시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
4 초 256 MB 49 22 16 40.000%

문제

사과나라에는 n 개의 도시들이 존재하며, 이 중 k 개의 도시는 국왕 구사과가 자주 방문하는 중요한 도시들이다. 또한 사과나라에는 m 개의 도시와 도시를 잇는 도로가 존재한다. 각각의 도시들은 1~n의 번호가 매겨져 있다.

어느 날 갑자기 사과나라에 폭풍이 몰아쳤다. 이 폭풍은 사과나라 건국 이래 최대 규모의 자연 재해였으며, 이 때문에 모든 도로들은 제 구실을 하지 못하게 되었다. 따라서 사과나라의 대신들은 도시들 간의 교류를 이어나가기 위해 도로들을 재건하기로 결정하였다. 이를 위해, 대신들은 각각의 도로를 재건하는 데 드는 비용을 조사하여 알아내었다.

그러나, 평소 사치와 향락에 찌든 생활을 하던 구사과 때문에 사과나라의 국고는 텅텅 비어버렸고, 이 때문에 모든 도로를 재건할 수는 없었다. 대신들은 일단 급한 대로 모든 중요한 도시가 서로 이어질 수 있도록 (즉, 각각의 중요한 도시들에서 다른 모든 중요한 도시에 도달할 수 있도록) 우선적으로 도로를 재건하고자 한다.

대신들은 세계 최고의 프로그래머인 당신에게 모든 중요한 도시가 서로 이어질 수 있도록 도로를 재건하는 최소 비용을 알아내도록 의뢰하였다. 우매한 사과나라 사람들에게 당신의 실력을 보여 주자.

입력

첫 번째 줄에는 도시의 개수 n, 중요한 도시의 개수 k, 도로의 개수 m이 공백으로 구분되어 주어진다.

두 번째 줄에는 공백으로 구분된 k개의 수들이 주어진다. 이 수들은 1 이상 n 이하의 서로 다른 정수들로, 중요한 도시들의 번호를 나타낸다.

다음 줄부터는 m개의 줄에 걸쳐 각 도로에 대한 정보가 주어진다. 각 줄에는 세 정수 a, b, c가 주어진다. 이는 이 도로가 도시 a와 도시 b를 잇고 있으며, 이 도로를 재건하는 데에 c의 비용이 소모된다는 뜻이다.

모든 도시들이 도로를 통해 연결되어 있음을 가정해도 좋다.

  • 1 ≤ c ≤ 109
  • n ≥ k
  • 2 ≤ k ≤ 5
  • n ≤ 105
  • 1 ≤ m ≤ 2 ⋅ 105

출력

당신은 모든 중요한 도시가 서로 이어질 수 있도록 도로를 재건하는 최소 비용을 하나의 정수로 출력해야 한다.

