시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 127 48 27 44.262%

문제

사람들은 민혁이가 9999번 문제를 풀 수 있다와 없다를 가지고 투표를 진행하려고 한다. 사람들은 보통 자신의 생각대로 투표하지만, 가끔 자신의 친구와 의견이 충돌되는 것을 막기 위해서 자신의 생각과 반대로 투표하는 경우도 있다.

민혁이가 9999번 문제를 풀 수 있다고 생각한 사람과 없다고 생각한 사람의 목록이 주어지고, 사람들 사이의 친구 관계가 입력으로 주어진다. 

친구 사이에 투표한 결과가 서로 다른 관계의 수와 자신의 생각과 반대로 투표를 해야 하는 사람 수의 합을 최소로 하기 위해서 각 사람들이 어떻게 투표를 해야 하는지 구하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다.

각 테스트 케이스의 첫째 줄에는 사람의 수 N과 친구 관계의 수 M이 주어진다. (2 ≤ N ≤ 300, 1 ≤ M ≤ N(N-1)/2)

둘째 줄에는 각 사람의 생각을 나타내는 N개의 수가 주어진다. 1은 민혁이가 9999번 문제를 풀 수 있다고 생각한 사람, 0은 없다고 생각한 사람이다. 정보는 1번사람부터 순서대로 주어진다.

다음 M개의 줄에는 친구 관계인 두 사람의 번호가 주어진다. 사람은 1번부터 N번까지 번호가 매겨져 있다.

입력의 마지막 줄에는 N = M = 0이며, 이 경우는 처리하지 않아야 한다.

출력

각 테스트 케이스 마다, 친구 사이에 투표한 결과가 서로 다른 관계의 수와 자신의 생각과 반대로 투표를 해야 하는 사람 수의 합의 최솟값을 출력한다.

예제 입력 1

3 3
1 0 0
1 2
1 3
3 2
6 6
1 1 1 0 0 0
1 2
2 3
4 2
3 5
4 5
5 6
0 0

예제 출력 1

1
2

힌트

첫째 테스트 케이스의 경우에 첫 번째 사람이 자신의 생각과 반대로 투표를 하면 되며, 두 번째 경우에는 자신의 생각대로 투표를 하면 된다.

