시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
3 초 128 MB 1 0 0 0.000%

문제

평면 위에 점이 여러 개 주어진다. 이 점을 모두 지나는 지그재그 선을 찾으려고 한다. 이 때, 전환점(turning point)의 개수를 가장 적게 하려고 한다. 또, 전환점의 개수가 같은 경우에는 선의 길이가 가장 작은 것을 찾으려고 한다.

예를 들어, 아래와 같이 평면 위에 점이 9개가 있다고 하자.

지그재그 선은 여러 선분으로 이루어져 있고, 각 선분은 점을 두 개 이상 지나야 한다.

지그재그 선은 선이 꺽일 수 있는데, 이 꺽이는 지점을 전환점(turning point)라고 한다. 전환점은 주어진 점 위에 있을 수도 있고, 아닐 수도 있다.

왼쪽 지그재그 선의 길이: 8 + 3√2 ≃ 12.242641, 오른쪽 지그재그 선의 길이: 2√2 + (6 + 1/2) + 5√5/2 ≃ 14.918597

위의 그림은 주어진 점을 지나는 지그재그 선이고 두 선 모두 전환점의 개수는 3개이다. 왼쪽 지그재그 선의 길이는 오른쪽 지그재그 선의 길이보다 짧다. 또, 왼쪽 지그재그 선은 주어진 아홉 개의 점을 지나는 가장 짧은 지그재그 선이다.

전환점을 네 개 갖는 지그재그 선은 아래와 같다. 이 선의 길이는 위의 그림의 길이보다 짧지만, 전환점의 수가 더 많기 때문에 정답이 아니다.

아래와 같이 점이 7개 있고, 그 점을 잇는 두가지로 이었다고 하자. 이 때, 왼쪽의 길이가 오른쪽보다 더 길지만, 정답은 왼쪽 그림이 된다. 그 이유는 지그재그 선의 모든 선분은 점을 두 개 이상 지나야 하기 때문이다.

점이 주어졌을 때, 지그재그 선을 구하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스의 첫째 줄에는 점의 개수 n이 주어진다. 다음 n개의 줄에는 점의 좌표가 주어진다.

모든 좌표는 음이 아닌 정수이고, 공백으로 구분되어 있다. n은 2이상 10이하의 자연수이고, x,y좌표는 0이상 10이하의 정수이다. 점의 순서는 별 의미가 없다.

출력

각 테스트 케이스에 대해서, 가장 전환점을 갖는 지그재그 선 중 가장 짧은 것의 전환점의 개수와 길이를 출력한다. 선의 길이는 정답과의 오차가 0.0001까지 허용된다.

가장 작은 전환점의 개수는 최대 4개이며, 따라서 선분의 개수는 최대 5개가 된다.

예제 입력 1

2
0 0
10 9
4
0 0
3 1
0 3
3 3
10
2 2
4 2
6 2
2 4
4 4
6 4
2 6
4 6
6 6
3 3
10
0 0
2 0
4 0
0 2
2 2
4 2
0 4
2 4
4 4
6 8
9
0 0
1 0
3 0
0 1
1 1
3 1
0 2
1 2
2 2
10
0 0
1 0
0 1
1 1
9 9
9 10
10 9
10 10
0 2
10 8
10
0 0
0 10
2 0
2 1
2 7
2 10
5 1
6 7
9 2
10 9
0

예제 출력 1

0 13.45362405
1 18.48683298
3 24.14213562
4 24.94813673
3 12.24264069
3 60.78289622
3 502.7804353

힌트

첫 번째 데이터: 

두 번째 데이터: 

세 번째 데이터: 

네 번째 데이터: 

