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문제

고대의 보물이 묻힌 동굴이 발견되었다.

보물의 가치는 어마어마해서 한 번 탐사하는 데 성공하면 세계 최고의 부자가 될 수 있을 만했다.

한 운 좋은 고고학 회사가 탐사의 전반적인 작업을 모두 맡게 되었다.

당신은 그 회사의 인턴으로 참여중이다.

지금까지의 작업 진척도는 다음과 같다.

  • 가영은 두 명의 프로젝트 총괄자 중 하나이며, 보석 감정의 대가이다. 가영이는 탐사할 동굴에 묻힌 모든 보물의 가치를 정리하는 데 성공했다.
  • 나희도 가영과 같은 프로젝트 총괄자이다. 나희는 모든 보물의 가치를 시장가치와 탐사 비용을 고려하여 동굴 하나당 어느 정도의 수익을 얻을 수 있을지 수치화하여 정리하였다.
  • 다미는 프로젝트 매니저의 자격으로 참가하였다. 다미는 동굴 탐사에 필요할 만한 모든 장비를 자체적인 판단에 따라 주문하였다. 하지만 탐사대원들과의 소통이 부족했던 탓에 다미가 주문한 탐사 기기 중 일부는 동굴에 들어갈 수 없을 정도로 커서 탐사 작업에 동원될 수가 없었다.
  • 그런 이유로 다미는 해고되었고, 라라가 새로 다미의 역할을 맡게 되었다. 라라는 다미가 주문했던 기기들이 탐사 작업에 동원될 수 있을 만큼 동굴을 넓힐 수 있는 장치들을 주문하였다. 그리고 탐사 작업이 끝난 후 탐사에 동원된 장비들을 회수할 추가적인 장비를 주문하는 것을 회사의 예산으로 해결할 수 있는지를 예산 총괄자에게 물어보았다.
  • 마리는 예산 총괄자이다. 마리는 라라가 장비를 끌어올릴 추가적인 장비를 회사의 예산으로 구매하는 데 반대하였고, 이것은 라라가 추가적인 장비를 도입하지 않기로 결정하는 데 큰 공헌을 하였다.
  • 여덟 시간에 걸친 기나긴 회의 끝에, 회사의 예산으로는 더 이상의 장비를 도입할 수 없을 것이라는 분석이 나왔다. 그래서 우선적으로 나희가 수치화한 이익에 따라 가장 많은 이익을 낼 동굴만을 탐사하고, 그 과정에 도입된 장비들은 그냥 동굴 안에 묻힌 채 버려두고 그 상태로 탐사권을 다른 회사에 팔기로 하였다.
  • 탐사권을 다른 회사에 판매하기 위해 경제학 전공의 바다가 고용되었다. 바다는 탐사 작업이 끝난 후 거래 전문가이자 바다의 언니인 사랑이와 상의해서 최대의 가치로 탐사권을 다른 회사에 판매할 예정이다.

당신은 프로젝트 매니저 가영이가 프로젝트 초창기에 고용한 기술자이다. 당신은 이제 나희가 수치화한 이익 수치에 따라 어느 동굴들을 탐사하는 것이 최대의 이익이 될 지 계산해야 한다. 동굴을 넓히거나 동굴을 탐사하는 데 드는 추가적인 비용은 이미 다미와 라라에 의해 계산되어 있다. 이를 모두 고려하여 각 동굴마다 얻을 수 있는 최대의 이익이 각 동굴마다 수치화되어 주어질 것이다. 동굴의 지도는 아영이를 리더로 한 탐사대원들에 의해 이미 완성되어 있기 때문에 정확도는 100%에 달한다.

이제 순차적으로 탐사할 수 있는 순서대로 한 동굴에서 얻을 수 있는 손실과 이득을 계산하여 종합한 이익 표가 당신에게 주어진다. 처음으로 탐사해야만 하는, 입구의 역할을 하는 동굴은 항상 첫 번째 동굴이며, 다른 동굴들은 주어진 순서대로만 탐사할 수 있다. 어떤 동굴에서 탐사를 끝낸 뒤 이전 동굴로 장비를 다시 돌려놓는 데 필요한 추가적인 장비는 마리의 결정에 의해 도입하지 않기로 하였기에, 한 번 동굴에 입장하면 이제 그 동굴보다 깊이 있으며 서로 직접 연결된 동굴들로만 탐사를 진행할 수 있다.

