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문제

숭이는 자신이 가신 열쇠더미의 절반을 혜빈이에게 주려고 한다. 열쇠는 나선형을 따라 밀어서 열쇠 고리에 걸거나 분리할 수 있다. 같은 방식으로 열쇠 고리도 서로 연결하거나 분리 할 수 있다. 열쇠 고리에 열쇠를 연결하는 작업은 성가신 작업이기 때문에(숭이는 혜빈이가 손톱에 네일아트를 해주기 때문에 손톱을 다쳐선 안 된다) 이 과정을 최소로 하여 연결하려고 한다.

열쇠를 연결하거나 분리하거나, 열쇠 고리를 연결하거나 분리하는 것은 하나의 작업으로 간주된다. 열쇠를 밀어서 연결하거나 분리하는것은 고리를 연결하거나 분리하는 것에 비해 비해 매우 힘들기 때문에 숭이는 열쇠를 연결하거나 분리하는 과정을 최소로 하려고 한다. 만약 열쇠를 연결하거나 분리하는 횟수가 서로 같다면 열쇠 고리를 연결하거나 분리하는 과정을 최소로 해야 한다.

모든 작업이 완료되면, 숭이는 혜빈이에게 열쇠 더미를 건네준다(정확히 숭이꺼, 혜빈이꺼 두덩이로 분리되어야 한다). 예외가 되는 경우는 숭이가 갖는 열쇠 더미가 없거나 혜빈이에게 줄 수 있는 열쇠 더미가 없는 경우이다. 각각의 열쇠는 반드시 하나의 고리에 연결되어 있어야 한다. 열쇠 고리는 남은것이 생길 수 있다. 이때에는 두 그룹에서 분리시킨다

아래의 왼쪽 그림은 네개의 열쇠와 세개의 고리로 연결되어 있는 초기 상태를 나타낸다. 숭이는 혜빈이에게 2개의 열쇠인 N,R을 주려고 한다. 이때에 두 번의 열쇠 동작과 한번의 고리 동작으로 줄 수 있다. 이러한 결과가 아래의 오른쪽 그림이다.

입력

각각의 테스트 케이스는 하나 또는 여러개의 줄로 이루어져 있다. 각각의 테스트 케이스는 2개 문자로 이루어져 있다. 영어 소문자는 열쇠 고리를 나타내며 대문자는 열쇠를 나타낸다. 입력된 2개의 문자는 열쇠와 고리가 연결된 상태를 나타내거나, 고리와 고리가 연결된 상태를 나타낸다. 테스트 케이스 마지막 줄에는 0이 주어진다.

A부터 M까지의 열쇠는 숭이가 갖고, N부터 Z까지의 열쇠는 혜빈이에게 준다.

두 개의 문자가 모두 대문자인 경우는 없다. 테스트 케이스 내에서 같은 쌍으로 이루어진 문자열은 주어지지 않는다. 각각의 열쇠는 반드시 하나의 고리에 연결되어야 한다. 초기에 주어지는 열쇠 상태에서 고리에는 반드시 열쇠가 연결되어 있다(분리하면서 고리만 존재하는 경우는 발생할 수 있다). 존재하는 모든 열쇠와 고리는 반드시 한번 이상 주어진다.

출력

각각의 테스트 케이스에 대해서 열쇠를 연결하거나 분리하는 최소 횟수와 고리를 연결하거나 분리하는 최소 횟수를 출력한다.

만일 그러한 경우가 없다면 "impossible"을 출력한다.

