시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 60 27 18 41.860%

문제

스도쿠가 세계적으로 유행이 된 이후에, 비슷한 퍼즐이 매우 많이 나왔다. 게임 매거진 2009년 7월호에는 스도쿠와 도미노를 혼합한 게임인 스도미노쿠가 소개되었다. 

이 퍼즐은 스도쿠 규칙을 따른다. 스도쿠는 9×9 크기의 그리드를 1부터 9까지 숫자를 이용해서 채워야 한다. 스도쿠는 다음과 같은 조건을 만족하게 숫자를 채워야 한다.

  • 각 행에는 1부터 9까지 숫자가 하나씩 있어야 한다.
  • 각 열에는 1부터 9까지 숫자가 하나씩 있어야 한다.
  • 3×3크기의 정사각형에는 1부터 9가지 숫자가 하나씩 있어야 한다.

스도미노쿠의 그리드에는 1부터 9까지 숫자가 쓰여져 있고, 나머지 72칸은 도미노 타일 36개로 채워야 한다. 도미노 타일은 1부터 9까지 서로 다른 숫자의 가능한 쌍이 모두 포함되어 있다. (1+2, 1+3, 1+4, 1+5, 1+6, 1+7, 1+8, 1+9, 2+3, 2+4, 2+5, ...) 1+2와 2+1은 같은 타일이기 때문에, 따로 구분하지 않는다. 도미노 타일은 회전 시킬 수 있다. 또, 3×3 크기의 정사각형의 경계에 걸쳐서 놓여질 수도 있다.

왼쪽 그림은 퍼즐의 초기 상태를 나타내고, 오른쪽은 퍼즐을 푼 상태이다.

스도미노쿠의 퍼즐의 초기 상태가 주어졌을 때, 퍼즐을 푸는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스의 첫째 줄에는 채워져 있는 도미노의 개수 N이 주어진다. (10 ≤ N ≤ 35) 다음 N개 줄에는 도미노 하나를 나타내는 U LU V LV가 주어진다. U는 도미노에 써 있는 한 숫자이고, LU는 길이가 2인 문자열로 U의 위치를 나타낸다. V와 LV는 도미노에 써 있는 다른 숫자를 나타낸다. 도미노의 위치는 문제에 나와있는 그림을 참고한다. 입력으로 주어지는 도미노의 각 숫자 위치는 항상 인접해 있다.

N개의 도미노의 정보가 주어진 다음 줄에는 채워져 있는 숫자의 위치가 주어진다. 위치는 도미노의 위치를 나타낸 방법과 같은 방법으로 주어진다.

모든 도미노와 숫자가 겹치는 경우는 없다.

입력의 마지막 줄에는 0이 하나 주어진다.

출력

각 퍼즐에 대해서, 스도쿠를 푼 결과를 출력한다. 항상 답이 유일한 경우만 입력으로 주어진다.

예제 입력 1

10
6 B2 1 B3
2 C4 9 C3
6 D3 8 E3
7 E1 4 F1
8 B7 4 B8
3 F5 2 F6
7 F7 6 F8
5 G4 9 G5 
7 I8 8 I9
7 C9 2 B9
C5 A3 D9 I4 A9 E5 A2 C6 I1
11
5 I9 2 H9
6 A5 7 A6
4 B8 6 C8
3 B5 8 B4
3 C3 2 D3
9 D2 8 E2
3 G2 5 H2
1 A2 8 A1
1 H8 3 I8
8 I3 7 I4
4 I6 9 I7
I5 E6 D1 F2 B3 G9 H7 C9 E5
0

예제 출력 1

Puzzle 1
872643195
361975842
549218637
126754983
738169254
495832761
284597316
657381429
913426578
Puzzle 2
814267593
965831247
273945168
392176854
586492371
741358629
137529486
459683712
628714935