모든 동굴은 첫 번째 동굴에서 도달 가능하다.

입력

입력의 첫 줄엔 테스트 케이스의 수 T가 주어진다. (1 ≤ T ≤ 10)

각 테스트 케이스의 첫 줄엔 탐사할 수 있는 동굴의 수 N과 서로 직접 연결된 동굴 쌍의 수 E가 주어진다. (1 ≤ N ≤ 2 · 10 4; 0 ≤ E ≤ 105)

그리고 바로 다음 줄에 N개의 정수 v 1, v2, ... , vN이 주어진다. 이는 각 동굴을 탐사해서 얻을 수 있는 보물의 가치를 수치화한 것이다. (0 ≤ vi ≤ 104)

이후 E줄에 걸쳐 세 정수 a e be ce가 주어진다. 이는 동굴 ae가 be와 직접 연결되어 있으며, 동굴을 넓히고 작업 장비를 be에 들여놓는 데에 ce만큼의 작업 비용이 든다는 것을 의미한다. (1 ≤ ae, be ≤ N; 0 ≤ ce ≤ 104)

항상 탐사의 시작은 1번 동굴이다. 1번 동굴을 탐사하지 않고서는 다른 동굴에 입장하는 것이 불가능하다.

동굴 be가 ae보다 깊이 있는 경우로만 입력이 주어진다.

출력

각 테스트 케이스마다 두 줄을 출력한다.

첫 줄엔 동굴을 탐사함으로써 얻을 수 있는 최대 이익과 그 때 방문한 동굴의 수를 출력하고,

두 번째 줄엔 그 이익을 얻을 수 있는 경로를 방문 순으로 출력한다.

이때, 그 이익을 얻을 수 있는 경로가 여러 개라면 아무 것이나 출력하면 된다.

예제 입력 1

3
1 0
10
4 3
10 20 30 40
1 2 19
1 3 23
1 4 34
4 4
10 20 30 40
1 2 10
2 4 20
1 3 20
3 4 10