[{"problem_id":"3894","problem_lang":"0","title":"\uc9c0\uadf8\uc7ac\uadf8","description":"<p>\r\n\t\ud3c9\uba74 \uc704\uc5d0 \uc810\uc774 \uc5ec\ub7ec \uac1c \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \uc810\uc744 \ubaa8\ub450 \uc9c0\ub098\ub294 \uc9c0\uadf8\uc7ac\uadf8 \uc120\uc744 \ucc3e\uc73c\ub824\uace0 \ud55c\ub2e4. \uc774 \ub54c, \uc804\ud658\uc810(turning point)\uc758 \uac1c\uc218\ub97c \uac00\uc7a5 \uc801\uac8c \ud558\ub824\uace0 \ud55c\ub2e4. \ub610, \uc804\ud658\uc810\uc758 \uac1c\uc218\uac00 \uac19\uc740 \uacbd\uc6b0\uc5d0\ub294 \uc120\uc758 \uae38\uc774\uac00 \uac00\uc7a5 \uc791\uc740 \uac83\uc744 \ucc3e\uc73c\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uc608\ub97c \ub4e4\uc5b4, \uc544\ub798\uc640 \uac19\uc774 \ud3c9\uba74 \uc704\uc5d0 \uc810\uc774 9\uac1c\uac00 \uc788\ub2e4\uace0 \ud558\uc790.<\/p>\r\n\r\n<p>\r\n\t<img alt=\"\" src=\"\/upload\/images\/z1.png\" style=\"width: 161px; height: 143px;\" \/><\/p>\r\n\r\n<p>\r\n\t\uc9c0\uadf8\uc7ac\uadf8 \uc120\uc740 \uc5ec\ub7ec \uc120\ubd84\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, \uac01 \uc120\ubd84\uc740 \uc810\uc744 \ub450 \uac1c \uc774\uc0c1 \uc9c0\ub098\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uc9c0\uadf8\uc7ac\uadf8 \uc120\uc740 \uc120\uc774 \uaebd\uc77c \uc218 \uc788\ub294\ub370, \uc774 \uaebd\uc774\ub294 \uc9c0\uc810\uc744 \uc804\ud658\uc810(turning point)\ub77c\uace0 \ud55c\ub2e4. \uc804\ud658\uc810\uc740 \uc8fc\uc5b4\uc9c4 \uc810 \uc704\uc5d0 \uc788\uc744 \uc218\ub3c4 \uc788\uace0, \uc544\ub2d0 \uc218\ub3c4 \uc788\ub2e4.<\/p>\r\n\r\n<p>\r\n\t<img alt=\"\" src=\"\/upload\/images\/z2.png\" style=\"width: 486px; height: 137px;\" \/><\/p>\r\n\r\n<p>\r\n\t\uc67c\ucabd \uc9c0\uadf8\uc7ac\uadf8 \uc120\uc758 \uae38\uc774: 8 + 3&radic;2 \u2243 12.242641, \uc624\ub978\ucabd \uc9c0\uadf8\uc7ac\uadf8 \uc120\uc758 \uae38\uc774: 2&radic;2 + (6 + 1\/2) + 5&radic;5\/2 \u2243 14.918597<\/p>\r\n\r\n<p>\r\n\t\uc704\uc758 \uadf8\ub9bc\uc740 \uc8fc\uc5b4\uc9c4 \uc810\uc744 \uc9c0\ub098\ub294 \uc9c0\uadf8\uc7ac\uadf8 \uc120\uc774\uace0 \ub450 \uc120 \ubaa8\ub450 \uc804\ud658\uc810\uc758 \uac1c\uc218\ub294 3\uac1c\uc774\ub2e4. \uc67c\ucabd \uc9c0\uadf8\uc7ac\uadf8 \uc120\uc758 \uae38\uc774\ub294 \uc624\ub978\ucabd \uc9c0\uadf8\uc7ac\uadf8 \uc120\uc758 \uae38\uc774\ubcf4\ub2e4 \uc9e7\ub2e4. \ub610, \uc67c\ucabd \uc9c0\uadf8\uc7ac\uadf8 \uc120\uc740 \uc8fc\uc5b4\uc9c4 \uc544\ud649 \uac1c\uc758 \uc810\uc744 \uc9c0\ub098\ub294 \uac00\uc7a5 \uc9e7\uc740 \uc9c0\uadf8\uc7ac\uadf8 \uc120\uc774\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uc804\ud658\uc810\uc744 \ub124 \uac1c \uac16\ub294 \uc9c0\uadf8\uc7ac\uadf8 \uc120\uc740 \uc544\ub798\uc640 \uac19\ub2e4. \uc774 \uc120\uc758 \uae38\uc774\ub294 \uc704\uc758 \uadf8\ub9bc\uc758 \uae38\uc774\ubcf4\ub2e4 \uc9e7\uc9c0\ub9cc, \uc804\ud658\uc810\uc758 \uc218\uac00 \ub354 \ub9ce\uae30 \ub54c\ubb38\uc5d0 \uc815\ub2f5\uc774 \uc544\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\r\n\t<img alt=\"\" src=\"\/upload\/images\/z3.png\" style=\"width: 148px; height: 98px;\" \/><\/p>\r\n\r\n<p>\r\n\t\uc544\ub798\uc640 \uac19\uc774 \uc810\uc774 7\uac1c \uc788\uace0, \uadf8 \uc810\uc744 \uc787\ub294 \ub450\uac00\uc9c0\ub85c \uc774\uc5c8\ub2e4\uace0 \ud558\uc790. \uc774 \ub54c, \uc67c\ucabd\uc758 \uae38\uc774\uac00 \uc624\ub978\ucabd\ubcf4\ub2e4 \ub354 \uae38\uc9c0\ub9cc, \uc815\ub2f5\uc740 \uc67c\ucabd \uadf8\ub9bc\uc774 \ub41c\ub2e4. \uadf8 \uc774\uc720\ub294 \uc9c0\uadf8\uc7ac\uadf8 \uc120\uc758 \ubaa8\ub4e0 \uc120\ubd84\uc740 \uc810\uc744 \ub450 \uac1c \uc774\uc0c1 \uc9c0\ub098\uc57c \ud558\uae30 \ub54c\ubb38\uc774\ub2e4.