예제 입력 1

ab
bc
aA
aN
Rb
cB
0
aA
bB
Cc
0
aA
aZ
0
aA
bB
cC
xX
yY
ax
xb
by
yc
0

예제 출력 1

Case 1: 2 1
Case 2: 0 2
Case 3: impossible
Case 4: 0 7
[{"problem_id":"4208","problem_lang":"0","title":"\uc5f4\uc1e0","description":"<p>\uc22d\uc774\ub294 \uc790\uc2e0\uc774 \uac00\uc2e0 \uc5f4\uc1e0\ub354\ubbf8\uc758 \uc808\ubc18\uc744 \ud61c\ube48\uc774\uc5d0\uac8c \uc8fc\ub824\uace0 \ud55c\ub2e4. \uc5f4\uc1e0\ub294 \ub098\uc120\ud615\uc744 \ub530\ub77c \ubc00\uc5b4\uc11c \uc5f4\uc1e0 \uace0\ub9ac\uc5d0 \uac78\uac70\ub098 \ubd84\ub9ac\ud560 \uc218 \uc788\ub2e4. \uac19\uc740 \ubc29\uc2dd\uc73c\ub85c \uc5f4\uc1e0 \uace0\ub9ac\ub3c4 \uc11c\ub85c \uc5f0\uacb0\ud558\uac70\ub098 \ubd84\ub9ac \ud560 \uc218 \uc788\ub2e4. \uc5f4\uc1e0 \uace0\ub9ac\uc5d0 \uc5f4\uc1e0\ub97c \uc5f0\uacb0\ud558\ub294 \uc791\uc5c5\uc740 \uc131\uac00\uc2e0 \uc791\uc5c5\uc774\uae30 \ub54c\ubb38\uc5d0(\uc22d\uc774\ub294 \ud61c\ube48\uc774\uac00 \uc190\ud1b1\uc5d0 \ub124\uc77c\uc544\ud2b8\ub97c \ud574\uc8fc\uae30 \ub54c\ubb38\uc5d0 \uc190\ud1b1\uc744 \ub2e4\uccd0\uc120 \uc548 \ub41c\ub2e4) \uc774 \uacfc\uc815\uc744 \ucd5c\uc18c\ub85c \ud558\uc5ec \uc5f0\uacb0\ud558\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc5f4\uc1e0\ub97c \uc5f0\uacb0\ud558\uac70\ub098 \ubd84\ub9ac\ud558\uac70\ub098, \uc5f4\uc1e0 \uace0\ub9ac\ub97c \uc5f0\uacb0\ud558\uac70\ub098 \ubd84\ub9ac\ud558\ub294 \uac83\uc740 \ud558\ub098\uc758 \uc791\uc5c5\uc73c\ub85c \uac04\uc8fc\ub41c\ub2e4. \uc5f4\uc1e0\ub97c \ubc00\uc5b4\uc11c \uc5f0\uacb0\ud558\uac70\ub098 \ubd84\ub9ac\ud558\ub294\uac83\uc740 \uace0\ub9ac\ub97c \uc5f0\uacb0\ud558\uac70\ub098 \ubd84\ub9ac\ud558\ub294 \uac83\uc5d0 \ube44\ud574 \ube44\ud574 \ub9e4\uc6b0 \ud798\ub4e4\uae30 \ub54c\ubb38\uc5d0 \uc22d\uc774\ub294 \uc5f4\uc1e0\ub97c \uc5f0\uacb0\ud558\uac70\ub098 \ubd84\ub9ac\ud558\ub294 \uacfc\uc815\uc744 \ucd5c\uc18c\ub85c \ud558\ub824\uace0 \ud55c\ub2e4. \ub9cc\uc57d \uc5f4\uc1e0\ub97c \uc5f0\uacb0\ud558\uac70\ub098 \ubd84\ub9ac\ud558\ub294 \ud69f\uc218\uac00 \uc11c\ub85c \uac19\ub2e4\uba74 \uc5f4\uc1e0 \uace0\ub9ac\ub97c \uc5f0\uacb0\ud558\uac70\ub098 \ubd84\ub9ac\ud558\ub294 \uacfc\uc815\uc744 \ucd5c\uc18c\ub85c \ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \uc791\uc5c5\uc774 \uc644\ub8cc\ub418\uba74, \uc22d\uc774\ub294 \ud61c\ube48\uc774\uc5d0\uac8c \uc5f4\uc1e0 \ub354\ubbf8\ub97c \uac74\ub124\uc900\ub2e4(\uc815\ud655\ud788 \uc22d\uc774\uaebc, \ud61c\ube48\uc774\uaebc \ub450\ub369\uc774\ub85c \ubd84\ub9ac\ub418\uc5b4\uc57c \ud55c\ub2e4). \uc608\uc678\uac00 \ub418\ub294 \uacbd\uc6b0\ub294 \uc22d\uc774\uac00 \uac16\ub294 \uc5f4\uc1e0 \ub354\ubbf8\uac00 \uc5c6\uac70\ub098 \ud61c\ube48\uc774\uc5d0\uac8c \uc904 \uc218 \uc788\ub294 \uc5f4\uc1e0 \ub354\ubbf8\uac00 \uc5c6\ub294 \uacbd\uc6b0\uc774\ub2e4. \uac01\uac01\uc758 \uc5f4\uc1e0\ub294 \ubc18\ub4dc\uc2dc \ud558\ub098\uc758 \uace0\ub9ac\uc5d0 \uc5f0\uacb0\ub418\uc5b4 \uc788\uc5b4\uc57c \ud55c\ub2e4. \uc5f4\uc1e0 \uace0\ub9ac\ub294 \ub0a8\uc740\uac83\uc774 \uc0dd\uae38 \uc218 \uc788\ub2e4. \uc774\ub54c\uc5d0\ub294 \ub450 \uadf8\ub8f9\uc5d0\uc11c \ubd84\ub9ac\uc2dc\ud0a8\ub2e4<\/p>\r\n\r\n<p>\uc544\ub798\uc758 \uc67c\ucabd \uadf8\ub9bc\uc740 \ub124\uac1c\uc758 \uc5f4\uc1e0\uc640 \uc138\uac1c\uc758 \uace0\ub9ac\ub85c \uc5f0\uacb0\ub418\uc5b4 \uc788\ub294 \ucd08\uae30 \uc0c1\ud0dc\ub97c \ub098\ud0c0\ub0b8\ub2e4. \uc22d\uc774\ub294 \ud61c\ube48\uc774\uc5d0\uac8c 2\uac1c\uc758 \uc5f4\uc1e0\uc778 N,R\uc744 \uc8fc\ub824\uace0 \ud55c\ub2e4. \uc774\ub54c\uc5d0 \ub450 \ubc88\uc758 \uc5f4\uc1e0 \ub3d9\uc791\uacfc \ud55c\ubc88\uc758 \uace0\ub9ac \ub3d9\uc791\uc73c\ub85c \uc904 \uc218 \uc788\ub2e4. \uc774\ub7ec\ud55c \uacb0\uacfc\uac00 \uc544\ub798\uc758 \uc624\ub978\ucabd \uadf8\ub9bc\uc774\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/keys.png\" style=\"height:190px; width:529px\" \/><\/p>\r\n","input":"<p>\uac01\uac01\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ud558\ub098 \ub610\ub294 \uc5ec\ub7ec\uac1c\uc758 \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uac01\uac01\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 2\uac1c \ubb38\uc790\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uc601\uc5b4 \uc18c\ubb38\uc790\ub294 \uc5f4\uc1e0 \uace0\ub9ac\ub97c \ub098\ud0c0\ub0b4\uba70 \ub300\ubb38\uc790\ub294 \uc5f4\uc1e0\ub97c \ub098\ud0c0\ub0b8\ub2e4. \uc785\ub825\ub41c 2\uac1c\uc758 \ubb38\uc790\ub294 \uc5f4\uc1e0\uc640 \uace0\ub9ac\uac00 \uc5f0\uacb0\ub41c \uc0c1\ud0dc\ub97c \ub098\ud0c0\ub0b4\uac70\ub098, \uace0\ub9ac\uc640 \uace0\ub9ac\uac00 \uc5f0\uacb0\ub41c \uc0c1\ud0dc\ub97c \ub098\ud0c0\ub0b8\ub2e4. \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>A\ubd80\ud130 M\uae4c\uc9c0\uc758 \uc5f4\uc1e0\ub294 \uc22d\uc774\uac00 \uac16\uace0, N\ubd80\ud130 Z\uae4c\uc9c0\uc758 \uc5f4\uc1e0\ub294 \ud61c\ube48\uc774\uc5d0\uac8c \uc900\ub2e4.<\/p>\r\n\r\n<p>\ub450 \uac1c\uc758 \ubb38\uc790\uac00 \ubaa8\ub450 \ub300\ubb38\uc790\uc778 \uacbd\uc6b0\ub294 \uc5c6\ub2e4. \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ub0b4\uc5d0\uc11c \uac19\uc740 \uc30d\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ubb38\uc790\uc5f4\uc740 \uc8fc\uc5b4\uc9c0\uc9c0 \uc54a\ub294\ub2e4. \uac01\uac01\uc758 \uc5f4\uc1e0\ub294 \ubc18\ub4dc\uc2dc \ud558\ub098\uc758 \uace0\ub9ac\uc5d0 \uc5f0\uacb0\ub418\uc5b4\uc57c \ud55c\ub2e4. \ucd08\uae30\uc5d0 \uc8fc\uc5b4\uc9c0\ub294 \uc5f4\uc1e0 \uc0c1\ud0dc\uc5d0\uc11c \uace0\ub9ac\uc5d0\ub294 \ubc18\ub4dc\uc2dc \uc5f4\uc1e0\uac00 \uc5f0\uacb0\ub418\uc5b4 \uc788\ub2e4(\ubd84\ub9ac\ud558\uba74\uc11c \uace0\ub9ac\ub9cc \uc874\uc7ac\ud558\ub294 \uacbd\uc6b0\ub294 \ubc1c\uc0dd\ud560 \uc218 \uc788\ub2e4). \uc874\uc7ac\ud558\ub294 \ubaa8\ub4e0 \uc5f4\uc1e0\uc640 \uace0\ub9ac\ub294 \ubc18\ub4dc\uc2dc \ud55c\ubc88 \uc774\uc0c1 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01\uac01\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c \uc5f4\uc1e0\ub97c \uc5f0\uacb0\ud558\uac70\ub098 \ubd84\ub9ac\ud558\ub294 \ucd5c\uc18c \ud69f\uc218\uc640 \uace0\ub9ac\ub97c \uc5f0\uacb0\ud558\uac70\ub098 \ubd84\ub9ac\ud558\ub294 \ucd5c\uc18c \ud69f\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc77c \uadf8\ub7ec\ud55c \uacbd\uc6b0\uac00 \uc5c6\ub2e4\uba74 &quot;impossible&quot;\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"4208","problem_lang":"1","title":"Keys","description":"<p>Adam