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27985번 - 멘토링 매칭 스페셜 저지다국어

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문제

한과영에는 졸업생 선배들의 도움을 원하는 학생들이 많이 있다. 다행히도, 카이스트에는 학생들을 돕고자 하는 졸업생들이 많이 있다. 그래서 은하는 학생들이 도움을 받을 수 있게끔 한과영 학생들과 카이스트 학생들을 연결해 주는 멘토링 매칭 시스템을 만드려고 한다.

매칭 시스템은 시스템에 등록된 $N$명의 한과영 학생들과 $N$명의 카이스트 학생들을 일대일로 매칭시킨다. 한과영과 카이스트 학생들은 1ドル$번부터 $N$번까지의 학번을 가지고 있다.

$N$명의 한과영 학생들은 각자 한 명씩의 카이스트 학생과 연결된다. 두 명 이상의 한과영 학생들이 동일한 카이스트 학생과 연결되는 일은 없다. 또한 한과영 학생들은 각자 $N$명의 카이스트 학생들에 대한 선호도를 가지고 있다. 선호도가 같은 경우는 없다.

그런데, 카이스트 학생들은 과제 때문에 너어어어어무 피곤하기 때문에, 한과영 학생들에 대한 선호도를 오직 학번만 가지고 결정한다. 구체적으로, 자신의 학번과 어떤 한과영 학생의 학번의 차가 더 클수록, 그 학생을 더 선호하게 된다. 차가 같은 한과영 학생끼리는 학번이 더 작은 한과영 학생이 더 선호된다.

은하는 매칭이 stable matching이 되기를 원하지만 과제도 하고, 시험공부도 하고, 마인크래프트 건축도 하고, 리듬게임도 하느라 바쁘다. 은하가 stable matching을 이룰 수 있도록 도와주자!

입력

첫 번째 줄에 정수 $N$이 주어진다.

두 번째 줄부터 $N$개의 줄에 걸쳐서 정수가 $N$개씩 주어진다. 각 정수는 1ドル$ 이상 $N$ 이하이며, $i+1$번째 줄의 $k$번째 정수가 $j$라면 $i$번 한과영 학생은 $j$번 카이스트 학생을 $k$번째로 선호한다는 뜻이다.

출력

첫 번째 줄에 $N$개의 정수들을 출력한다. $i$번째 정수가 $j$라면 $i$번 한과영 학생과 $j$번 카이스트 학생을 연결한다는 뜻이다.

답이 여러 개 존재한다면 아무거나 출력해도 상관없다.

제한

  • 1ドル \leq N \leq 20$

예제 입력 1

2
2 1
1 2

예제 출력 1

2 1

예제 입력 2

5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5

예제 출력 2

3 4 5 2 1

노트

어떤 매칭에 대해, 어떤 연결되지 못한 두 학생의 쌍 $(i, j)$가 다음 조건을 만족할 때 unstable하다고 한다.

  • $i$는 그의 파트너보다 $j$를 더 선호한다.
  • $j$는 그의 파트너보다 $i$를 더 선호한다.

Stable matching이란 unstable한 쌍이 없는 매칭을 의미한다.