[{"problem_id":"9169","problem_lang":"0","title":"\ub098\ub294 9999\ubc88 \ubb38\uc81c\ub97c \ud480 \uc218 \uc788\ub2e4","description":"<p>\uc0ac\ub78c\ub4e4\uc740 \ubbfc\ud601\uc774\uac00 <a href=\"https:\/\/www.acmicpc.net\/problem\/9999\">9999\ubc88 \ubb38\uc81c<\/a>\ub97c \ud480 \uc218 \uc788\ub2e4\uc640 \uc5c6\ub2e4\ub97c \uac00\uc9c0\uace0 \ud22c\ud45c\ub97c \uc9c4\ud589\ud558\ub824\uace0 \ud55c\ub2e4. \uc0ac\ub78c\ub4e4\uc740 \ubcf4\ud1b5 \uc790\uc2e0\uc758 \uc0dd\uac01\ub300\ub85c \ud22c\ud45c\ud558\uc9c0\ub9cc, \uac00\ub054 \uc790\uc2e0\uc758 \uce5c\uad6c\uc640 \uc758\uacac\uc774 \ucda9\ub3cc\ub418\ub294 \uac83\uc744 \ub9c9\uae30 \uc704\ud574\uc11c \uc790\uc2e0\uc758 \uc0dd\uac01\uacfc \ubc18\ub300\ub85c&nbsp;\ud22c\ud45c\ud558\ub294 \uacbd\uc6b0\ub3c4 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ubbfc\ud601\uc774\uac00 9999\ubc88 \ubb38\uc81c\ub97c \ud480 \uc218 \uc788\ub2e4\uace0 \uc0dd\uac01\ud55c \uc0ac\ub78c\uacfc \uc5c6\ub2e4\uace0 \uc0dd\uac01\ud55c \uc0ac\ub78c\uc758 \ubaa9\ub85d\uc774 \uc8fc\uc5b4\uc9c0\uace0, \uc0ac\ub78c\ub4e4 \uc0ac\uc774\uc758 \uce5c\uad6c \uad00\uacc4\uac00 \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\uce5c\uad6c \uc0ac\uc774\uc5d0 \ud22c\ud45c\ud55c \uacb0\uacfc\uac00 \uc11c\ub85c \ub2e4\ub978 \uad00\uacc4\uc758 \uc218\uc640 \uc790\uc2e0\uc758 \uc0dd\uac01\uacfc \ubc18\ub300\ub85c \ud22c\ud45c\ub97c \ud574\uc57c \ud558\ub294 \uc0ac\ub78c \uc218\uc758 \ud569\uc744&nbsp;\ucd5c\uc18c\ub85c \ud558\uae30 \uc704\ud574\uc11c \uac01 \uc0ac\ub78c\ub4e4\uc774 \uc5b4\ub5bb\uac8c \ud22c\ud45c\ub97c \ud574\uc57c \ud558\ub294\uc9c0&nbsp;\uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uc785\ub825\uc740&nbsp;\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 \uc0ac\ub78c\uc758 \uc218 N\uacfc \uce5c\uad6c \uad00\uacc4\uc758 \uc218 M\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (2 &le; N &le; 300, 1 &le; M &le; N(N-1)\/2)<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0\ub294 \uac01 \uc0ac\ub78c\uc758 \uc0dd\uac01\uc744 \ub098\ud0c0\ub0b4\ub294 N\uac1c\uc758 \uc218\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. 1\uc740 \ubbfc\ud601\uc774\uac00 9999\ubc88 \ubb38\uc81c\ub97c \ud480 \uc218 \uc788\ub2e4\uace0 \uc0dd\uac01\ud55c \uc0ac\ub78c, 0\uc740 \uc5c6\ub2e4\uace0 \uc0dd\uac01\ud55c \uc0ac\ub78c\uc774\ub2e4. \uc815\ubcf4\ub294 1\ubc88\uc0ac\ub78c\ubd80\ud130 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c M\uac1c\uc758 \uc904\uc5d0\ub294 \uce5c\uad6c \uad00\uacc4\uc778 \ub450 \uc0ac\ub78c\uc758 \ubc88\ud638\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc0ac\ub78c\uc740 1\ubc88\ubd80\ud130 N\ubc88\uae4c\uc9c0 \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 N = M = 0\uc774\uba70, \uc774 \uacbd\uc6b0\ub294 \ucc98\ub9ac\ud558\uc9c0 \uc54a\uc544\uc57c \ud55c\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ub9c8\ub2e4,&nbsp;\uce5c\uad6c \uc0ac\uc774\uc5d0 \ud22c\ud45c\ud55c \uacb0\uacfc\uac00 \uc11c\ub85c \ub2e4\ub978 \uad00\uacc4\uc758 \uc218\uc640 \uc790\uc2e0\uc758 \uc0dd\uac01\uacfc \ubc18\ub300\ub85c \ud22c\ud45c\ub97c \ud574\uc57c \ud558\ub294 \uc0ac\ub78c \uc218\uc758 \ud569\uc758 \ucd5c\uc19f\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uccab\uc9f8 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uacbd\uc6b0\uc5d0 \uccab \ubc88\uc9f8 \uc0ac\ub78c\uc774 \uc790\uc2e0\uc758 \uc0dd\uac01\uacfc&nbsp;\ubc18\ub300\ub85c \ud22c\ud45c\ub97c \ud558\uba74 \ub418\uba70, \ub450 \ubc88\uc9f8 \uacbd\uc6b0\uc5d0\ub294 \uc790\uc2e0\uc758 \uc0dd\uac01\ub300\ub85c \ud22c\ud45c\ub97c \ud558\uba74 \ub41c\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9169","problem_lang":"1","title":"Coconuts","description":"<p>A group of n castle guards are voting to determine whether African swallows can carry coconuts. While each guard has his own personal opinion on the matter, a guard will often vote contrary to his beliefs in order to avoid disagreeing with the votes of his friends.<\/p>\r\n\r\n<p>You are given a list of guards who either do or do not believe in the coconut-carrying capacity of African swallows, and a list of all pairs of guards who are friends. Your task is to determine how each guard must vote in order to minimize the sum of the total number of disagreements between friends and the total number of guards who must vote against their own beliefs.<\/p>\r\n","input":"<p>The input to this problem will contain multiple test cases. Each test case begins with a single line containing an integer n (where 2 &le; n &le; 300), the number of guards, and an integer m (where 1 &le; m &le; n(n-1)\/2), the number of pairs of guards who are friends. The second line of the test case contains n integers, where the ith integer is 1 if the ith guard believes in the ability of African swallows to carry coconuts, and 0 otherwise. Finally, the next m lines of the test case each contain two distinct integers i and j (where 1 &le; i, j &le; n), indicating that guards i and j are friends. Guards within each pair of friends may be listed in any order, but no pair of guards will be repeated. The input is terminated by an invalid test case with n = m = 0, which should not be processed.<\/p>\r\n","output":"<p>For each input test case, print a single line containing the minimum possible sum of the total number of disagreements between all friends plus the total number of guards who must vote against their own beliefs.<\/p>\r\n","hint":"<p>In the first test case, the best result is achieved when all guards vote that African swallows cannot carry coconuts. Here, there is only a penalty of 1 for the first guard voting against his beliefs.<\/p>\r\n\r\n<p>In the second test case, the best result is achieved when each guard votes for his beliefs. The penalty of 2 arises from the disagreements between guards 2 and 4, and guards 3 and 5.<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]