예제 입력 1

4 3 6
1 3 4
1 2 4
1 3 9
1 4 6
2 3 2
2 4 5
3 4 8

예제 출력 1

11
[{"problem_id":"12752","problem_lang":"0","title":"\ub3c4\uc2dc\ub4e4","description":"<p>\uc0ac\uacfc\ub098\ub77c\uc5d0\ub294 n \uac1c\uc758 \ub3c4\uc2dc\ub4e4\uc774 \uc874\uc7ac\ud558\uba70, \uc774 \uc911 k \uac1c\uc758 \ub3c4\uc2dc\ub294 \uad6d\uc655 \uad6c\uc0ac\uacfc\uac00 \uc790\uc8fc \ubc29\ubb38\ud558\ub294 \uc911\uc694\ud55c \ub3c4\uc2dc\ub4e4\uc774\ub2e4. \ub610\ud55c \uc0ac\uacfc\ub098\ub77c\uc5d0\ub294 m \uac1c\uc758 \ub3c4\uc2dc\uc640 \ub3c4\uc2dc\ub97c \uc787\ub294 \ub3c4\ub85c\uac00 \uc874\uc7ac\ud55c\ub2e4. \uac01\uac01\uc758 \ub3c4\uc2dc\ub4e4\uc740 1~n\uc758 \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc5b4\ub290 \ub0a0 \uac11\uc790\uae30 \uc0ac\uacfc\ub098\ub77c\uc5d0 \ud3ed\ud48d\uc774 \ubab0\uc544\ucce4\ub2e4. \uc774 \ud3ed\ud48d\uc740 \uc0ac\uacfc\ub098\ub77c \uac74\uad6d \uc774\ub798 \ucd5c\ub300 \uaddc\ubaa8\uc758 \uc790\uc5f0 \uc7ac\ud574\uc600\uc73c\uba70, \uc774 \ub54c\ubb38\uc5d0 \ubaa8\ub4e0 \ub3c4\ub85c\ub4e4\uc740 \uc81c \uad6c\uc2e4\uc744 \ud558\uc9c0 \ubabb\ud558\uac8c \ub418\uc5c8\ub2e4. \ub530\ub77c\uc11c \uc0ac\uacfc\ub098\ub77c\uc758 \ub300\uc2e0\ub4e4\uc740 \ub3c4\uc2dc\ub4e4 \uac04\uc758 \uad50\ub958\ub97c \uc774\uc5b4\ub098\uac00\uae30 \uc704\ud574 \ub3c4\ub85c\ub4e4\uc744 \uc7ac\uac74\ud558\uae30\ub85c \uacb0\uc815\ud558\uc600\ub2e4. \uc774\ub97c \uc704\ud574, \ub300\uc2e0\ub4e4\uc740 \uac01\uac01\uc758 \ub3c4\ub85c\ub97c \uc7ac\uac74\ud558\ub294 \ub370 \ub4dc\ub294 \ube44\uc6a9\uc744 \uc870\uc0ac\ud558\uc5ec \uc54c\uc544\ub0b4\uc5c8\ub2e4.<\/p>\r\n\r\n<p>\uadf8\ub7ec\ub098, \ud3c9\uc18c \uc0ac\uce58\uc640 \ud5a5\ub77d\uc5d0 \ucc0c\ub4e0 \uc0dd\ud65c\uc744 \ud558\ub358 \uad6c\uc0ac\uacfc \ub54c\ubb38\uc5d0 \uc0ac\uacfc\ub098\ub77c\uc758 \uad6d\uace0\ub294 \ud145\ud145 \ube44\uc5b4\ubc84\ub838\uace0, \uc774 \ub54c\ubb38\uc5d0 \ubaa8\ub4e0 \ub3c4\ub85c\ub97c \uc7ac\uac74\ud560 \uc218\ub294 \uc5c6\uc5c8\ub2e4. \ub300\uc2e0\ub4e4\uc740 \uc77c\ub2e8 \uae09\ud55c \ub300\ub85c <strong>\ubaa8\ub4e0 \uc911\uc694\ud55c \ub3c4\uc2dc\uac00 \uc11c\ub85c \uc774\uc5b4\uc9c8 \uc218 \uc788\ub3c4\ub85d <\/strong>(\uc989, \uac01\uac01\uc758 \uc911\uc694\ud55c \ub3c4\uc2dc\ub4e4\uc5d0\uc11c \ub2e4\ub978 \ubaa8\ub4e0 \uc911\uc694\ud55c \ub3c4\uc2dc\uc5d0 \ub3c4\ub2ec\ud560 \uc218 \uc788\ub3c4\ub85d) \uc6b0\uc120\uc801\uc73c\ub85c \ub3c4\ub85c\ub97c \uc7ac\uac74\ud558\uace0\uc790 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub300\uc2e0\ub4e4\uc740 \uc138\uacc4 \ucd5c\uace0\uc758 \ud504\ub85c\uadf8\ub798\uba38\uc778 \ub2f9\uc2e0\uc5d0\uac8c <strong>\ubaa8\ub4e0 \uc911\uc694\ud55c \ub3c4\uc2dc\uac00 \uc11c\ub85c \uc774\uc5b4\uc9c8 \uc218 \uc788\ub3c4\ub85d \ub3c4\ub85c\ub97c \uc7ac\uac74\ud558\ub294 \ucd5c\uc18c \ube44\uc6a9<\/strong>\uc744 \uc54c\uc544\ub0b4\ub3c4\ub85d \uc758\ub8b0\ud558\uc600\ub2e4. \uc6b0\ub9e4\ud55c \uc0ac\uacfc\ub098\ub77c \uc0ac\ub78c\ub4e4\uc5d0\uac8c \ub2f9\uc2e0\uc758 \uc2e4\ub825\uc744 \ubcf4\uc5ec \uc8fc\uc790.