시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

이제 사각형의 경계선과 선분의 교차점에 관한 간단한 기하 문제를 풀어볼 것이다.

매우 다행히도 사각형은 항상 축에 평행한 형태로만 놓여 있다.

어떤 사각형과 어떤 선분의 교차점은 항상 0개이거나, 1개이거나, 2개이거나, 무한하다.

각각의 경우에 대한 몇 가지 예제는 아래와 같다.

(a) 교점이 0개인 경우

(b) 교점이 1개인 경우

(c) 교점이 2개인 경우

(d) 교점이 무한히 많은 경우

입력

첫 줄에 테스트 케이스의 수 T가 주어진다.

각 테스트 케이스는 4개의 정수로 시작한다. 각 정수는 xmin, ymin, xmax, ymax이며, 이것은 사각형의 왼쪽 아래 꼭짓점이 (xmin, ymin)이고 오른쪽 위 꼭짓점이 (xmax, ymax)임을 의미한다. (-10,000 ≤ xmin < xmax ≤ 10,000, -10,000 ≤ ymin < ymax ≤ 10,000그 다음 줄에도 4개의 정수 x1, y1, x2, y2가 주어진다. 이는 선분의 한쪽 끝점이 (x1,y1)이며 다른쪽 끝점이 (x2,y2)임을 의미한다. (-10,000 ≤ x1, y1, x2, y2 ≤ 10,000)

선분의 길이는 항상 0보다 크다.

출력

테스트 케이스마다 하나의 정수를 출력한다.

만일 주어진 사각형과 선분의 교차점의 개수가 유한하다면 교차점의 개수를 출력하고, 교차점이 무한히 많다면 4를 출력한다.

예제 입력 1

16
0 0 8 4
2 6 -2 3
0 0 8 4
0 4 9 4
0 0 8 4
3 5 6 6
0 0 8 4
-2 5 10 -1
0 0 8 4
0 5 8 5
0 0 8 4
4 3 4 1
0 0 8 4
-2 3 2 5
0 0 8 4
2 4 6 4
0 0 8 4
0 4 4 7
0 0 8 4
4 2 4 4
0 0 8 4
4 2 8 4
0 0 8 4
0 2 3 4
0 0 8 4
-4 0 12 4
0 0 8 4
4 8 4 -1
0 0 8 4
0 -2 0 6
0 0 8 4
3 4 10 4