힌트

[{"problem_id":"4574","problem_lang":"0","title":"\uc2a4\ub3c4\ubbf8\ub178\ucfe0","description":"<p>\uc2a4\ub3c4\ucfe0\uac00 \uc138\uacc4\uc801\uc73c\ub85c \uc720\ud589\uc774 \ub41c \uc774\ud6c4\uc5d0, \ube44\uc2b7\ud55c \ud37c\uc990\uc774 \ub9e4\uc6b0 \ub9ce\uc774 \ub098\uc654\ub2e4. \uac8c\uc784 \ub9e4\uac70\uc9c4 2009\ub144 7\uc6d4\ud638\uc5d0\ub294 \uc2a4\ub3c4\ucfe0\uc640 \ub3c4\ubbf8\ub178\ub97c \ud63c\ud569\ud55c \uac8c\uc784\uc778 \uc2a4\ub3c4\ubbf8\ub178\ucfe0\uac00 \uc18c\uac1c\ub418\uc5c8\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\uc774 \ud37c\uc990\uc740 \uc2a4\ub3c4\ucfe0 \uaddc\uce59\uc744 \ub530\ub978\ub2e4. \uc2a4\ub3c4\ucfe0\ub294 9&times;9 \ud06c\uae30\uc758 \uadf8\ub9ac\ub4dc\ub97c 1\ubd80\ud130 9\uae4c\uc9c0 \uc22b\uc790\ub97c \uc774\uc6a9\ud574\uc11c \ucc44\uc6cc\uc57c \ud55c\ub2e4. \uc2a4\ub3c4\ucfe0\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uc870\uac74\uc744 \ub9cc\uc871\ud558\uac8c \uc22b\uc790\ub97c \ucc44\uc6cc\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uac01 \ud589\uc5d0\ub294 1\ubd80\ud130 9\uae4c\uc9c0 \uc22b\uc790\uac00 \ud558\ub098\uc529 \uc788\uc5b4\uc57c \ud55c\ub2e4.<\/li>\r\n\t<li>\uac01 \uc5f4\uc5d0\ub294 1\ubd80\ud130 9\uae4c\uc9c0 \uc22b\uc790\uac00 \ud558\ub098\uc529 \uc788\uc5b4\uc57c \ud55c\ub2e4.<\/li>\r\n\t<li>3&times;3\ud06c\uae30\uc758 \uc815\uc0ac\uac01\ud615\uc5d0\ub294 1\ubd80\ud130 9\uac00\uc9c0 \uc22b\uc790\uac00 \ud558\ub098\uc529 \uc788\uc5b4\uc57c \ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc2a4\ub3c4\ubbf8\ub178\ucfe0\uc758 \uadf8\ub9ac\ub4dc\uc5d0\ub294 1\ubd80\ud130 9\uae4c\uc9c0 \uc22b\uc790\uac00 \uc4f0\uc5ec\uc838 \uc788\uace0, \ub098\uba38\uc9c0 72\uce78\uc740 \ub3c4\ubbf8\ub178 \ud0c0\uc77c 36\uac1c\ub85c \ucc44\uc6cc\uc57c \ud55c\ub2e4. \ub3c4\ubbf8\ub178 \ud0c0\uc77c\uc740 1\ubd80\ud130 9\uae4c\uc9c0 \uc11c\ub85c \ub2e4\ub978 \uc22b\uc790\uc758 \uac00\ub2a5\ud55c \uc30d\uc774 \ubaa8\ub450 \ud3ec\ud568\ub418\uc5b4 \uc788\ub2e4. (1+2, 1+3, 1+4, 1+5, 1+6, 1+7, 1+8, 1+9, 2+3, 2+4, 2+5, ...) 1+2\uc640 2+1\uc740 \uac19\uc740 \ud0c0\uc77c\uc774\uae30 \ub54c\ubb38\uc5d0, \ub530\ub85c \uad6c\ubd84\ud558\uc9c0 \uc54a\ub294\ub2e4. \ub3c4\ubbf8\ub178 \ud0c0\uc77c\uc740 \ud68c\uc804 \uc2dc\ud0ac \uc218 \uc788\ub2e4. \ub610, 3&times;3 \ud06c\uae30\uc758 \uc815\uc0ac\uac01\ud615\uc758 \uacbd\uacc4\uc5d0 \uac78\uccd0\uc11c \ub193\uc5ec\uc9c8 \uc218\ub3c4 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc67c\ucabd \uadf8\ub9bc\uc740 \ud37c\uc990\uc758 \ucd08\uae30 \uc0c1\ud0dc\ub97c \ub098\ud0c0\ub0b4\uace0, \uc624\ub978\ucabd\uc740 \ud37c\uc990\uc744 \ud47c \uc0c1\ud0dc\uc774\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/example1.png\" style=\"height:352px; width:352px\" \/><img alt=\"\" src=\"\/upload\/images\/example1-soln.png\" style=\"height:352px; width:352px\" \/><\/p>\r\n\r\n<p>\uc2a4\ub3c4\ubbf8\ub178\ucfe0\uc758 \ud37c\uc990\uc758 \ucd08\uae30 \uc0c1\ud0dc\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ud37c\uc990\uc744 \ud478\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. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \ucc44\uc6cc\uc838 \uc788\ub294 \ub3c4\ubbf8\ub178\uc758 \uac1c\uc218 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (10 &le; N &le; 35) \ub2e4\uc74c N\uac1c \uc904\uc5d0\ub294 \ub3c4\ubbf8\ub178 \ud558\ub098\ub97c \ub098\ud0c0\ub0b4\ub294 U LU V LV\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. U\ub294 \ub3c4\ubbf8\ub178\uc5d0 \uc368 \uc788\ub294 \ud55c \uc22b\uc790\uc774\uace0, LU\ub294 \uae38\uc774\uac00 2\uc778 \ubb38\uc790\uc5f4\ub85c U\uc758 \uc704\uce58\ub97c \ub098\ud0c0\ub0b8\ub2e4. V\uc640 LV\ub294 \ub3c4\ubbf8\ub178\uc5d0 \uc368 \uc788\ub294 \ub2e4\ub978 \uc22b\uc790\ub97c \ub098\ud0c0\ub0b8\ub2e4. \ub3c4\ubbf8\ub178\uc758 \uc704\uce58\ub294 \ubb38\uc81c\uc5d0 \ub098\uc640\uc788\ub294 \uadf8\ub9bc\uc744 \ucc38\uace0\ud55c\ub2e4. \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c0\ub294 \ub3c4\ubbf8\ub178\uc758 \uac01 \uc22b\uc790 \uc704\uce58\ub294 \ud56d\uc0c1 \uc778\uc811\ud574 \uc788\ub2e4.