시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 224 45 28 25.688%

문제

성공한 벤쳐회사 "봉씨"의 사장 연종이는 사업을 미국으로 확장하기로 결정했다.

봉씨는 LA에 있는 투자자들을 만나기 위해 미국으로 출발했다. 하지만, 비행기를 내리고 보니 그곳은 LA가 아니었다. 연종이의 비서는 아는 미국 도시가 뉴욕밖에 없었기 때문에, 당연히 사장의 항공편을 뉴욕행으로 예약한 것이다.

연종이는 LA까지 가는 비용을 최대한 줄이려고 한다. 따라서, 그는 비행기를 타는 대신에 차를 빌려서 이동할 것이다.

미국에는 N개의 도시가 있고, 각 도시는 1번부터 N번까지 번호가 매겨져 있다. 또, M개의 도로가 있다. 도로는 두 도시를 연결하며, 한 방향으로만 움직일 수 있다.

뉴욕의 도시 번호는 1번이고, LA의 번호는 2번이다. 

연종이의 회사는 구글을 넘는 가치를 지니고 있기 때문에, 연종이가 방문하는 도시에 경호원을 고용하려고 한다. 이때, 고용해야하는 경호원의 수를 최소화하는 프로그램을 작성하시오. 어떤 도시에서 경호원을 고용하면, 몇 번을 방문하더라도 재고용하지 않아도 된다. 연종이는 뉴욕에서 출발해서 LA를 방문했다가 다시 뉴욕으로 돌아온다.

입력

첫째 줄에는 N과 M이 주어진다. (2 ≤ N ≤ 100, 2 ≤ M ≤ 200)

다음 M개의 줄에는 서로 다른 정수 A와 B가 주어진다. (1 ≤ A, B ≤ N) 이 두 숫자는 도로에 대한 정보이고, A에서 B로 가는 도로라는 뜻이다. 같은 도로가 두 번이상 주어지는 경우는 없지만, 반대 방향 도로(B -> A)가 주어질 수는 있다.

출력

첫재 줄에 뉴욕에서 LA로 갔다가, 다시 뉴욕으로 돌아오는 경로 중 고용해야하는 경호원의 수의 최솟값을 출력한다. 항상 답이 존재하는 경우만 입력으로 주어진다.