[{"problem_id":"27985","problem_lang":"0","title":"\uba58\ud1a0\ub9c1 \ub9e4\uce6d","description":"<p>\ud55c\uacfc\uc601\uc5d0\ub294 \uc878\uc5c5\uc0dd \uc120\ubc30\ub4e4\uc758 \ub3c4\uc6c0\uc744 \uc6d0\ud558\ub294 \ud559\uc0dd\ub4e4\uc774 \ub9ce\uc774 \uc788\ub2e4. \ub2e4\ud589\ud788\ub3c4, \uce74\uc774\uc2a4\ud2b8\uc5d0\ub294 \ud559\uc0dd\ub4e4\uc744 \ub3d5\uace0\uc790 \ud558\ub294 \uc878\uc5c5\uc0dd\ub4e4\uc774 \ub9ce\uc774 \uc788\ub2e4. \uadf8\ub798\uc11c \uc740\ud558\ub294 \ud559\uc0dd\ub4e4\uc774 \ub3c4\uc6c0\uc744 \ubc1b\uc744 \uc218 \uc788\uac8c\ub054 \ud55c\uacfc\uc601 \ud559\uc0dd\ub4e4\uacfc \uce74\uc774\uc2a4\ud2b8 \ud559\uc0dd\ub4e4\uc744 \uc5f0\uacb0\ud574 \uc8fc\ub294 \uba58\ud1a0\ub9c1 \ub9e4\uce6d \uc2dc\uc2a4\ud15c\uc744 \ub9cc\ub4dc\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub9e4\uce6d \uc2dc\uc2a4\ud15c\uc740 \uc2dc\uc2a4\ud15c\uc5d0 \ub4f1\ub85d\ub41c $N$\uba85\uc758 \ud55c\uacfc\uc601 \ud559\uc0dd\ub4e4\uacfc $N$\uba85\uc758 \uce74\uc774\uc2a4\ud2b8 \ud559\uc0dd\ub4e4\uc744 \uc77c\ub300\uc77c\ub85c \ub9e4\uce6d\uc2dc\ud0a8\ub2e4. \ud55c\uacfc\uc601\uacfc \uce74\uc774\uc2a4\ud2b8 \ud559\uc0dd\ub4e4\uc740 $1$\ubc88\ubd80\ud130 $N$\ubc88\uae4c\uc9c0\uc758 \ud559\ubc88\uc744 \uac00\uc9c0\uace0 \uc788\ub2e4. <\/p>\r\n\r\n<p>$N$\uba85\uc758 \ud55c\uacfc\uc601 \ud559\uc0dd\ub4e4\uc740 \uac01\uc790 \ud55c \uba85\uc529\uc758 \uce74\uc774\uc2a4\ud2b8 \ud559\uc0dd\uacfc \uc5f0\uacb0\ub41c\ub2e4. \ub450 \uba85 \uc774\uc0c1\uc758 \ud55c\uacfc\uc601 \ud559\uc0dd\ub4e4\uc774 \ub3d9\uc77c\ud55c \uce74\uc774\uc2a4\ud2b8 \ud559\uc0dd\uacfc \uc5f0\uacb0\ub418\ub294 \uc77c\uc740 \uc5c6\ub2e4. \ub610\ud55c \ud55c\uacfc\uc601 \ud559\uc0dd\ub4e4\uc740 \uac01\uc790 $N$\uba85\uc758 \uce74\uc774\uc2a4\ud2b8 \ud559\uc0dd\ub4e4\uc5d0 \ub300\ud55c \uc120\ud638\ub3c4\ub97c \uac00\uc9c0\uace0 \uc788\ub2e4. \uc120\ud638\ub3c4\uac00 \uac19\uc740 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uadf8\ub7f0\ub370, \uce74\uc774\uc2a4\ud2b8 \ud559\uc0dd\ub4e4\uc740 \uacfc\uc81c \ub54c\ubb38\uc5d0 \ub108\uc5b4\uc5b4\uc5b4\uc5b4\ubb34 \ud53c\uace4\ud558\uae30 \ub54c\ubb38\uc5d0, \ud55c\uacfc\uc601 \ud559\uc0dd\ub4e4\uc5d0 \ub300\ud55c \uc120\ud638\ub3c4\ub97c \uc624\uc9c1 \ud559\ubc88\ub9cc \uac00\uc9c0\uace0 \uacb0\uc815\ud55c\ub2e4. \uad6c\uccb4\uc801\uc73c\ub85c, \uc790\uc2e0\uc758 \ud559\ubc88\uacfc \uc5b4\ub5a4 \ud55c\uacfc\uc601 \ud559\uc0dd\uc758 \ud559\ubc88\uc758 \ucc28\uac00 \ub354 \ud074\uc218\ub85d, \uadf8 \ud559\uc0dd\uc744 \ub354 \uc120\ud638\ud558\uac8c \ub41c\ub2e4. \ucc28\uac00 \uac19\uc740 \ud55c\uacfc\uc601 \ud559\uc0dd\ub07c\ub9ac\ub294 \ud559\ubc88\uc774 \ub354 \uc791\uc740 \ud55c\uacfc\uc601 \ud559\uc0dd\uc774 \ub354 \uc120\ud638\ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc740\ud558\ub294 \ub9e4\uce6d\uc774 <strong>stable matching<\/strong>\uc774 \ub418\uae30\ub97c \uc6d0\ud558\uc9c0\ub9cc \uacfc\uc81c\ub3c4 \ud558\uace0, \uc2dc\ud5d8\uacf5\ubd80\ub3c4 \ud558\uace0, \ub9c8\uc778\ud06c\ub798\ud504\ud2b8 \uac74\ucd95\ub3c4 \ud558\uace0, \ub9ac\ub4ec\uac8c\uc784\ub3c4 \ud558\ub290\ub77c \ubc14\uc058\ub2e4. \uc740\ud558\uac00 stable matching\uc744 \uc774\ub8f0 \uc218 \uc788\ub3c4\ub85d \ub3c4\uc640\uc8fc\uc790!<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \uc815\uc218 $N$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\ubd80\ud130 $N$\uac1c\uc758 \uc904\uc5d0 \uac78\uccd0\uc11c \uc815\uc218\uac00 $N$\uac1c\uc529 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \uc815\uc218\ub294 $1$ \uc774\uc0c1 $N$ \uc774\ud558\uc774\uba70, $i+1$\ubc88\uc9f8 \uc904\uc758 $k$\ubc88\uc9f8 \uc815\uc218\uac00 $j$\ub77c\uba74 $i$\ubc88 \ud55c\uacfc\uc601 \ud559\uc0dd\uc740 $j$\ubc88 \uce74\uc774\uc2a4\ud2b8 \ud559\uc0dd\uc744 $k$\ubc88\uc9f8\ub85c \uc120\ud638\ud55c\ub2e4\ub294 \ub73b\uc774\ub2e4.