시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 9 6 6 66.667%

문제

행렬은 글자로 채워져 있는 직사각형 표이다. 정사각형 행렬은 열의 수와 행의 수가 같을 때이다. 정사각형 행렬 M이 대칭이라면, 모든 i,j쌍에 대해서 Mij = Mji를 만족할 때이다.

아래 두 행렬은 대칭인 경우이다.

AAB        AAA
ACC        ABA
BCC        AAA

아래 두 행렬은 대칭이 아닌 경우이다.

ABCD        AAB
ABCD        ACA
ABCD        DAA
ABCD

사용할 수 있는 문자가 주어졌을 때, 이 문자를 모두 사용해서 만들 수 있는 대칭행렬 중에서, 사전순으로 앞서는 행렬의 열의 부분집합을 출력하는 프로그램을 작성하시오.

어떤 행렬의 열의 부분집합이란 특정 열을 제외하고는 모두 지워버린 행렬이다. 아래와 같은 행렬을 살펴보자.

AAB
ACC
BCC

위 행렬의 1,3열의 부분집합은 다음과 같다. (2열에 등장하는 문자를 모두 지워버리면 된다.)

AB
AC
BC

두 행렬 A와 B를 사전순으로 비교하려면, 각 행렬을 행을 순서대로 모두 이어붙여 긴 문자열로 만든 뒤 문자열 비교를 한다고 생각하면 된다.

입력

첫째 줄에 두 정수 N과 K가 주어진다. N은 행렬의 크기이고, K는 사용할 수 있는 서로 다른 문자의 개수이다. (1 ≤ N ≤ 30000, 1 ≤ K ≤ 26)

다음 K개 줄에는 사용할 수 있는 문자와 그 개수가 공백으로 구분되어 주어진다. 문자는 모두 알파벳 대문자이다. 예를 들어, "A 3"은 A를 3번 사용할 수 있다는 뜻이다.

사용할 수 있는 문자의 개수는 정확히 N2개이다.

다음 줄에는 열의 부분집합의 크기 P가 주어진다. (1 ≤ P ≤ 50)

마지막 줄에는, P개의 숫자가 주어지고, 열의 부분집합의 내용이다. 각 숫자는 1보다 크거나 같고, N보다 작거나 같으며, 오름차순으로 정렬되어 있고, 중복되지 않는다.

출력

주어진 문자로 대칭행렬을 만드는 것이 가능하다면, 행렬의 열의 부분집합을 출력한다. 만약, 불가능하다면 "IMPOSSIBLE"을 출력한다. (따옴표는 출력하지 않는다)

