시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 126 35 26 25.000%

문제

다각형은 그 경계 위에 놓인 모든 점과 그 안의 모든 영역으로 구성되어 있다. 이러한 다각형 중에서 앞으로 이 문제에서 다룰 다각형은 다음과 같은 특성을 만족하는 것으로 한다.

  1. 다각형 안의 임의의 두 점을 잇는 선분이 완전히 그 다각형 안에 속해 있다.
  2. 세 개 이상의 꼭짓점으로 이루어져 있다.
  3. 세 꼭짓점이 한 직선 위에 있는 경우는 없다.

이러한 특성을 만족하는 두 다각형 A, B가 있을 때, 이들의 민코프스키(Minkowski) 합은, A에 속하는 모든 영역의 좌표 (x1, y1)와 B에 속하는 모든 영역의 좌표 (x2, y2)에 대해, 있을 수 있는 모든 (x1+x2, y1+y2) 조합이 나타내는 영역의 도형이다. 다음은 두 삼각형과 이들의 민코프스키 합을 그림으로 나타낸 것이다.

두 다각형이 주어졌을 때, 두 다각형의 민코프스키 합을 구하는 프로그램을 작성하시오. 만약 민코프스키 합이 여러 개의 다각형으로 이루어진다면 다음의 우선순위에 따라 하나의 다각형만을 구하도록 한다. 번호가 작은 것이 우선순위가 높은 것이다.

  1. 꼭짓점의 개수가 가장 작은 것
  2. 면적이 가장 작은 것
  3. 다각형을 이루는 모든 좌표들 중 최소 x좌표가 가장 작은 것
  4. 다각형을 이루는 모든 좌표들 중 최소 y좌표가 가장 작은 것

입력

첫째 줄에 두 다각형 A와 B의 꼭짓점 개수 N과 M이 주어진다. (3<=N, M<=1,000) 다음 N개의 줄에는 다각형 A를 이루는 꼭짓점의 좌표가, 그 다음 M개의 줄에는 다각형 B를 이루는 꼭짓점의 좌표가 주어진다. 좌표는 x좌표와 y좌표가 빈칸을 사이에 두고 순서대로 주어지며, 반시계 방향으로 입력된다. 모든 좌표는 100,000,000을 넘지 않는 음이 아닌 정수이다.

출력

첫째 줄에 우리가 구하고자 하는 다각형의 꼭짓점의 개수를 출력한다. 다음 줄부터는 다각형을 이루는 꼭짓점의 x좌표와 y좌표를 한 줄에 한 쌍씩 반시계 방향으로 출력한다. 출력되는 첫 번째 꼭짓점은 x좌표가 가장 작은 점으로 하며, x좌표가 가장 작은 점이 여러 개 있을 경우 y좌표가 가장 작은 점으로 한다.

예제 입력 1

3 3
0 0
1 0
1 1
0 1
0 0
1 0

예제 출력 1

5
0 0
2 0
2 1
1 2
0 1

힌트

민코프스키(Minkowski, Hermann. 1864~1909)는 독일에서 활동한 러시아 수학자로 기하학에 공리계를 도입한 것으로 잘 알려진 힐베르트(Hilbert, David. 1862~1943)와 친교를 맺고 함께 괴팅켄 대학을 세계 수학의 중심지로 만들었다. 괴팅겐 대학은 20세기 들어 노벨상 수상자인 막스 보른, 제임스 프랑크, 베르너 하이젠베르크, 막스 폰 라우에 등 현대물리학의 대가들을 배출한 바 있으며 실제로 민코프스키 또한 <공간과 시간> 등의 저서에서 4차원적 시공간에 대해 논하며 아인슈타인의 상대성이론의 형성에도 공헌한 것으로 알려져 있다.