예제 출력 1

10 1
1
17 2
1 3
50 3
1 3 4
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\uc804\ubb38\uac00\uc774\uc790 \ubc14\ub2e4\uc758 \uc5b8\ub2c8\uc778 \uc0ac\ub791\uc774\uc640 \uc0c1\uc758\ud574\uc11c \ucd5c\ub300\uc758 \uac00\uce58\ub85c \ud0d0\uc0ac\uad8c\uc744 \ub2e4\ub978 \ud68c\uc0ac\uc5d0 \ud310\ub9e4\ud560 \uc608\uc815\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ub2f9\uc2e0\uc740 \ud504\ub85c\uc81d\ud2b8 \ub9e4\ub2c8\uc800 \uac00\uc601\uc774\uac00 \ud504\ub85c\uc81d\ud2b8 \ucd08\ucc3d\uae30\uc5d0 \uace0\uc6a9\ud55c \uae30\uc220\uc790\uc774\ub2e4. \ub2f9\uc2e0\uc740 \uc774\uc81c \ub098\ud76c\uac00 \uc218\uce58\ud654\ud55c \uc774\uc775 \uc218\uce58\uc5d0 \ub530\ub77c \uc5b4\ub290 \ub3d9\uad74\ub4e4\uc744 \ud0d0\uc0ac\ud558\ub294 \uac83\uc774 \ucd5c\ub300\uc758 \uc774\uc775\uc774 \ub420 \uc9c0 \uacc4\uc0b0\ud574\uc57c \ud55c\ub2e4. \ub3d9\uad74\uc744 \ub113\ud788\uac70\ub098 \ub3d9\uad74\uc744 \ud0d0\uc0ac\ud558\ub294 \ub370 \ub4dc\ub294 \ucd94\uac00\uc801\uc778 \ube44\uc6a9\uc740 \uc774\ubbf8 \ub2e4\ubbf8\uc640 \ub77c\ub77c\uc5d0 \uc758\ud574 \uacc4\uc0b0\ub418\uc5b4 \uc788\ub2e4. \uc774\ub97c \ubaa8\ub450 \uace0\ub824\ud558\uc5ec \uac01 \ub3d9\uad74\ub9c8\ub2e4 \uc5bb\uc744 \uc218 \uc788\ub294 \ucd5c\ub300\uc758 \uc774\uc775\uc774 \uac01 \ub3d9\uad74\ub9c8\ub2e4 \uc218\uce58\ud654\ub418\uc5b4 \uc8fc\uc5b4\uc9c8 \uac83\uc774\ub2e4. \ub3d9\uad74\uc758 \uc9c0\ub3c4\ub294 \uc544\uc601\uc774\ub97c \ub9ac\ub354\ub85c \ud55c \ud0d0\uc0ac\ub300\uc6d0\ub4e4\uc5d0 \uc758\ud574 \uc774\ubbf8 \uc644\uc131\ub418\uc5b4 \uc788\uae30 \ub54c\ubb38\uc5d0 \uc815\ud655\ub3c4\ub294 100%\uc5d0 \ub2ec\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc774\uc81c \uc21c\ucc28\uc801\uc73c\ub85c \ud0d0\uc0ac\ud560 \uc218 \uc788\ub294 \uc21c\uc11c\ub300\ub85c \ud55c \ub3d9\uad74\uc5d0\uc11c \uc5bb\uc744 \uc218 \uc788\ub294 \uc190\uc2e4\uacfc \uc774\ub4dd\uc744 \uacc4\uc0b0\ud558\uc5ec \uc885\ud569\ud55c \uc774\uc775 \ud45c\uac00 \ub2f9\uc2e0\uc5d0\uac8c \uc8fc\uc5b4\uc9c4\ub2e4. \ucc98\uc74c\uc73c\ub85c \ud0d0\uc0ac\ud574\uc57c\ub9cc \ud558\ub294, \uc785\uad6c\uc758 \uc5ed\ud560\uc744 \ud558\ub294 \ub3d9\uad74\uc740 \ud56d\uc0c1 \uccab \ubc88\uc9f8 \ub3d9\uad74\uc774\uba70, \ub2e4\ub978 \ub3d9\uad74\ub4e4\uc740 \uc8fc\uc5b4\uc9c4 \uc21c\uc11c\ub300\ub85c\ub9cc \ud0d0\uc0ac\ud560 \uc218 \uc788\ub2e4. \uc5b4\ub5a4 \ub3d9\uad74\uc5d0\uc11c \ud0d0\uc0ac\ub97c \ub05d\ub0b8 \ub4a4 \uc774\uc804 \ub3d9\uad74\ub85c \uc7a5\ube44\ub97c \ub2e4\uc2dc \ub3cc\ub824\ub193\ub294 \ub370 \ud544\uc694\ud55c \ucd94\uac00\uc801\uc778 \uc7a5\ube44\ub294 \ub9c8\ub9ac\uc758 \uacb0\uc815\uc5d0 \uc758\ud574 \ub3c4\uc785\ud558\uc9c0 \uc54a\uae30\ub85c \ud558\uc600\uae30\uc5d0, \ud55c \ubc88 \ub3d9\uad74\uc5d0 \uc785\uc7a5\ud558\uba74 \uc774\uc81c \uadf8 \ub3d9\uad74\ubcf4\ub2e4 \uae4a\uc774 \uc788\uc73c\uba70 \uc11c\ub85c \uc9c1\uc811 \uc5f0\uacb0\ub41c \ub3d9\uad74\ub4e4\ub85c\ub9cc \ud0d0\uc0ac\ub97c \uc9c4\ud589\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \ub3d9\uad74\uc740 \uccab \ubc88\uc9f8 \ub3d9\uad74\uc5d0\uc11c \ub3c4\ub2ec \uac00\ub2a5\ud558\ub2e4.