예제 입력 1

6 7
1 3
3 4
4 5
5 1
4 2
2 6
6 3

예제 출력 1

6

힌트

다음과 같이 이동하면 된다. 1->3->4->2->6->3->4->5->1

[{"problem_id":"2795","problem_lang":"0","title":"\uc0ac\uc5c5 \ud655\uc7a5","description":"<p>\r\n\t\uc131\uacf5\ud55c \ubca4\uccd0\ud68c\uc0ac &quot;\ubd09\uc528&quot;\uc758 \uc0ac\uc7a5 \uc5f0\uc885\uc774\ub294 \uc0ac\uc5c5\uc744 \ubbf8\uad6d\uc73c\ub85c \ud655\uc7a5\ud558\uae30\ub85c \uacb0\uc815\ud588\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ubd09\uc528\ub294 LA\uc5d0 \uc788\ub294 \ud22c\uc790\uc790\ub4e4\uc744 \ub9cc\ub098\uae30 \uc704\ud574 \ubbf8\uad6d\uc73c\ub85c \ucd9c\ubc1c\ud588\ub2e4. \ud558\uc9c0\ub9cc, \ube44\ud589\uae30\ub97c \ub0b4\ub9ac\uace0 \ubcf4\ub2c8 \uadf8\uacf3\uc740 LA\uac00 \uc544\ub2c8\uc5c8\ub2e4. \uc5f0\uc885\uc774\uc758 \ube44\uc11c\ub294 \uc544\ub294 \ubbf8\uad6d \ub3c4\uc2dc\uac00 \ub274\uc695\ubc16\uc5d0 \uc5c6\uc5c8\uae30 \ub54c\ubb38\uc5d0, \ub2f9\uc5f0\ud788 \uc0ac\uc7a5\uc758 \ud56d\uacf5\ud3b8\uc744 \ub274\uc695\ud589\uc73c\ub85c \uc608\uc57d\ud55c \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uc5f0\uc885\uc774\ub294 LA\uae4c\uc9c0 \uac00\ub294 \ube44\uc6a9\uc744 \ucd5c\ub300\ud55c \uc904\uc774\ub824\uace0 \ud55c\ub2e4. \ub530\ub77c\uc11c, \uadf8\ub294 \ube44\ud589\uae30\ub97c \ud0c0\ub294 \ub300\uc2e0\uc5d0 \ucc28\ub97c \ube4c\ub824\uc11c \uc774\ub3d9\ud560 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ubbf8\uad6d\uc5d0\ub294 N\uac1c\uc758 \ub3c4\uc2dc\uac00 \uc788\uace0, \uac01 \ub3c4\uc2dc\ub294 1\ubc88\ubd80\ud130 N\ubc88\uae4c\uc9c0 \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\ub2e4. \ub610, M\uac1c\uc758 \ub3c4\ub85c\uac00 \uc788\ub2e4. \ub3c4\ub85c\ub294 \ub450 \ub3c4\uc2dc\ub97c \uc5f0\uacb0\ud558\uba70, \ud55c \ubc29\ud5a5\uc73c\ub85c\ub9cc \uc6c0\uc9c1\uc77c \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ub274\uc695\uc758 \ub3c4\uc2dc \ubc88\ud638\ub294 1\ubc88\uc774\uace0, LA\uc758 \ubc88\ud638\ub294 2\ubc88\uc774\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\r\n\t\uc5f0\uc885\uc774\uc758 \ud68c\uc0ac\ub294 \uad6c\uae00\uc744 \ub118\ub294 \uac00\uce58\ub97c \uc9c0\ub2c8\uace0 \uc788\uae30 \ub54c\ubb38\uc5d0, \uc5f0\uc885\uc774\uac00 \ubc29\ubb38\ud558\ub294 \ub3c4\uc2dc\uc5d0 \uacbd\ud638\uc6d0\uc744 \uace0\uc6a9\ud558\ub824\uace0 \ud55c\ub2e4. \uc774\ub54c, \uace0\uc6a9\ud574\uc57c\ud558\ub294 \uacbd\ud638\uc6d0\uc758 \uc218\ub97c \ucd5c\uc18c\ud654\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \uc5b4\ub5a4 \ub3c4\uc2dc\uc5d0\uc11c \uacbd\ud638\uc6d0\uc744 \uace0\uc6a9\ud558\uba74, \uba87 \ubc88\uc744 \ubc29\ubb38\ud558\ub354\ub77c\ub3c4 \uc7ac\uace0\uc6a9\ud558\uc9c0 \uc54a\uc544\ub3c4 \ub41c\ub2e4. \uc5f0\uc885\uc774\ub294 \ub274\uc695\uc5d0\uc11c \ucd9c\ubc1c\ud574\uc11c LA\ub97c \ubc29\ubb38\ud588\ub2e4\uac00 \ub2e4\uc2dc \ub274\uc695\uc73c\ub85c \ub3cc\uc544\uc628\ub2e4.<\/p>\r\n\r\n","input":"<p>\r\n\t\uccab\uc9f8 \uc904\uc5d0\ub294 N\uacfc M\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (2 &le; N &le; 100, 2 &le; M &le; 200)<\/p>\r\n\r\n<p>\r\n\t\ub2e4\uc74c M\uac1c\uc758 \uc904\uc5d0\ub294 \uc11c\ub85c \ub2e4\ub978 \uc815\uc218 A\uc640 B\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; A, B &le; N) \uc774 \ub450 \uc22b\uc790\ub294 \ub3c4\ub85c\uc5d0 \ub300\ud55c \uc815\ubcf4\uc774\uace0, A\uc5d0\uc11c B\ub85c \uac00\ub294 \ub3c4\ub85c\ub77c\ub294 \ub73b\uc774\ub2e4. \uac19\uc740 \ub3c4\ub85c\uac00 \ub450 \ubc88\uc774\uc0c1 \uc8fc\uc5b4\uc9c0\ub294 \uacbd\uc6b0\ub294 \uc5c6\uc9c0\ub9cc, \ubc18\ub300 \ubc29\ud5a5 \ub3c4\ub85c(B -&gt; A)\uac00 \uc8fc\uc5b4\uc9c8 \uc218\ub294 \uc788\ub2e4.<\/p>\r\n","output":"<p>\r\n\t\uccab\uc7ac \uc904\uc5d0 \ub274\uc695\uc5d0\uc11c LA\ub85c \uac14\ub2e4\uac00, \ub2e4\uc2dc \ub274\uc695\uc73c\ub85c \ub3cc\uc544\uc624\ub294 \uacbd\ub85c \uc911 \uace0\uc6a9\ud574\uc57c\ud558\ub294 \uacbd\ud638\uc6d0\uc758 \uc218\uc758 \ucd5c\uc19f\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4. \ud56d\uc0c1 \ub2f5\uc774 \uc874\uc7ac\ud558\ub294 \uacbd\uc6b0\ub9cc \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","hint":"<p>\r\n\t\ub2e4\uc74c\uacfc \uac19\uc774 \uc774\ub3d9\ud558\uba74 \ub41c\ub2e4. 1-&gt;3-&gt;4-&gt;2-&gt;6-&gt;3-&gt;4-&gt;5-&gt;1<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2795","problem_lang":"1","title":"KAMPANJA","description":"<p>The elections are nearing, so President Amabo Kcarab is planning a tour of the States, with speeches in WDC and LA. To provide adequate security, the Secret Service needs to constantly monitor all cities that the President will pass through (including WDC and LA).<\/p>\r\n\r\n<p>Of course, the federal budget needs to be spent responsibly, so the President will not be using AF1, but will be travelling by car. Also, the Secret Service will plan the President&#39;s tour from WDC to LA and back to WDC such that the least possible number of cities needs to be monitored.<\/p>\r\n\r\n<p>For this problem, assume that the States consist of N cities, denoted by numbers from 1 to N, and M unidirectional Interstates, with each Interstate linking two different cities. WDC is city number 1, LA number 2.<\/p>\r\n\r\n<p>Write a program to compute the minimum number of cities that need to be monitored such that there exists a path from WDC to LA and back to WDC passing only through monitored cities.<\/p>\r\n","input":"<p>The first line of input contains the two integers N and M (2 &le; N &le; 100, 2 &le; M &le; 200), the number of cities and the number of Interstates linking the cities, respectively.<\/p>\r\n\r\n<p>Each of the following M lines contains two different integers A, B (1 &le; A, B &le; N), the beginning and ending city served by the given Interstate. No two Interstates link the same two cities in the same direction, but two Interstates can link the same two cities in opposite directions.<\/p>\r\n","output":"<p>The first and only line of output must contain the minimum number of cities that need to be monitored.<\/p>\r\n\r\n<p>Note: Test data will ensure that a solution will always exist.<\/p>\r\n","hint":"<p>The President can take the following route: 1 -&gt; 3 -&gt; 4 -&gt; 2 -&gt; 6 -&gt; 3 -&gt; 4 -&gt; 5 -&gt; 1. Since he needs to pass through each city at least once, the solution is 6.<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]