<\/p>\r\n\r\n<p>\r\n\t<img alt=\"\" src=\"\/upload\/images\/z4.png\" style=\"width: 427px; height: 74px;\" \/><\/p>\r\n\r\n<p>\r\n\t\uc810\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc9c0\uadf8\uc7ac\uadf8 \uc120\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\r\n\t\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \uc810\uc758 \uac1c\uc218 n\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c n\uac1c\uc758 \uc904\uc5d0\ub294 \uc810\uc758 \uc88c\ud45c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ubaa8\ub4e0 \uc88c\ud45c\ub294 \uc74c\uc774 \uc544\ub2cc \uc815\uc218\uc774\uace0, \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc788\ub2e4. n\uc740 2\uc774\uc0c1 10\uc774\ud558\uc758 \uc790\uc5f0\uc218\uc774\uace0, x,y\uc88c\ud45c\ub294 0\uc774\uc0c1 10\uc774\ud558\uc758 \uc815\uc218\uc774\ub2e4. \uc810\uc758 \uc21c\uc11c\ub294 \ubcc4 \uc758\ubbf8\uac00 \uc5c6\ub2e4.<\/p>\r\n","output":"<p>\r\n\t\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \uac00\uc7a5 \uc804\ud658\uc810\uc744 \uac16\ub294 \uc9c0\uadf8\uc7ac\uadf8 \uc120 \uc911 \uac00\uc7a5 \uc9e7\uc740 \uac83\uc758 \uc804\ud658\uc810\uc758 \uac1c\uc218\uc640 \uae38\uc774\ub97c \ucd9c\ub825\ud55c\ub2e4. \uc120\uc758 \uae38\uc774\ub294 \uc815\ub2f5\uacfc\uc758 \uc624\ucc28\uac00 0.0001\uae4c\uc9c0 \ud5c8\uc6a9\ub41c\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uac00\uc7a5 \uc791\uc740 \uc804\ud658\uc810\uc758 \uac1c\uc218\ub294 \ucd5c\ub300 4\uac1c\uc774\uba70, \ub530\ub77c\uc11c \uc120\ubd84\uc758 \uac1c\uc218\ub294 \ucd5c\ub300 5\uac1c\uac00 \ub41c\ub2e4.<\/p>\r\n","hint":"<p>\r\n\t\uccab \ubc88\uc9f8 \ub370\uc774\ud130:&nbsp;<img alt=\"\" src=\"\/upload\/images\/zh1.png\" style=\"width: 163px; height: 166px;\" \/><\/p>\r\n<p>\r\n\t\ub450 \ubc88\uc9f8 \ub370\uc774\ud130:&nbsp;<img alt=\"\" src=\"\/upload\/images\/zh2.png\" style=\"width: 158px; height: 164px;\" \/><\/p>\r\n<p>\r\n\t\uc138 \ubc88\uc9f8 \ub370\uc774\ud130:&nbsp;<img alt=\"\" src=\"\/upload\/images\/zh3.png\" style=\"width: 162px; height: 162px;\" \/><\/p>\r\n<p>\r\n\t\ub124 \ubc88\uc9f8 \ub370\uc774\ud130:&nbsp;<img alt=\"\" src=\"\/upload\/images\/zh4.png\" style=\"width: 158px; height: 161px;\" \/><\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3894","problem_lang":"1","title":"Zigzag","description":"<p>Given several points on a plane, let&rsquo;s try to solve a puzzle connecting them with a zigzag line. The puzzle is to find the zigzag line that passes through all the given points with the minimum number of turns. Moreover, when there are several zigzag lines with the minimum number of turns, the shortest one among them should be found.<\/p>\r\n\r\n<p>For example, consider nine points given in Figure 10.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/z1.png\" style=\"height:143px; opacity:0.9; width:161px\" \/><\/p>\r\n\r\n<p>Figure 10: Given nine points<\/p>\r\n\r\n<p>A zigzag line is composed of several straight line segments. Here, the rule requests that each line segment should pass through two or more given points.