[{"problem_id":"2244","problem_lang":"0","title":"\ubbfc\ucf54\ud504\uc2a4\ud0a4 \ud569","description":"<p>\ub2e4\uac01\ud615\uc740 \uadf8 \uacbd\uacc4 \uc704\uc5d0 \ub193\uc778 \ubaa8\ub4e0 \uc810\uacfc \uadf8 \uc548\uc758 \ubaa8\ub4e0 \uc601\uc5ed\uc73c\ub85c \uad6c\uc131\ub418\uc5b4 \uc788\ub2e4. \uc774\ub7ec\ud55c \ub2e4\uac01\ud615 \uc911\uc5d0\uc11c \uc55e\uc73c\ub85c \uc774 \ubb38\uc81c\uc5d0\uc11c \ub2e4\ub8f0 \ub2e4\uac01\ud615\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \ud2b9\uc131\uc744 \ub9cc\uc871\ud558\ub294 \uac83\uc73c\ub85c \ud55c\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>\ub2e4\uac01\ud615 \uc548\uc758 \uc784\uc758\uc758 \ub450 \uc810\uc744 \uc787\ub294 \uc120\ubd84\uc774 \uc644\uc804\ud788 \uadf8 \ub2e4\uac01\ud615 \uc548\uc5d0 \uc18d\ud574 \uc788\ub2e4.<\/li>\r\n\t<li>\uc138 \uac1c \uc774\uc0c1\uc758 \uaf2d\uc9d3\uc810\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/li>\r\n\t<li>\uc138 \uaf2d\uc9d3\uc810\uc774 \ud55c \uc9c1\uc120 \uc704\uc5d0 \uc788\ub294 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uc774\ub7ec\ud55c \ud2b9\uc131\uc744 \ub9cc\uc871\ud558\ub294 \ub450 \ub2e4\uac01\ud615 A, B\uac00 \uc788\uc744 \ub54c, \uc774\ub4e4\uc758 \ubbfc\ucf54\ud504\uc2a4\ud0a4(Minkowski) \ud569\uc740, A\uc5d0 \uc18d\ud558\ub294 \ubaa8\ub4e0 \uc601\uc5ed\uc758 \uc88c\ud45c (x1, y1)\uc640 B\uc5d0 \uc18d\ud558\ub294 \ubaa8\ub4e0 \uc601\uc5ed\uc758 \uc88c\ud45c (x2, y2)\uc5d0 \ub300\ud574, \uc788\uc744 \uc218 \uc788\ub294 \ubaa8\ub4e0 (x1+x2, y1+y2) \uc870\ud569\uc774 \ub098\ud0c0\ub0b4\ub294 \uc601\uc5ed\uc758 \ub3c4\ud615\uc774\ub2e4. \ub2e4\uc74c\uc740 \ub450 \uc0bc\uac01\ud615\uacfc \uc774\ub4e4\uc758 \ubbfc\ucf54\ud504\uc2a4\ud0a4 \ud569\uc744 \uadf8\ub9bc\uc73c\ub85c \ub098\ud0c0\ub0b8 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/JudgeOnline\/upload\/201008\/min.PNG\" style=\"height:156px; width:478px\" \/><\/p>\r\n\r\n<p>\ub450 \ub2e4\uac01\ud615\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ub450 \ub2e4\uac01\ud615\uc758 \ubbfc\ucf54\ud504\uc2a4\ud0a4 \ud569\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \ub9cc\uc57d \ubbfc\ucf54\ud504\uc2a4\ud0a4 \ud569\uc774 \uc5ec\ub7ec \uac1c\uc758 \ub2e4\uac01\ud615\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4\ub2e4\uba74 \ub2e4\uc74c\uc758 \uc6b0\uc120\uc21c\uc704\uc5d0 \ub530\ub77c \ud558\ub098\uc758 \ub2e4\uac01\ud615\ub9cc\uc744 \uad6c\ud558\ub3c4\ub85d \ud55c\ub2e4. \ubc88\ud638\uac00 \uc791\uc740 \uac83\uc774 \uc6b0\uc120\uc21c\uc704\uac00 \ub192\uc740 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>\uaf2d\uc9d3\uc810\uc758 \uac1c\uc218\uac00 \uac00\uc7a5 \uc791\uc740 \uac83<\/li>\r\n\t<li>\uba74\uc801\uc774 \uac00\uc7a5 \uc791\uc740 \uac83<\/li>\r\n\t<li>\ub2e4\uac01\ud615\uc744 \uc774\ub8e8\ub294 \ubaa8\ub4e0 \uc88c\ud45c\ub4e4 \uc911 \ucd5c\uc18c x\uc88c\ud45c\uac00 \uac00\uc7a5 \uc791\uc740 \uac83<\/li>\r\n\t<li>\ub2e4\uac01\ud615\uc744 \uc774\ub8e8\ub294 \ubaa8\ub4e0 \uc88c\ud45c\ub4e4 \uc911 \ucd5c\uc18c y\uc88c\ud45c\uac00 \uac00\uc7a5 \uc791\uc740 \uac83<\/li>\r\n<\/ol>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub450 \ub2e4\uac01\ud615 A\uc640 B\uc758 \uaf2d\uc9d3\uc810 \uac1c\uc218 N\uacfc M\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (3&lt;=N, M&lt;=1,000) \ub2e4\uc74c N\uac1c\uc758 \uc904\uc5d0\ub294 \ub2e4\uac01\ud615 A\ub97c \uc774\ub8e8\ub294 \uaf2d\uc9d3\uc810\uc758 \uc88c\ud45c\uac00, \uadf8 \ub2e4\uc74c M\uac1c\uc758 \uc904\uc5d0\ub294 \ub2e4\uac01\ud615 B\ub97c \uc774\ub8e8\ub294 \uaf2d\uc9d3\uc810\uc758 \uc88c\ud45c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc88c\ud45c\ub294 x\uc88c\ud45c\uc640 y\uc88c\ud45c\uac00 \ube48\uce78\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c0\uba70, \ubc18\uc2dc\uacc4 \ubc29\ud5a5\uc73c\ub85c \uc785\ub825\ub41c\ub2e4. \ubaa8\ub4e0 \uc88c\ud45c\ub294 100,000,000\uc744 \ub118\uc9c0 \uc54a\ub294 \uc74c\uc774 \uc544\ub2cc \uc815\uc218\uc774\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc6b0\ub9ac\uac00 \uad6c\ud558\uace0\uc790 \ud558\ub294 \ub2e4\uac01\ud615\uc758 \uaf2d\uc9d3\uc810\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub2e4\uc74c \uc904\ubd80\ud130\ub294 \ub2e4\uac01\ud615\uc744 \uc774\ub8e8\ub294 \uaf2d\uc9d3\uc810\uc758 x\uc88c\ud45c\uc640 y\uc88c\ud45c\ub97c \ud55c \uc904\uc5d0 \ud55c \uc30d\uc529 \ubc18\uc2dc\uacc4 \ubc29\ud5a5\uc73c\ub85c \ucd9c\ub825\ud55c\ub2e4. \ucd9c\ub825\ub418\ub294 \uccab \ubc88\uc9f8 \uaf2d\uc9d3\uc810\uc740 x\uc88c\ud45c\uac00 \uac00\uc7a5 \uc791\uc740 \uc810\uc73c\ub85c \ud558\uba70, x\uc88c\ud45c\uac00 \uac00\uc7a5 \uc791\uc740 \uc810\uc774 \uc5ec\ub7ec \uac1c \uc788\uc744 \uacbd\uc6b0 y\uc88c\ud45c\uac00 \uac00\uc7a5 \uc791\uc740 \uc810\uc73c\ub85c \ud55c\ub2e4.<\/p>\r\n","hint":"<p>\ubbfc\ucf54\ud504\uc2a4\ud0a4(Minkowski, Hermann. 1864~1909)\ub294 \ub3c5\uc77c\uc5d0\uc11c \ud65c\ub3d9\ud55c \ub7ec\uc2dc\uc544 \uc218\ud559\uc790\ub85c \uae30\ud558\ud559\uc5d0 \uacf5\ub9ac\uacc4\ub97c \ub3c4\uc785\ud55c \uac83\uc73c\ub85c \uc798 \uc54c\ub824\uc9c4 \ud790\ubca0\ub974\ud2b8(Hilbert, David. 1862~1943)\uc640 \uce5c\uad50\ub97c \ub9fa\uace0 \ud568\uaed8 \uad34\ud305\ucf04 \ub300\ud559\uc744 \uc138\uacc4 \uc218\ud559\uc758 \uc911\uc2ec\uc9c0\ub85c \ub9cc\ub4e4\uc5c8\ub2e4. \uad34\ud305\uac90 \ub300\ud559\uc740 20\uc138\uae30 \ub4e4\uc5b4 \ub178\ubca8\uc0c1 \uc218\uc0c1\uc790\uc778 \ub9c9\uc2a4 \ubcf4\ub978, \uc81c\uc784\uc2a4 \ud504\ub791\ud06c, \ubca0\ub974\ub108 \ud558\uc774\uc820\ubca0\ub974\ud06c, \ub9c9\uc2a4 \ud3f0 \ub77c\uc6b0\uc5d0 \ub4f1 \ud604\ub300\ubb3c\ub9ac\ud559\uc758 \ub300\uac00\ub4e4\uc744 \ubc30\ucd9c\ud55c \ubc14 \uc788\uc73c\uba70 \uc2e4\uc81c\ub85c \ubbfc\ucf54\ud504\uc2a4\ud0a4 \ub610\ud55c &lt;\uacf5\uac04\uacfc \uc2dc\uac04&gt; \ub4f1\uc758 \uc800\uc11c\uc5d0\uc11c 4\ucc28\uc6d0\uc801 \uc2dc\uacf5\uac04\uc5d0 \ub300\ud574 \ub17c\ud558\uba70 \uc544\uc778\uc288\ud0c0\uc778\uc758 \uc0c1\ub300\uc131\uc774\ub860\uc758 \ud615\uc131\uc5d0\ub3c4 \uacf5\ud5cc\ud55c \uac83\uc73c\ub85c \uc54c\ub824\uc838 \uc788\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2244","problem_lang":"1","title":"Polygon","description":"<p>A polygon consists of all points on or enclosed by its border. A convex polygon has the property that for any two points X and Y of the polygon, the line segment connecting X and Y is inside the polygon. All polygons in this task are convex polygons with at least two vertices, and all vertices in a polygon are different and have integer coordinates. No three vertices of the polygon are collinear. The word &quot;polygon&quot; below always refers to such polygons.