시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
3 초 (하단 참고) 256 MB 1251 372 234 31.283%

문제

N×M 보드 위에서 할 수 있는 게임이 있다. 보드는 크기가 1×1인 정사각형 칸으로 나누어져 있다. 보드의 각 칸은 빈 칸 또는 장애물이다. 장애물은 아래 그림에선 어두운 사각형으로 표시되어져 있다.

게임을 시작하려면 보드의 빈 칸 위에 공을 하나 놓아야 한다. 아래 그림에서 공은 회색 점으로 표시되어져 있다. 게임은 단계로 이루어져 있고, 각 단계는 아래와 같이 구성되어져 있다.

  • 위, 아래, 오른쪽, 왼쪽 중 방향 하나를 고른 다음, 그 방향으로 공을 계속해서 이동시킨다.
  • 공은 장애물, 보드의 경계, 이미 공이 지나갔던 칸을 만나기 전까지 계속해서 이동한다.

게임은 공이 더 이상 이동할 수 없을 때 끝난다. 이 때, 모든 빈 칸을 공이 방문한 적이 있어야 한다.

아래 그림은 총 10단계 만에 모든 칸을 방문하는 방법이다.

보드의 상태가 주어졌을 때, 모든 칸을 방문하기 위한 이동 횟수의 최솟값을 구하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다.

각 테스트 케이스의 첫째 줄에는 보드의 크기를 나타내는 N과 M이 주어진다. N은 세로 크기, M은 가로 크기이고, 두 값은 30보다 작거나 같은 자연수이다. 둘째 줄부터 N개의 줄에는 보드의 상태가 주어진다. 보드의 상태는 장애물을 나타내는 '*'과 빈 칸을 나타내는 '.'으로 이루어져 있다.

입력으로 주어진 보드가 장애물로만 이루어진 경우는 없다.

출력

각 테스트 케이스마다 보드의 모든 빈 칸을 방문하는 최소 이동 횟수를 출력한다. 출력 형식은 예제를 참고한다.

만약, 모든 빈 칸을 방문할 수 없다면 최소 이동 횟수는 -1이다. 가능한 이동 경로의 수는 1,000,000개를 넘지 않는다.

