시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 1 1 1 100.000%

문제

강호는 친구들과 함께 맥주를 먹으면서 다트를 하러왔다.

강호와 친구들은 다트 게임 중 가장 쉬운 게임 중 하나인 501을 한다. 두 플레이어는 N점 점수를 가진 상태로 시작하며, 서로 턴을 번갈아가면서 다트를 던진다. 각 플레이어는 다트로 맞춘 점수만큼 점수가 감소하게 되며, 점수는 음수가 될 수 없다. 만약, 점수가 감소했을 때, 음수가 되어야 하면, 점수는 그대로 유지된다. 두 플레이어 중에서 먼저 0점을 만든 사람이 게임을 승리하게 된다. 아래 그림은 이번 게임에서 사용할 다트판이다.

두 사람 A와 B는 서로 다른 전략을 가지고 게임을 하려고 한다.

A는 다트를 무작위로 던지며, 다트판의 각 칸을 맞출 확률이 모두 같으며, B는 자신이 승리할 확률이 가장 높은 칸을 겨냥해서 다트를 던진다. 이 때, B는 겨냥한 칸과 좌우로 인접한 칸만 맞추며, 각각의 칸을 맞출 확률은 같다.

두 플레이어의 초기 점수가 주어졌을 때, 각 플레이어가 이길 확률을 구하는 프로그램을 작성하시오. 누가 다트를 먼저 던지냐에 따라서, 확률이 다르다.

입력

첫째 줄에 초기 점수 N (1 ≤ N ≤ 501)이 주어지며, N = 0인 경우에 입력의 종료를 나타낸다.

출력

각각의 입력에 대해서, A가 다트를 먼저 던졌을 때 이길 확률과 B가 먼저 던졌을 때 이길 확률을 출력한다. 정답과의 절대/상대 오차는 10-8까지 허용한다.