<\/p>\r\n","output":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 $N$\uac1c\uc758 \uc815\uc218\ub4e4\uc744 \ucd9c\ub825\ud55c\ub2e4. $i$\ubc88\uc9f8 \uc815\uc218\uac00 $j$\ub77c\uba74 $i$\ubc88 \ud55c\uacfc\uc601 \ud559\uc0dd\uacfc $j$\ubc88 \uce74\uc774\uc2a4\ud2b8 \ud559\uc0dd\uc744 \uc5f0\uacb0\ud55c\ub2e4\ub294 \ub73b\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub2f5\uc774 \uc5ec\ub7ec \uac1c \uc874\uc7ac\ud55c\ub2e4\uba74 \uc544\ubb34\uac70\ub098 \ucd9c\ub825\ud574\ub3c4 \uc0c1\uad00\uc5c6\ub2e4.<\/p>\r\n","hint":"<p>\uc5b4\ub5a4 \ub9e4\uce6d\uc5d0 \ub300\ud574, \uc5b4\ub5a4 \uc5f0\uacb0\ub418\uc9c0 <strong>\ubabb\ud55c<\/strong> \ub450 \ud559\uc0dd\uc758 \uc30d $(i, j)$\uac00 \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\ud560 \ub54c <strong>unstable<\/strong>\ud558\ub2e4\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>$i$\ub294 \uadf8\uc758 \ud30c\ud2b8\ub108\ubcf4\ub2e4 $j$\ub97c \ub354 \uc120\ud638\ud55c\ub2e4.<\/li>\r\n\t<li>$j$\ub294 \uadf8\uc758 \ud30c\ud2b8\ub108\ubcf4\ub2e4 $i$\ub97c \ub354 \uc120\ud638\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p><strong>Stable matching<\/strong>\uc774\ub780 <strong>unstable<\/strong>\ud55c \uc30d\uc774 \uc5c6\ub294 \ub9e4\uce6d\uc744 \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$1 \\leq N \\leq 20$<\/li>\r\n<\/ul>\r\n"},{"problem_id":"27985","problem_lang":"1","title":"Mentoring Matching","description":"<p>In KSA, many students want help from seniors who have already graduated. Fortunately, there are also many graduates from KAIST who want to help KSA students. Therefore, Eunha will make a mentoring matching system that connects seniors and juniors so that juniors can get help.<\/p>\r\n\r\n<p>This matching system works as follows: $N$ KSA students and $N$ KAIST students registered in the system match one-to-one. Each KSA and KAIST students have student numbers from $1$ to $N$.<\/p>\r\n\r\n<p>Each of the $N$ KSA students is matched with one KAIST student. No two KSA students are matched with the same KAIST student. Additionally, they have all set preferences for $N$ KAIST seniors. There are no cases of the same preference.<\/p>\r\n\r\n<p>However, KAIST students are tooooooo&nbsp;tired of their homework, so they only choose their preferences for KSA students based on their student number. Precisely, the larger their student number differs from the corresponding KSA student&#39;s number, the more they prefer that student. Also, all KAIST students prefer the KSA student with a smaller student number&nbsp;if all the other conditions are the same.<\/p>\r\n\r\n<p>Eunha hopes to achieve <strong>stable matching<\/strong>. However, she is very busy with tasks such as homework, studying for exams, building in Minecraft, and playing rhythm games. Help her to find stable matching!<\/p>\r\n","input":"<p>The first line contains an integer $N$.<\/p>\r\n\r\n<p>The next $N$ lines contains $N$ integers each, from $1$ to $N$. If the $k$-th integer on the $i+1$-th line is $j$, it means that KAIST student $j$ is the $k$-th most preferred student by KSA student $i$.<\/p>\r\n","output":"<p>Print $N$ integers on the first line. If the $i$-th integer is $j$, KSA student $i$ and KAIST student $j$ are matched.<\/p>\r\n\r\n<p>If there are multiple solutions, print any of them.&nbsp;<\/p>\r\n","hint":"<p>Given a matching, an unmatched pair of students $(i, j)$ is called <strong>unstable<\/strong>&nbsp;if:<\/p>\r\n\r\n<ul>\r\n\t<li>$i$ prefers $j$ to its assigned partner.<\/li>\r\n\t<li>$j$ prefers $i$ to its assigned partner.<\/li>\r\n<\/ul>\r\n\r\n<p><strong>Stable matching<\/strong>&nbsp;is matching with no unstable pairs.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$1 \\leq N \\leq 20$<\/li>\r\n<\/ul>\r\n"}]

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School > 한국과학영재학교 > 2022 Fall CS2 Final Mock Exam D번

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