예제 입력 1

5 5
**...
.....
....*
..*..
.....
3 4
****
*...
*..*

예제 출력 1

Case 1: 10
Case 2: 3
[{"problem_id":"9944","problem_lang":"0","title":"NxM \ubcf4\ub4dc \uc644\uc8fc\ud558\uae30","description":"<p dir=\"ltr\">N&times;M \ubcf4\ub4dc \uc704\uc5d0\uc11c \ud560 \uc218 \uc788\ub294 \uac8c\uc784\uc774 \uc788\ub2e4. \ubcf4\ub4dc\ub294 \ud06c\uae30\uac00 1&times;1\uc778 \uc815\uc0ac\uac01\ud615 \uce78\uc73c\ub85c \ub098\ub204\uc5b4\uc838&nbsp;\uc788\ub2e4. \ubcf4\ub4dc\uc758 \uac01 \uce78\uc740 \ube48 \uce78 \ub610\ub294 \uc7a5\uc560\ubb3c\uc774\ub2e4. \uc7a5\uc560\ubb3c\uc740 \uc544\ub798 \uadf8\ub9bc\uc5d0\uc120 \uc5b4\ub450\uc6b4 \uc0ac\uac01\ud615\uc73c\ub85c \ud45c\uc2dc\ub418\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p dir=\"ltr\">\uac8c\uc784\uc744 \uc2dc\uc791\ud558\ub824\uba74 \ubcf4\ub4dc\uc758 \ube48 \uce78 \uc704\uc5d0&nbsp;\uacf5\uc744&nbsp;\ud558\ub098 \ub193\uc544\uc57c \ud55c\ub2e4.&nbsp;\uc544\ub798 \uadf8\ub9bc\uc5d0\uc11c \uacf5\uc740 \ud68c\uc0c9 \uc810\uc73c\ub85c \ud45c\uc2dc\ub418\uc5b4\uc838 \uc788\ub2e4. \uac8c\uc784\uc740 \ub2e8\uacc4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, \uac01 \ub2e8\uacc4\ub294 \uc544\ub798\uc640 \uac19\uc774 \uad6c\uc131\ub418\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<ul dir=\"ltr\">\r\n\t<li>\uc704, \uc544\ub798, \uc624\ub978\ucabd, \uc67c\ucabd \uc911 \ubc29\ud5a5 \ud558\ub098\ub97c \uace0\ub978 \ub2e4\uc74c, \uadf8 \ubc29\ud5a5\uc73c\ub85c \uacf5\uc744 \uacc4\uc18d\ud574\uc11c \uc774\ub3d9\uc2dc\ud0a8\ub2e4.<\/li>\r\n\t<li>\uacf5\uc740 \uc7a5\uc560\ubb3c, \ubcf4\ub4dc\uc758 \uacbd\uacc4, \uc774\ubbf8 \uacf5\uc774 \uc9c0\ub098\uac14\ub358 \uce78\uc744 \ub9cc\ub098\uae30 \uc804\uae4c\uc9c0 \uacc4\uc18d\ud574\uc11c \uc774\ub3d9\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uac8c\uc784\uc740 \uacf5\uc774 \ub354 \uc774\uc0c1 \uc774\ub3d9\ud560 \uc218 \uc5c6\uc744 \ub54c&nbsp;\ub05d\ub09c\ub2e4. \uc774 \ub54c, \ubaa8\ub4e0 \ube48 \uce78\uc744 \uacf5\uc774 \ubc29\ubb38\ud55c \uc801\uc774 \uc788\uc5b4\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc544\ub798 \uadf8\ub9bc\uc740 \ucd1d 10\ub2e8\uacc4 \ub9cc\uc5d0 \ubaa8\ub4e0 \uce78\uc744 \ubc29\ubb38\ud558\ub294 \ubc29\ubc95\uc774\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"\/upload\/images2\/fboard.png\" style=\"height: 150px; width: 167px;\" \/><\/p>\r\n\r\n<p>\ubcf4\ub4dc\uc758 \uc0c1\ud0dc\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ubaa8\ub4e0 \uce78\uc744 \ubc29\ubb38\ud558\uae30 \uc704\ud55c \uc774\ub3d9 \ud69f\uc218\uc758 \ucd5c\uc19f\uac12\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \ubcf4\ub4dc\uc758 \ud06c\uae30\ub97c \ub098\ud0c0\ub0b4\ub294 N\uacfc M\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. N\uc740 \uc138\ub85c \ud06c\uae30, M\uc740 \uac00\ub85c \ud06c\uae30\uc774\uace0, \ub450 \uac12\uc740 30\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uc790\uc5f0\uc218\uc774\ub2e4. \ub458\uc9f8 \uc904\ubd80\ud130 N\uac1c\uc758 \uc904\uc5d0\ub294 \ubcf4\ub4dc\uc758 \uc0c1\ud0dc\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ubcf4\ub4dc\uc758 \uc0c1\ud0dc\ub294 \uc7a5\uc560\ubb3c\uc744 \ub098\ud0c0\ub0b4\ub294 &#39;*&#39;\uacfc \ube48 \uce78\uc744 \ub098\ud0c0\ub0b4\ub294&nbsp;&#39;.&#39;\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \ubcf4\ub4dc\uac00 \uc7a5\uc560\ubb3c\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc9c4 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.<\/p>\r\n","output":"<p dir=\"ltr\">\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \ubcf4\ub4dc\uc758 \ubaa8\ub4e0 \ube48 \uce78\uc744 \ubc29\ubb38\ud558\ub294 \ucd5c\uc18c \uc774\ub3d9 \ud69f\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. \ucd9c\ub825 \ud615\uc2dd\uc740 \uc608\uc81c\ub97c \ucc38\uace0\ud55c\ub2e4.<\/p>\r\n\r\n<p dir=\"ltr\">\ub9cc\uc57d, \ubaa8\ub4e0 \ube48 \uce78\uc744 \ubc29\ubb38\ud560 \uc218 \uc5c6\ub2e4\uba74 \ucd5c\uc18c \uc774\ub3d9 \ud69f\uc218\ub294 -1\uc774\ub2e4.&nbsp;\uac00\ub2a5\ud55c \uc774\ub3d9 \uacbd\ub85c\uc758 \uc218\ub294 1,000,000\uac1c\ub97c \ub118\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9944","problem_lang":"1","title":"Full Board","description":"<p>A game starts with an M &times; N board with some squares marked as &ldquo;obstacles&rdquo; (drawn as dark squares in the figure below). The player chooses a starting position for a ball (drawn as solid gray dot) and chooses a direction (up, down, left, or right) to advance. Once the direction is chosen, the ball will advance in that direction until it hits an obstacle, the boundary of the board, or its own trajectory. When it hits one of these, the ball stops. Then the player is allowed to choose another direction, and the ball will advance in the same manner. The game ends when no legal move can be made. The player wins if and only if the trajectory includes all the empty squares on the board. The figure below traces a trajectory that shows one way to win the game in 10 steps.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images2\/fboard.png\" style=\"height:219px; width:244px\" \/><\/p>\r\n\r\n<p>Given an initial setting of a board, write a program to calculate the minimum number of steps to win the game.<\/p>\r\n","input":"<p>Each case on the input file begins with two integers m and n (1 &le; m, n &le; 30), indicating the size of board.The next m lines describe the initial setting of the board. Each line contains n characters, either &lsquo;*&rsquo; or &lsquo;.&rsquo;, indicating if the corresponding square is an obstacle or empty, respectively. [For example, see below for the input file corresponding to the case in the figure above.] It is guaranteed that the initial board is not fully covered by obstacles. Process until end-of-file; there is no end of data flag.<\/p>\r\n","output":"<p>Output the minimum number of steps to cover the board. Follow the format exactly: &ldquo;Case&rdquo;, one space, the case number, a colon and one space, and one integer indicating the minimum number of steps to win the game, or if there is no way to win, the number -1. Do not print any trailing spaces<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ICPC > Regionals > North America > North Central North America Regional > NCNA 2013 F번

  • 빠진 조건을 찾은 사람: jh05013
  • 문제의 오타를 찾은 사람: sky1357

시간 제한 안내

아래 적혀있지 않은 시간 제한은 언어 도움말에 적혀있는 기준을 따른다.

  • Python 3: 30초
  • PyPy3: 30초
  • Python 2: 30초
  • PyPy2: 30초