예제 입력 1

5
100
0

예제 출력 1

0.136363636364 0.909090909091
0.072504908290 0.950215081962
[{"problem_id":"3858","problem_lang":"0","title":"\ub2e4\ud2b8","description":"<p>\uac15\ud638\ub294 \uce5c\uad6c\ub4e4\uacfc \ud568\uaed8 \ub9e5\uc8fc\ub97c \uba39\uc73c\uba74\uc11c \ub2e4\ud2b8\ub97c \ud558\ub7ec\uc654\ub2e4.<\/p>\r\n\r\n<p>\uac15\ud638\uc640 \uce5c\uad6c\ub4e4\uc740 \ub2e4\ud2b8 \uac8c\uc784 \uc911 \uac00\uc7a5 \uc26c\uc6b4 \uac8c\uc784 \uc911 \ud558\ub098\uc778 501\uc744 \ud55c\ub2e4. \ub450 \ud50c\ub808\uc774\uc5b4\ub294 N\uc810 \uc810\uc218\ub97c \uac00\uc9c4 \uc0c1\ud0dc\ub85c \uc2dc\uc791\ud558\uba70, \uc11c\ub85c \ud134\uc744 \ubc88\uac08\uc544\uac00\uba74\uc11c \ub2e4\ud2b8\ub97c \ub358\uc9c4\ub2e4. \uac01 \ud50c\ub808\uc774\uc5b4\ub294 \ub2e4\ud2b8\ub85c \ub9de\ucd98 \uc810\uc218\ub9cc\ud07c \uc810\uc218\uac00 \uac10\uc18c\ud558\uac8c \ub418\uba70, \uc810\uc218\ub294 \uc74c\uc218\uac00 \ub420 \uc218 \uc5c6\ub2e4. \ub9cc\uc57d, \uc810\uc218\uac00 \uac10\uc18c\ud588\uc744 \ub54c, \uc74c\uc218\uac00 \ub418\uc5b4\uc57c \ud558\uba74, \uc810\uc218\ub294 \uadf8\ub300\ub85c \uc720\uc9c0\ub41c\ub2e4. \ub450 \ud50c\ub808\uc774\uc5b4 \uc911\uc5d0\uc11c \uba3c\uc800 0\uc810\uc744 \ub9cc\ub4e0 \uc0ac\ub78c\uc774 \uac8c\uc784\uc744 \uc2b9\ub9ac\ud558\uac8c \ub41c\ub2e4. \uc544\ub798 \uadf8\ub9bc\uc740 \uc774\ubc88 \uac8c\uc784\uc5d0\uc11c \uc0ac\uc6a9\ud560 \ub2e4\ud2b8\ud310\uc774\ub2e4.<\/p>\r\n\r\n<p style=\"text-align:center\"><img alt=\"\" src=\"\/upload\/images2\/dart.png\" style=\"height:170px; line-height:20.8px; opacity:0.9; text-align:center; width:182px\" \/><\/p>\r\n\r\n<p>\ub450 \uc0ac\ub78c A\uc640 B\ub294 \uc11c\ub85c \ub2e4\ub978 \uc804\ub7b5\uc744 \uac00\uc9c0\uace0 \uac8c\uc784\uc744 \ud558\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>A\ub294 \ub2e4\ud2b8\ub97c \ubb34\uc791\uc704\ub85c \ub358\uc9c0\uba70, \ub2e4\ud2b8\ud310\uc758 \uac01 \uce78\uc744 \ub9de\ucd9c \ud655\ub960\uc774 \ubaa8\ub450 \uac19\uc73c\uba70, B\ub294 \uc790\uc2e0\uc774 \uc2b9\ub9ac\ud560 \ud655\ub960\uc774 \uac00\uc7a5 \ub192\uc740 \uce78\uc744 \uaca8\ub0e5\ud574\uc11c \ub2e4\ud2b8\ub97c \ub358\uc9c4\ub2e4. \uc774 \ub54c, B\ub294 \uaca8\ub0e5\ud55c \uce78\uacfc \uc88c\uc6b0\ub85c \uc778\uc811\ud55c \uce78\ub9cc \ub9de\ucd94\uba70, \uac01\uac01\uc758 \uce78\uc744 \ub9de\ucd9c \ud655\ub960\uc740 \uac19\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ud50c\ub808\uc774\uc5b4\uc758 \ucd08\uae30 \uc810\uc218\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uac01 \ud50c\ub808\uc774\uc5b4\uac00 \uc774\uae38 \ud655\ub960\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \ub204\uac00 \ub2e4\ud2b8\ub97c \uba3c\uc800 \ub358\uc9c0\ub0d0\uc5d0 \ub530\ub77c\uc11c, \ud655\ub960\uc774 \ub2e4\ub974\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ucd08\uae30 \uc810\uc218 N (1 &le; N &le; 501)\uc774 \uc8fc\uc5b4\uc9c0\uba70, N = 0\uc778 \uacbd\uc6b0\uc5d0 \uc785\ub825\uc758 \uc885\ub8cc\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n","output":"<p>\uac01\uac01\uc758 \uc785\ub825\uc5d0 \ub300\ud574\uc11c, A\uac00 \ub2e4\ud2b8\ub97c \uba3c\uc800 \ub358\uc84c\uc744 \ub54c \uc774\uae38 \ud655\ub960\uacfc B\uac00 \uba3c\uc800 \ub358\uc84c\uc744 \ub54c \uc774\uae38 \ud655\ub960\uc744 \ucd9c\ub825\ud55c\ub2e4. \uc815\ub2f5\uacfc\uc758 \uc808\ub300\/\uc0c1\ub300 \uc624\ucc28\ub294 10<sup>-8<\/sup>\uae4c\uc9c0 \ud5c8\uc6a9\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3858","problem_lang":"1","title":"Darts","description":"<p>After a long week of work at the ICPC Headquarters, Bill and his friends usually go to a small pub on Friday evenings to have a couple of beers and play darts. All of them are well aware of the fact that their ability at darts decreases at the same rate as the amount of beer left in their mugs.<\/p>\r\n\r\n<p>They always play 501, one of the easiest games. Players start with a score of N points (typically, N = 501, hence the name) and take turns throwing darts. The score of each player decreases by the value of the section hit by the dart, unless the score becomes negative, in which case it remains unchanged. The first player to reach a score of 0 wins. The figure below shows the dartboard with which the game is played.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"\/upload\/images2\/dart.png\" style=\"height:170px; width:182px\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">Figure 1: Dartboard<\/p>\r\n\r\n<p>As the clock ticks closer to midnight and they start running out of beer, everyone wonders the same: is it worth trying to aim the dart at a specific section? Or is it better just to throw the dart at a random section on the dartboard? You are asked to deal with the question by finding out what would happen if two players (A and B) applying these two different strategies were to play against each other:<\/p>\r\n\r\n<p>Player A throws the darts at random, and consequently they land with equal probability in each of the sections of the dartboard.<br \/>\r\nIf Player B aims at a certain section, the dart has the same probability of landing in the correct one as in each of the two adjacent ones (the neighbouring regions to the left and right). Moreover, he is completely aware of his ability and sober enough to aim at the section that maximizes his probability of winning.<\/p>\r\n\r\n<p>Given the initial score of both players, can you determine the probability that the first player wins? Of course, being the first to throw a dart might be advantageous, so the answer depends on who plays first.<\/p>\r\n","input":"<p>The input consists of a series of lines, each containing an integer N (1 &le; N &le; 501), the initial score of both players. A case with N = 0 marks the end of the input and must not be processed.<\/p>\r\n","output":"<p>For each number in the input, your program should output a line containing two real numbers: the probability that A wins if A throws the first dart, and the probability that B wins if B throws the first dart. Your answers should be accurate to within an absolute or relative error of 10<sup>&minus;8<\/sup>.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]