<\/p>\r\n\r\n<p>A zigzag line may turn at some of the given points or anywhere else. There may be some given points passed more than once.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/ziza.png\" style=\"height:190px; width:544px\" \/><\/p>\r\n\r\n<p>Figure 11: Zigzag lines with three turning points.<\/p>\r\n\r\n<p>Two zigzag lines with three turning points are depicted in Figure 11 (a) and (b) for the same set of given points shown in Figure 10. The length of the zigzag line in Figure 11 (a) is shorter than that in Figure 11 (b). In fact, the length of the zigzag line in Figure 11 (a) is the shortest so that it is the solution for the nine points given in Figure 10.<\/p>\r\n\r\n<p>Another zigzag line with four turning points is depicted in Figure 12. Its length is shorter than those in Figure 11, however, the number of turning points is greater than those in Figure 11, and thus, it is not the solution.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/ziza2.png\" style=\"height:122px; width:165px\" \/><\/p>\r\n\r\n<p>Figure 12: Zigzag line with four turning points.<\/p>\r\n\r\n<p>There are two zigzag lines that passes another set of given points depicted in Figure 13 (a) and (b).<\/p>\r\n\r\n<p>Both have the same number of turning points, and the line in (a) is longer than that in (b). However, the solution is (a), because one of the segments of the zigzag line in (b) passes only one given point, violating the rule.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/ziza3.png\" style=\"height:107px; width:444px\" \/><\/p>\r\n\r\n<p>Figure 13: Zigzag line with two turning points (a), and not a zigzag line concerned (b).<\/p>\r\n\r\n<p>Your job is to write a program that solves this puzzle.<\/p>\r\n","input":"<p>The input consists of multiple datasets, followed by a line containing one zero. Each dataset has the following format.<\/p>\r\n\r\n<pre>\r\nn\r\nx<sub>1<\/sub> y<sub>1<\/sub>\r\n...\r\nx<sub>n<\/sub> y<sub>n<\/sub><\/pre>\r\n\r\n<p>Every input item in a dataset is a non-negative integer. Items in a line are separated by a single space.<\/p>\r\n\r\n<p>n is the number of the given points. x<sub>k<\/sub> and y<sub>k<\/sub> (k = 1, ..., n) indicate the position of the k-th point. The order of the points is meaningless. You can assume that 2 &le; n &le; 10, 0 &le; x<sub>k<\/sub> &le; 10, and 0 &le; y<sub>k<\/sub> &le; 10.<\/p>\r\n","output":"<p>For each dataset, the minimum number of turning points and the length of the shortest zigzag line with that number of turning points should be printed, separated by a space in a line. The length should be in a decimal fraction with an error less than 0.0001 (= 1.0 &times; 10<sup>&minus;4<\/sup>).<\/p>\r\n\r\n<p>You may assume that the minimum number of turning points is at most four, that is, the number of line segments is at most five.<\/p>\r\n\r\n<p>The example solutions for the first four datasets in the sample input are depicted in Figure 14 and 15.<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/upload\/images\/ziza4.png\" style=\"height:690px; width:613px\" \/><\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]