<\/p>\r\n","input":"<p>\uc785\ub825\uc758 \uccab \uc904\uc5d4 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; T &le; 10)<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab \uc904\uc5d4 \ud0d0\uc0ac\ud560 \uc218 \uc788\ub294 \ub3d9\uad74\uc758 \uc218 N\uacfc \uc11c\ub85c \uc9c1\uc811 \uc5f0\uacb0\ub41c \ub3d9\uad74 \uc30d\uc758 \uc218 E\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; N &le; 2 &middot; 10 <sup>4<\/sup>; 0 &le; E &le; 10<sup>5<\/sup>)<\/p>\r\n\r\n<p>\uadf8\ub9ac\uace0 \ubc14\ub85c \ub2e4\uc74c \uc904\uc5d0 N\uac1c\uc758 \uc815\uc218 v <sub>1<\/sub>, v<sub>2<\/sub>, ... , v<sub>N<\/sub>\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub294 \uac01 \ub3d9\uad74\uc744 \ud0d0\uc0ac\ud574\uc11c \uc5bb\uc744 \uc218 \uc788\ub294 \ubcf4\ubb3c\uc758 \uac00\uce58\ub97c \uc218\uce58\ud654\ud55c \uac83\uc774\ub2e4. (0 &le; v<sub>i<\/sub> &le; 10<sup>4<\/sup>)<\/p>\r\n\r\n<p>\uc774\ud6c4 E\uc904\uc5d0 \uac78\uccd0 \uc138 \uc815\uc218 a <sub>e<\/sub> b<sub>e<\/sub> c<sub>e<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub294 \ub3d9\uad74 a<sub>e<\/sub>\uac00 b<sub>e<\/sub>\uc640 \uc9c1\uc811 \uc5f0\uacb0\ub418\uc5b4 \uc788\uc73c\uba70, \ub3d9\uad74\uc744 \ub113\ud788\uace0 \uc791\uc5c5 \uc7a5\ube44\ub97c b<sub>e<\/sub>\uc5d0 \ub4e4\uc5ec\ub193\ub294 \ub370\uc5d0 c<sub>e<\/sub>\ub9cc\ud07c\uc758 \uc791\uc5c5 \ube44\uc6a9\uc774 \ub4e0\ub2e4\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4. (1 &le; a<sub>e<\/sub>, b<sub>e<\/sub> &le; N; 0 &le; c<sub>e<\/sub> &le; 10<sup>4<\/sup>)<\/p>\r\n\r\n<p>\ud56d\uc0c1 \ud0d0\uc0ac\uc758 \uc2dc\uc791\uc740 1\ubc88 \ub3d9\uad74\uc774\ub2e4. 1\ubc88 \ub3d9\uad74\uc744 \ud0d0\uc0ac\ud558\uc9c0 \uc54a\uace0\uc11c\ub294 \ub2e4\ub978 \ub3d9\uad74\uc5d0 \uc785\uc7a5\ud558\ub294 \uac83\uc774 \ubd88\uac00\ub2a5\ud558\ub2e4.<\/p>\r\n\r\n<p>\ub3d9\uad74 b<sub>e<\/sub>\uac00 a<sub>e<\/sub>\ubcf4\ub2e4 \uae4a\uc774 \uc788\ub294 \uacbd\uc6b0\ub85c\ub9cc \uc785\ub825\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \ub450 \uc904\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uccab \uc904\uc5d4 \ub3d9\uad74\uc744 \ud0d0\uc0ac\ud568\uc73c\ub85c\uc368 \uc5bb\uc744 \uc218 \uc788\ub294 \ucd5c\ub300 \uc774\uc775\uacfc \uadf8 \ub54c \ubc29\ubb38\ud55c \ub3d9\uad74\uc758 \uc218\ub97c \ucd9c\ub825\ud558\uace0,<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d4 \uadf8 \uc774\uc775\uc744 \uc5bb\uc744 \uc218 \uc788\ub294 \uacbd\ub85c\ub97c \ubc29\ubb38 \uc21c\uc73c\ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc774\ub54c, \uadf8 \uc774\uc775\uc744 \uc5bb\uc744 \uc218 \uc788\ub294 \uacbd\ub85c\uac00 \uc5ec\ub7ec \uac1c\ub77c\uba74 \uc544\ubb34 \uac83\uc774\ub098 \ucd9c\ub825\ud558\uba74 \ub41c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"10273","problem_lang":"1","title":"Connected Caves","description":"<p>You&rsquo;re an intern at Greedy Cave Plundering Corporation. Your new job is to help with one of GCPC &rsquo;s projects: extracting valuable gemstones from a network of connected caves.<\/p>\r\n\r\n<p>The history of the project so far:<\/p>\r\n\r\n<ul>\r\n\t<li>Tom, one of the project managers, has hired Jill, a gemstone expert. She has already surveyed these caves and determined the value of all gemstones in each cave.<\/li>\r\n\t<li>Ruby, another project manager (PM), has been busy &ldquo;guesstimating&rdquo; a time frame, the budget and possible profits for this project.<\/li>\r\n\t<li>Evelyn and Jerry (also PMs) have hired two cave diggers and instructed them to extract thegemstones.<\/li>\r\n\t<li>The cave diggers needed equipment to extract the gemstones and transport them to the surface. So Jimmy (another PM) ordered some machines. Sadly, he did not communicate well with the cave diggers - he bought machines that are way too big for the current passage ways between caves.