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 \ub3c4\uc2dc\uc758 \uac1c\uc218 n, \uc911\uc694\ud55c \ub3c4\uc2dc\uc758 \uac1c\uc218 k, \ub3c4\ub85c\uc758 \uac1c\uc218 m\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0\ub294 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub41c k\uac1c\uc758 \uc218\ub4e4\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \uc218\ub4e4\uc740 1 \uc774\uc0c1 n \uc774\ud558\uc758 \uc11c\ub85c \ub2e4\ub978 \uc815\uc218\ub4e4\ub85c, \uc911\uc694\ud55c \ub3c4\uc2dc\ub4e4\uc758 \ubc88\ud638\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc904\ubd80\ud130\ub294 m\uac1c\uc758 \uc904\uc5d0 \uac78\uccd0 \uac01 \ub3c4\ub85c\uc5d0 \ub300\ud55c \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \uc904\uc5d0\ub294 \uc138 \uc815\uc218 a, b, c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub294 \uc774 \ub3c4\ub85c\uac00 \ub3c4\uc2dc a\uc640 \ub3c4\uc2dc b\ub97c \uc787\uace0 \uc788\uc73c\uba70, \uc774 \ub3c4\ub85c\ub97c \uc7ac\uac74\ud558\ub294 \ub370\uc5d0 c\uc758 \ube44\uc6a9\uc774 \uc18c\ubaa8\ub41c\ub2e4\ub294 \ub73b\uc774\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \ub3c4\uc2dc\ub4e4\uc774 \ub3c4\ub85c\ub97c \ud1b5\ud574 \uc5f0\uacb0\ub418\uc5b4 \uc788\uc74c\uc744 \uac00\uc815\ud574\ub3c4 \uc88b\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>1 &le; c &le; 10<sup>9<\/sup><\/li>\r\n\t<li>n &ge; k<\/li>\r\n\t<li>2 &le; k &le; 5<\/li>\r\n\t<li>n &le; 10<sup>5<\/sup><\/li>\r\n\t<li>1 &le; m &le; 2 &sdot; 10<sup>5<\/sup><\/li>\r\n<\/ul>\r\n","output":"<p>\ub2f9\uc2e0\uc740 <strong>\ubaa8\ub4e0 \uc911\uc694\ud55c \ub3c4\uc2dc\uac00 \uc11c\ub85c \uc774\uc5b4\uc9c8 \uc218 \uc788\ub3c4\ub85d \ub3c4\ub85c\ub97c \uc7ac\uac74\ud558\ub294 \ucd5c\uc18c \ube44\uc6a9<\/strong>\uc744 \ud558\ub098\uc758 \uc815\uc218\ub85c \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"12752","problem_lang":"1","title":"Cities","description":"<p>There are n cities in Byteland, and k of them are important cities frequently visited by the king of Byteland.<\/p>\r\n\r\n<p>There are also m roads in the country, each of them connecting two cities. Unfortunately, the condition of the roads is so bad that the king cannot drive through them at full speed with his sports car.<\/p>\r\n\r\n<p>For each road, the cost for renovating it is known. Your task is to choose which roads will be renovated so that all k important cities are connected with renovated roads, and the total cost is as low as possible.<\/p>\r\n","input":"<p>The first input line contains three integers n, k and m: the number of cities, the number of important cities and the number of roads. The cities are numbered 1, 2, ..., n. The second input line contains k integers: the important cities.<\/p>\r\n\r\n<p>Finally, the input contains m lines that describe the roads. Each line contains three integers a, b and c, meaning that there is a bidirectional road between cities a and b, and the renovation cost for the road is c.<\/p>\r\n\r\n<p>You may assume that there is a route between any two cities.<\/p>\r\n\r\n<ul>\r\n\t<li>1 &le; c &le; 10<sup>9<\/sup><\/li>\r\n\t<li>n &ge; k<\/li>\r\n\t<li>2 &le; k &le; 5<\/li>\r\n\t<li>n &le; 10<sup>5<\/sup><\/li>\r\n\t<li>1 &le; m &le; 2 &sdot; 10<sup>5<\/sup><\/li>\r\n<\/ul>\r\n","output":"<p>You should output the minimum total cost for renovating the roads so that the king can travel between all important cities with his sports car.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Olympiad > Baltic Olympiad in Informatics > BOI 2016 4번

  • 문제를 번역한 사람: khsoo01