<\/p>\r\n\r\n<p>N\uac1c\uc758 \ub3c4\ubbf8\ub178\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c4 \ub2e4\uc74c \uc904\uc5d0\ub294 \ucc44\uc6cc\uc838 \uc788\ub294 \uc22b\uc790\uc758 \uc704\uce58\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc704\uce58\ub294 \ub3c4\ubbf8\ub178\uc758 \uc704\uce58\ub97c \ub098\ud0c0\ub0b8 \ubc29\ubc95\uacfc \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \ub3c4\ubbf8\ub178\uc640 \uc22b\uc790\uac00 \uacb9\uce58\ub294 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \ud558\ub098 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud37c\uc990\uc5d0 \ub300\ud574\uc11c, \uc2a4\ub3c4\ucfe0\ub97c \ud47c \uacb0\uacfc\ub97c \ucd9c\ub825\ud55c\ub2e4. \ud56d\uc0c1 \ub2f5\uc774 \uc720\uc77c\ud55c \uacbd\uc6b0\ub9cc \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"4574","problem_lang":"1","title":"Su-domino-ku","description":"<p>As if there were not already enough sudoku-like puzzles, the July 2009 issue of Games Magazine describes the following variant that combines facets of both sudoku and dominos. The puzzle is a form of a standard sudoku, in which there is a nine-by-nine grid that must be filled in using only digits 1 through 9. In a successful solution:<\/p>\r\n\r\n<ul>\r\n\t<li>Each row must contain each of the digits 1 through 9.<\/li>\r\n\t<li>Each column must contain each of the digits 1 through 9.<\/li>\r\n\t<li>Each of the indicated three-by-three squares must contain each of the digits 1 through 9.<\/li>\r\n<\/ul>\r\n\r\n<p>For a su-domino-ku, nine arbitrary cells are initialized with the numbers 1 to 9. This leaves 72 remaining cells. Those must be filled by making use of the following set of 36 domino tiles. The tile set includes one domino for each possible pair of unique numbers from 1 to 9 (e.g., 1+2, 1+3, 1+4, 1+5, 1+6, 1+7, 1+8, 1+9, 2+3, 2+4, 2+5, ...). Note well that there are not separate 1+2 and 2+1 tiles in the set; the single such domino can be rotated to provide either orientation. Also, note that dominos may cross the boundary of the three-by-three squares (as does the 2+9 domino in our coming example).<\/p>\r\n\r\n<p>To help you out, we will begin each puzzle by identifying the location of some of the dominos. For example, Figure 1 shows a sample puzzle in its initial state. Figure 2 shows the unique way to complete that puzzle.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/example1.png\" style=\"height:352px; opacity:0.9; width:352px\" \/><img alt=\"\" src=\"\/upload\/images\/example1-soln.png\" style=\"height:352px; width:352px\" \/><\/p>\r\n","input":"<p>Each puzzle description begins with a line containing an integer N, for 10 &le; N &le; 35, representing the number of dominos that are initially placed in the starting configuration. Following that are N lines, each describing a single domino as U LU V LV. Value U is one of the numbers on the domino, and LU is a two-character string representing the location of value U on the board based on the grid system diagrammed in Figure 1. The variables V and LV representing the respective value and location of the other half of the domino. For example, our first sample input beings with a domino described as 6 B2 1 B3. This corresponds to the domino with values 6+1 being placed on the board such that value 6 is in row B, column 2 and value 1 in row B, column 3. The two locations for a given domino will always be neighboring.<\/p>\r\n\r\n<p>After the specification of the N dominos will be a final line that describes the initial locations of the isolated numbers, ordered from 1 to 9, using the same row-column conventions for describing locations on the board. All initial numbers and dominos will be at unique locations.<\/p>\r\n\r\n<p>The input file ends with a line containing 0.<\/p>\r\n","output":"<p>For each puzzle, output an initial line identifying the puzzle number, as shown below. Following that, output the 9x9 sudoku board that can be formed with the set of dominos. There will be a unique solution for each puzzle.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > North America > Mid-Central Regional > 2011 Mid-Central Regional Programming Contest D번

  • 문제를 번역한 사람: baekjoon
  • 문제의 오타를 찾은 사람: kipa00