&nbsp;<\/p>\r\n\r\n<p>Given two polygons A and B, the Minkowski sum of A and B consists of all the points of the form (x1+x2, y1+y2) where (x1, y1) is a point in A and (x2, y2) is a point in B. It turns out that the Minkowski sum of polygons is also a polygon. The figure below shows an example: two triangles and their Minkowski sum.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/task1a.jpg\" style=\"height:156px; width:478px\" \/><\/p>\r\n\r\n<p>We study a reverse operation to the Minkowski sum. For a given polygon P, we are looking for two polygons A and B such that:&nbsp;<\/p>\r\n\r\n<ul>\r\n\t<li>P is the Minkowski sum of A and B,<\/li>\r\n\t<li>A has from 2 to 4 different vertices, i.e. it is a segment (2 vertices), a triangle (3 vertices) or a quadrilateral (4 vertices),<\/li>\r\n\t<li>A should have as many vertices, as possible, i.e.:\r\n\t<ul>\r\n\t\t<li>A should be a quadrilateral, if possible,<\/li>\r\n\t\t<li>if A cannot be a quadrilateral, it should be a triangle, if possible,<\/li>\r\n\t\t<li>otherwise it should be a segment.<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n<\/ul>\r\n\r\n<p>Clearly, neither A nor B can be equal to P because then the other summand would have to be a point, which is not a valid polygon.&nbsp;<\/p>\r\n\r\n<p>You are given a set of input files, each containing a description of a polygon P. For each input file you should find the polygons A and B, as required above, and create an output file containing descriptions of A and B. For the given input files such polygons A and B can always be found. If there are many correct results, you should find and output one of them. You should not submit any programs, just the output files.&nbsp;<\/p>\r\n","input":"<p>You are given 10 problem instances in the text files named polygon1.in to polygon10.in, where the number after polygon is the input number. Each input file is organized as follows. The first line contains one integer N: the number of vertices of the polygon P. The following N lines describe the vertices in a counter-clockwise order, one vertex per line. Line I+1 (for I = 1, 2, ..., N) contains two integers XI and YI, separated by a space: coordinates of the Ith vertex of the polygon. All input coordinates are non-negative integers.<\/p>\r\n","output":"<p>You are to submit 10 output files corresponding to the given input files which describe the required polygons A and B. The first line is to contain the text: #FILE polygon I where integer I (1&le; I &le;10)is the number of the respective input file.&nbsp;<\/p>\r\n\r\n<p>The output format is similar to the input format. The second line is to contain one integer NA: the number of vertices in A (2 &le;NA &le;4). The following NA lines describe the vertices of A in the counter-clockwise order, one vertex per line. Line I+2 (for I = 1, 2, ..., NA) contains two integers X and Y, separated by a space: coordinates of the Ith vertex of the polygon A.&nbsp;<\/p>\r\n\r\n<p>Line NA+3 should contain one integer NB: the number of vertices in B, (2 &le;NB). The following NB lines describe the vertices of B in the counter-clockwise order, one vertex per line. Line NA+J+3 (for J = 1, 2, ..., NB) contains two integers X and Y, separated by a space: coordinates of the Jth vertex of the polygon B.&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Olympiad > International Olympiad in Informatics > IOI 2004 3번

  • 잘못된 조건을 찾은 사람: doju
  • 잘못된 데이터를 찾은 사람: pjsdream