carries a bunch of keys attached to key rings, some of which may be connected to each other. The rings are common key rings, so a key can be attached to or detached from a ring by sliding along the spiral. In the same way, two rings can be connected or disconnected. Adam wants to give some of the keys to Brenda. Since manipulating the keys and rings is often an annoying task (and also dangerous to one&rsquo;s \ufb01ngernails), Adam is looking for a way to minimize the number of key and ring operations.<\/p>\r\n\r\n<p>Every key attachment, key detachment, ring connection, or ring disconnection is considered one operation. Since manipulating two rings is signi\ufb01cantly easier than sliding a key, we \ufb01rst want to minimize the number of keys being detached and attached. Among solutions with the same minimal number of key operations, you need to \ufb01nd the one with the minimal number of ring connections and disconnections.<\/p>\r\n\r\n<p>When all the operations are complete, Adam and Brenda must each carry one connected group of rings and keys. The only exception is when either of them would have no keys at all&mdash;in such a case, no ring is needed. Each key must be attached to exactly one ring. Some rings (but not keys) may be considered leftovers and may remain disconnected from the two groups.<\/p>\r\n\r\n<p>The left side of the following \ufb01gure shows an initial con\ufb01guration consisting of four keys on three rings. Adam wishes to give Brenda the two keys labeled N and R. This can be accomplished by two key operations and one ring operation, resulting in the con\ufb01guration shown on the right side of the \ufb01gure.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/keys.png\" style=\"height:190px; width:529px\" \/><\/p>\r\n","input":"<p>Each test case contains one or more lines, each containing a two letter string. Lowercase letters (a - z) represent key rings and uppercase letters (A - Z) represent keys. The two letters on a line specify either a key attached to a ring or two rings connected together. The end of each test case is denoted by a line containing the digit zero.<\/p>\r\n\r\n<p>Keys denoted by letters A through M remain with Adam, and keys denoted by letters N through Z are given to Brenda.<\/p>\r\n\r\n<p>No line contains two uppercase letters. No pair of letters are speci\ufb01ed more than once in the same test case. Each key is connected to exactly one ring. There are no &ldquo;circles&rdquo; in the ring con\ufb01gurations (disconnecting any two rings will increase the number of connected groups). All existing keys and rings are mentioned at least once.<\/p>\r\n","output":"<p>For each test case, display the case number followed by the minimal number of key attach\/detach operations and the minimal number of ring connect\/disconnect operations.<\/p>\r\n\r\n<p>If there is no way to split the keys as requested, display the case number and the word impossible instead of the two integers.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ICPC > World Finals > 2012 World Finals F번

  • 문제를 번역한 사람: lll4592