예제 입력 1

3 3
A 3
B 2
C 4
3
1 2 3

예제 출력 1

AAB
ACC
BCC
[{"problem_id":"2956","problem_lang":"0","title":"\ub300\uce6d \ud589\ub82c","description":"<p>\ud589\ub82c\uc740 \uae00\uc790\ub85c \ucc44\uc6cc\uc838 \uc788\ub294 \uc9c1\uc0ac\uac01\ud615 \ud45c\uc774\ub2e4. \uc815\uc0ac\uac01\ud615 \ud589\ub82c\uc740 \uc5f4\uc758 \uc218\uc640 \ud589\uc758 \uc218\uac00 \uac19\uc744 \ub54c\uc774\ub2e4. \uc815\uc0ac\uac01\ud615 \ud589\ub82c M\uc774 \ub300\uce6d\uc774\ub77c\uba74, \ubaa8\ub4e0 i,j\uc30d\uc5d0 \ub300\ud574\uc11c M<sub>ij<\/sub> = M<sub>ji<\/sub>\ub97c \ub9cc\uc871\ud560 \ub54c\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc544\ub798 \ub450 \ud589\ub82c\uc740 \ub300\uce6d\uc778 \uacbd\uc6b0\uc774\ub2e4.<\/p>\r\n\r\n<pre>\r\nAAB        AAA\r\nACC        ABA\r\nBCC        AAA<\/pre>\r\n\r\n<p>\uc544\ub798 \ub450 \ud589\ub82c\uc740 \ub300\uce6d\uc774 \uc544\ub2cc \uacbd\uc6b0\uc774\ub2e4.<\/p>\r\n\r\n<pre>\r\nABCD        AAB\r\nABCD        ACA\r\nABCD        DAA\r\nABCD<\/pre>\r\n\r\n<p>\uc0ac\uc6a9\ud560 \uc218 \uc788\ub294 \ubb38\uc790\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc774 \ubb38\uc790\ub97c \ubaa8\ub450 \uc0ac\uc6a9\ud574\uc11c \ub9cc\ub4e4 \uc218 \uc788\ub294 \ub300\uce6d\ud589\ub82c \uc911\uc5d0\uc11c, \uc0ac\uc804\uc21c\uc73c\ub85c \uc55e\uc11c\ub294 \ud589\ub82c\uc758 \uc5f4\uc758 \ubd80\ubd84\uc9d1\ud569\uc744 \ucd9c\ub825\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p>\uc5b4\ub5a4 \ud589\ub82c\uc758 \uc5f4\uc758 \ubd80\ubd84\uc9d1\ud569\uc774\ub780 \ud2b9\uc815 \uc5f4\uc744 \uc81c\uc678\ud558\uace0\ub294 \ubaa8\ub450 \uc9c0\uc6cc\ubc84\ub9b0 \ud589\ub82c\uc774\ub2e4. \uc544\ub798\uc640 \uac19\uc740 \ud589\ub82c\uc744 \uc0b4\ud3b4\ubcf4\uc790.<\/p>\r\n\r\n<pre>\r\nAAB\r\nACC\r\nBCC<\/pre>\r\n\r\n<p>\uc704 \ud589\ub82c\uc758 1,3\uc5f4\uc758 \ubd80\ubd84\uc9d1\ud569\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4. (2\uc5f4\uc5d0 \ub4f1\uc7a5\ud558\ub294 \ubb38\uc790\ub97c \ubaa8\ub450 \uc9c0\uc6cc\ubc84\ub9ac\uba74 \ub41c\ub2e4.)<\/p>\r\n\r\n<pre>\r\nAB\r\nAC\r\nBC<\/pre>\r\n\r\n<p>\ub450 \ud589\ub82c A\uc640 B\ub97c \uc0ac\uc804\uc21c\uc73c\ub85c \ube44\uad50\ud558\ub824\uba74, \uac01 \ud589\ub82c\uc744 \ud589\uc744 \uc21c\uc11c\ub300\ub85c \ubaa8\ub450 \uc774\uc5b4\ubd99\uc5ec \uae34 \ubb38\uc790\uc5f4\ub85c \ub9cc\ub4e0 \ub4a4 \ubb38\uc790\uc5f4 \ube44\uad50\ub97c \ud55c\ub2e4\uace0 \uc0dd\uac01\ud558\uba74 \ub41c\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub450 \uc815\uc218 N\uacfc K\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. N\uc740 \ud589\ub82c\uc758 \ud06c\uae30\uc774\uace0, K\ub294 \uc0ac\uc6a9\ud560 \uc218 \uc788\ub294 \uc11c\ub85c \ub2e4\ub978 \ubb38\uc790\uc758 \uac1c\uc218\uc774\ub2e4. (1 &le; N &le; 30000, 1 &le; K &le; 26)<\/p>\r\n\r\n<p>\ub2e4\uc74c K\uac1c \uc904\uc5d0\ub294 \uc0ac\uc6a9\ud560 \uc218 \uc788\ub294 \ubb38\uc790\uc640 \uadf8 \uac1c\uc218\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. \ubb38\uc790\ub294 \ubaa8\ub450 \uc54c\ud30c\ubcb3 \ub300\ubb38\uc790\uc774\ub2e4. \uc608\ub97c \ub4e4\uc5b4, &quot;A 3&quot;\uc740 A\ub97c 3\ubc88 \uc0ac\uc6a9\ud560 \uc218 \uc788\ub2e4\ub294 \ub73b\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc0ac\uc6a9\ud560 \uc218 \uc788\ub294 \ubb38\uc790\uc758 \uac1c\uc218\ub294 \uc815\ud655\ud788 N<sup>2<\/sup>\uac1c\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc904\uc5d0\ub294 \uc5f4\uc758 \ubd80\ubd84\uc9d1\ud569\uc758 \ud06c\uae30 P\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; P &le; 