예제 출력 1

0
4
0
2
0
0
1
4
1
1
1
2
2
2
4
4
[{"problem_id":"10255","problem_lang":"0","title":"\uad50\ucc28\uc810","description":"<p>\uc774\uc81c \uc0ac\uac01\ud615\uc758 \uacbd\uacc4\uc120\uacfc \uc120\ubd84\uc758 \uad50\ucc28\uc810\uc5d0 \uad00\ud55c \uac04\ub2e8\ud55c \uae30\ud558 \ubb38\uc81c\ub97c \ud480\uc5b4\ubcfc \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub9e4\uc6b0 \ub2e4\ud589\ud788\ub3c4 \uc0ac\uac01\ud615\uc740 \ud56d\uc0c1 \ucd95\uc5d0 \ud3c9\ud589\ud55c \ud615\ud0dc\ub85c\ub9cc \ub193\uc5ec \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc5b4\ub5a4 \uc0ac\uac01\ud615\uacfc \uc5b4\ub5a4 \uc120\ubd84\uc758 \uad50\ucc28\uc810\uc740 \ud56d\uc0c1 0\uac1c\uc774\uac70\ub098, 1\uac1c\uc774\uac70\ub098, 2\uac1c\uc774\uac70\ub098, \ubb34\ud55c\ud558\ub2e4.<\/p>\r\n\r\n<p>\uac01\uac01\uc758 \uacbd\uc6b0\uc5d0 \ub300\ud55c \uba87 \uac00\uc9c0 \uc608\uc81c\ub294 \uc544\ub798\uc640 \uac19\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img src=\"https:\/\/www.acmicpc.net\/upload\/images2\/inter1.png\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">(a) \uad50\uc810\uc774 0\uac1c\uc778 \uacbd\uc6b0<\/p>\r\n\r\n<p style=\"text-align: center;\"><img src=\"https:\/\/www.acmicpc.net\/upload\/images2\/inter2.png\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">(b) \uad50\uc810\uc774 1\uac1c\uc778 \uacbd\uc6b0<\/p>\r\n\r\n<p style=\"text-align: center;\"><img src=\"https:\/\/www.acmicpc.net\/upload\/images2\/inter3.png\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">(c) \uad50\uc810\uc774 2\uac1c\uc778 \uacbd\uc6b0<\/p>\r\n\r\n<p style=\"text-align: center;\"><img src=\"https:\/\/www.acmicpc.net\/upload\/images2\/inter4.png\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">(d) \uad50\uc810\uc774 \ubb34\ud55c\ud788 \ub9ce\uc740 \uacbd\uc6b0<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 4\uac1c\uc758 \uc815\uc218\ub85c \uc2dc\uc791\ud55c\ub2e4.&nbsp;<span style=\"line-height:1.6em\">\uac01 \uc815\uc218\ub294 xmin, ymin, xmax, ymax\uc774\uba70, \uc774\uac83\uc740 \uc0ac\uac01\ud615\uc758 \uc67c\ucabd \uc544\ub798 \uaf2d\uc9d3\uc810\uc774 (xmin, ymin)\uc774\uace0 \uc624\ub978\ucabd \uc704 \uaf2d\uc9d3\uc810\uc774 (xmax, ymax)\uc784\uc744 \uc758\ubbf8\ud55c\ub2e4.&nbsp;<\/span><span style=\"line-height:1.6em\">(-10,000 &le; xmin &lt; xmax &le; 10,000,<\/span><span style=\"line-height:1.6em\">&nbsp;-10,000 &le; ymin &lt; ymax &le; 10,000<\/span><span style=\"line-height:1.6em\">)&nbsp;<\/span><span style=\"line-height:1.6em\">\uadf8 \ub2e4\uc74c \uc904\uc5d0\ub3c4 4\uac1c\uc758 \uc815\uc218 x1, y1, x2, y2\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;<\/span><span style=\"line-height:1.6em\">\uc774\ub294 \uc120\ubd84\uc758 \ud55c\ucabd \ub05d\uc810\uc774 (x1,y1)\uc774\uba70 \ub2e4\ub978\ucabd \ub05d\uc810\uc774 (x2,y2)\uc784\uc744 \uc758\ubbf8\ud55c\ub2e4.&nbsp;<\/span><span style=\"line-height:1.6em\">(-10,000 &le; x1, y1, x2, y2 &le; 10,000)<\/span><\/p>\r\n\r\n<p>\uc120\ubd84\uc758 \uae38\uc774\ub294 \ud56d\uc0c1 0\ubcf4\ub2e4 \ud06c\ub2e4.<\/p>\r\n","output":"<p>\ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \ud558\ub098\uc758 \uc815\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc77c \uc8fc\uc5b4\uc9c4 \uc0ac\uac01\ud615\uacfc \uc120\ubd84\uc758 \uad50\ucc28\uc810\uc758 \uac1c\uc218\uac00 \uc720\ud55c\ud558\ub2e4\uba74 \uad50\ucc28\uc810\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud558\uace0, \uad50\ucc28\uc810\uc774 \ubb34\ud55c\ud788 \ub9ce\ub2e4\uba74 4\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"10255","problem_lang":"1","title":"Intersections","description":"<p>Your job is to write a program of solving a simple geometry problem for finding the number of intersection points of the boundary of a rectangle and a line segment. Each edge of a given rectangle is parallel to x-axis or y-axis. (You are very lucky!) The number of intersections between them is zero, one, two, or infinity. A case of &lsquo;infinity&rsquo; occurs in a situation in which an edge of the rectangle and the segment are overlapped partially or wholly. See the figure below which shows examples of several situations between a rectangle and a segment.<\/p>\r\n\r\n<p style=\"text-align:center\"><img alt=\"\" src=\"\/upload\/images2\/inter1.png\" style=\"height:127px; width:632px\" \/><\/p>\r\n\r\n<p style=\"text-align:center\">(a) Some examples of zero intersection between R and l.&nbsp;<\/p>\r\n\r\n<p style=\"text-align:center\"><img alt=\"\" src=\"\/upload\/images2\/inter2.png\" style=\"height:109px; width:638px\" \/><\/p>\r\n\r\n<p style=\"text-align:center\">(b) Some examples of one intersection between R and l.&nbsp;<\/p>\r\n\r\n<p style=\"text-align:center\"><img alt=\"\" src=\"\/upload\/images2\/inter3.png\" style=\"height:111px; width:640px\" \/><\/p>\r\n\r\n<p style=\"text-align:center\">(c) Some examples of two intersections between R and l.&nbsp;<\/p>\r\n\r\n<p style=\"text-align:center\"><img alt=\"\" src=\"\/upload\/images2\/inter4.png\" style=\"height:124px; width:635px\" \/><\/p>\r\n\r\n<p style=\"text-align:center\">(d) Some examples of infinite intersections between R and l.&nbsp;<\/p>\r\n\r\n<p style=\"text-align:center\">Figure 1. Examples of several situations between a rectangle R(blue) and a line segment l(red).<\/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 four integers xmin, ymin, xmax, and ymax representing a recrangle R, where (xmin, ymin) and (xmax, ymax) represent the coordinates of the lower left corner and upper right corner of R, respectively, -10,000 &le; xmin &lt; xmax &le; 10,000 and -10,000 &le; ymin &lt; ymax &le; 10,000. The next line contains four integers x1, y1, x2, and y2 representing a line segment l, where (x1, y1) and (x2, y2) represent the coordinates of two end poiunts of l, respectinely, -10,000 &le; x1, y1, x2, y2 &le; 10,000, and the length of l is greater than zero.<\/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 an integer representing the number of the intersections of the boundary of a rectangle and a line segment given by input. If the number of the intersections is infinity, then your program should output &quot;4&quot; instead.&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > Asia > Korea > Nationwide Internet Competition > Daejeon Nationalwide Internet Competition 2014 F번