\uc5d0\ub294 \ub450 \uc815\uc218 $x_i, y_i$\uac00 \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\ub9cc\uc57d \uc870\uac74\uc744 \ubaa8\ub450 \ub9cc\uc871\ud558\ub3c4\ub85d \uc810\ub4e4\uc744 \uc5f0\uacb0\ud558\ub294 \uac83\uc774 \ubd88\uac00\ub2a5\ud558\ub2e4\uba74, \uccab \uc904\uc5d0 <span style=\"color:#e74c3c;\"><code>-1<\/code><\/span>\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uadf8\ub807\uc9c0 \uc54a\uc744 \uacbd\uc6b0, \ub2f5\uc744 \ucd9c\ub825\ud55c\ub2e4. \uccab \uc904\uc5d0\ub294 \ub2f5\uc5d0 \uc0ac\uc6a9\ub41c \uc120\ubd84\uc758 \uac1c\uc218 $m$\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c $m$\uac1c\uc758 \uc904 \uc911 $i$\ubc88\uc9f8 \uc904\uc5d0\ub294 \ub450 \uc815\uc218 $a_i$\uc640 $b_i$, \ud55c \ubb38\uc790 $c_i$\ub97c \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \ucd9c\ub825\ud55c\ub2e4. \uc774\ub294 \ub2f5\uc5d0 \uc0ac\uc6a9\ub41c $i$\ubc88\uc9f8 \uc120\ubd84\uc774 $a_i$\ubc88\uc9f8, $b_i$\ubc88\uc9f8 \uc810\uc744 \ub05d\uc810\uc73c\ub85c \ud558\ub294 \uc120\ubd84\uc784\uc744 \uc758\ubbf8\ud558\uba70, $c_i$\uac00 <span style=\"color:#e74c3c;\"><code>R<\/code><\/span>\uc77c \uacbd\uc6b0 \ube68\uac04\uc0c9, <span style=\"color:#e74c3c;\"><code>B<\/code><\/span>\uc77c \uacbd\uc6b0 \ud30c\ub780\uc0c9\uc784\uc744 \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$3 \\le N \\le 2\\,000$<\/li>\r\n\t<li>\ubaa8\ub4e0 $1 \\le i \\le N$\uc5d0 \ub300\ud558\uc5ec $|x_i|, |y_i| \\le 1\\,000\\,000\\,000$<\/li>\r\n\t<li>\ubaa8\ub4e0 $1 \\le i&lt;j \\le N$\uc5d0 \ub300\ud558\uc5ec $(x_i, y_i) \\ne (x_j, y_j)$<\/li>\r\n\t<li>\uc8fc\uc5b4\uc9c4 $N$\uac1c\uc758 \uc810 \uc911 \uc138 \uc810\uc774 \ud55c \uc9c1\uc120 \uc704\uc5d0 \ub193\uc774\uac8c \ub418\ub294 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N \\le 5$<\/p>\r\n","subtask2":"<p>$N \\le 100$<\/p>\r\n","subtask3":"<p>\ucd94\uac00\uc801\uc778 \uc81c\uc57d \uc870\uac74\uc774 \uc5c6\ub2e4.<\/p>\r\n","sample_explain_1":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/557b3482-6ec7-4919-8185-525a687ee89f\/-\/preview\/\" \/><\/p>\r\n"},{"problem_id":"33805","problem_lang":"1","title":"Red and Blue","description":"<p>$N$ points are given on the Cartesian plane. The $i$-th point has coordinates $(x_i, y_i)$. All points are pairwise distinct, and no three points lie on a straight line.<\/p>\r\n\r\n<p>You must connect some pairs of points with either red or blue line segments so that the following conditions are satisfied:<\/p>\r\n\r\n<ul>\r\n\t<li>Considering only the red line segments, all the points must be connected.&nbsp;That is, for any two distinct points, there exists a path made up of red line segments that has those two points as its endpoints. The same must hold for the blue line segments.<\/li>\r\n\t<li>Any two line segments must not intersect, except possibly at their endpoints.<\/li>\r\n\t<li>The total number of line segments (regardless of their color) must be at most $2N - 2$.<\/li>\r\n<\/ul>\r\n\r\n<p>Determine whether it is possible to draw such segments to satisfy all the above conditions. If it is possible, output any valid configuration.<\/p>\r\n","input":"<p>The first line contains an integer $N$,&nbsp;the number of points.<\/p>\r\n\r\n<p>Each of the next $N$ lines contains two integers $x_i$ and $y_i$, separated by a space.<\/p>\r\n","output":"<p>If it is impossible to connect the points to satisfy all conditions, print <span style=\"color:#e74c3c;\"><code>-1<\/code><\/span>&nbsp;in the first line.<\/p>\r\n\r\n<p>Otherwise, the first line should contain an integer $m$,&nbsp;the number of line segments used.<\/p>\r\n\r\n<p>Each of the next $m$ lines contains two integers $a_i$ and $b_i$, and a character $c_i$, separated by spaces. Here, $a_i$ and $b_i$ are the endpoints of the $i$-th segment, and $c_i$ denotes its color. If the $i$-th segment is red, then $c_i$ would be <span style=\"color:#e74c3c;\"><code>R<\/code><\/span>; if it is blue, then $c_i $ would be <span style=\"color:#e74c3c;\"><code>B<\/code><\/span>.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$3 \\le N \\le 2\\,000$<\/li>\r\n\t<li>$|x_i|, |y_i| \\le 1\\,000\\,000\\,000$ for all $1 \\le i \\le N$<\/li>\r\n\t<li>$(x_i, y_i) \\ne (x_j, y_j)$ for all $1 \\le i&lt;j \\le N$<\/li>\r\n\t<li>There are&nbsp;no three points which forms a straight line.<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N \\le 5$<\/p>\r\n","subtask2":"<p>$N \\le 100$<\/p>\r\n","subtask3":"<p>No additional constraints.<\/p>\r\n","sample_explain_1":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/315122cd-df62-4436-9dcb-5dfc262dc2ea\/-\/preview\/\" \/><\/p>\r\n"}]