50)<\/p>\r\n\r\n<p>\ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294, P\uac1c\uc758 \uc22b\uc790\uac00 \uc8fc\uc5b4\uc9c0\uace0, \uc5f4\uc758 \ubd80\ubd84\uc9d1\ud569\uc758 \ub0b4\uc6a9\uc774\ub2e4. \uac01 \uc22b\uc790\ub294 1\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uace0, N\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc73c\uba70, \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc815\ub82c\ub418\uc5b4 \uc788\uace0, \uc911\ubcf5\ub418\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","output":"<p>\uc8fc\uc5b4\uc9c4 \ubb38\uc790\ub85c \ub300\uce6d\ud589\ub82c\uc744 \ub9cc\ub4dc\ub294 \uac83\uc774 \uac00\ub2a5\ud558\ub2e4\uba74, \ud589\ub82c\uc758 \uc5f4\uc758 \ubd80\ubd84\uc9d1\ud569\uc744 \ucd9c\ub825\ud55c\ub2e4. \ub9cc\uc57d, \ubd88\uac00\ub2a5\ud558\ub2e4\uba74 &quot;IMPOSSIBLE&quot;\uc744 \ucd9c\ub825\ud55c\ub2e4. (\ub530\uc634\ud45c\ub294 \ucd9c\ub825\ud558\uc9c0 \uc54a\ub294\ub2e4)<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2956","problem_lang":"1","title":"MATRICA","description":"<p>A matrix is a rectangular table of letters. A square matrix is a matrix with an equal number of rows and columns. A square matrix M is called symmetric if its letters are symmetric with respect to the main diagonal (Mij = Mji for all pairs of i and j).&nbsp;<\/p>\r\n\r\n<p>The following figure shows two symmetric matrices and one which is not symmetric:&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/symmatrix.png\" style=\"height:136px; width:557px\" \/><\/p>\r\n\r\n<p>Given a collection of available letters, you are to output a subset of columns in the lexicographically smallest symmetric matrix which can be composed using all the letters.&nbsp;<\/p>\r\n\r\n<p>If no such matrix exists, output &quot;IMPOSSIBLE&quot;.&nbsp;<\/p>\r\n\r\n<p>To determine if matrix A is lexicographically smaller than matrix B, consider their elements in rowmajor order (as if you concatenated all rows to form a long string). If the first element in which the matrices differ is smaller in A, then A is lexicographically smaller than B.<\/p>\r\n","input":"<p>The first line of input contains two integers N (1 &le; N &le; 30000) and K (1 &le; K &le; 26). N is the dimension of the matrix, while K is the number of distinct letters that will appear.&nbsp;<\/p>\r\n\r\n<p>Each of the following K lines contains an uppercase letter and a positive integer, separated by a space. The integer denotes how many corresponding letters are to be used. For example, if a line says &quot;A 3&quot;, then the letter A must appear three times in the output matrix.&nbsp;<\/p>\r\n\r\n<p>The total number of letters will be exactly N<sup>2<\/sup>. No letter will appear more than once in the input.&nbsp;<\/p>\r\n\r\n<p>The next line contains an integer P (1 &le; P &le; 50), the number of columns that must be output.&nbsp;<\/p>\r\n\r\n<p>The last line contains P integers, the indices of columns that must be output. The indices will be between 1 and N inclusive, given in increasing order and without duplicates<\/p>\r\n","output":"<p>If it is possible to compose a symmetric matrix from the given collection of letters, output the required columns on N lines, each containing P character, without spaces. Otherwise, output &quot;IMPOSSIBLE&quot; (quotes for clarity).&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Contest > Croatian Open Competition in Informatics > COCI 2008/2009 > Contest #3 4번

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