<\/li>\r\n\t<li>To fix this, Jimmy was fired and James, his successor, has ordered a very big drilling machine, so the cave diggers can widen the passage ways. However, James was fearful of cutting into his salary bonus, so he bought the cheapest machine he could find. Soon, after widening the passage way from the surface into cave 1, the cave diggers found out that the new drilling machine is very heavy and not so powerful, so it can only be used to widen a passage way that goes downwards. Once it has reached a lower cave, it can not be carried back up because of its weight.<\/li>\r\n\t<li>This is when Alice, the project manager in charge of budget planning, announced she would ignore further requests for more equipment.<\/li>\r\n\t<li>In an eight hour meeting discussing the problems of the project, it was decided to limit the project expenses. So, if further drilling would hurt profits or if the drilling machine reaches a cave where it can not go on, it will just be abandoned. Using the other machines, the cave diggers will then be able to harvest at least some of the gemstones. Afterwards, the dig site will probably be sold to another company. Ruby is already thinking about hiring her brother as a sales expert...<\/li>\r\n<\/ul>\r\n\r\n<p>This is where you come in. Tom has hired you to determine which passage ways should be widened and thereby which caves should be visited to maximize profits. Widening a passage way requires energy, materials and so on. You have to consider these costs. You will be given a map of all caves and passage ways. The map was created by the cave diggers, so it should be accurate. It contains only passage ways the drilling machine can handle, including the correct drilling direction. All caves in the map are reachable from cave one.<\/p>\r\n","input":"<p>The input starts with a line containing T, the number of test cases (1 &le; T &le; 10).<\/p>\r\n\r\n<p>Each test case starts with a line containing two integers: N, the number of caves, and E, the number of passage ways (1 &le; N &le; 2 &middot; 10<sup>4<\/sup>; 0 &le; E &le; 10<sup>5<\/sup>).<\/p>\r\n\r\n<p>The second line contains N integers v<sub>1<\/sub> v<sub>2<\/sub> . . . v<sub>N<\/sub> . v<sub>i<\/sub> describes the value of all gemstones in cave i (0 &le; v<sub>i<\/sub> &le; 104).<\/p>\r\n\r\n<p>Each of the next E lines contains three integers: a<sub>e<\/sub> b<sub>e<\/sub> c<sub>e<\/sub>. Such a line represents one of the possible direct passage ways from cave a<sub>e<\/sub> to cave b<sub>e<\/sub>, widening this passage way will cost c<sub>e<\/sub> (1 &le; a<sub>e<\/sub>, b<sub>e<\/sub> &le; N; 0 &le; c<sub>e<\/sub> &le; 10<sup>4<\/sup>). It is guaranteed that the input contains only valid digging directions, i.e. cave b<sub>e<\/sub> will be strictly deeper than a<sub>e<\/sub>.<\/p>\r\n\r\n<p>You always start from cave number 1, because the digging machine is already there and there are no caves above.<\/p>\r\n","output":"<p>Output two lines for every test case. In the first line print two integers P and C, where P is the profit of the best possible route from top to bottom and C is the number of visited caves on that path. In the second line print the IDs of those caves, ordered from top to bottom.<\/p>\r\n\r\n<p>If there are multiple solutions with optimal profit, print any.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

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ICPC > Regionals > Europe > Northwestern European Regional Contest > German Collegiate Programming Contest > GCPC 2014 D번