시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

수라바야 시는 N개의 분기점이 있는데, 0부터 $N - 1$로 번호가 매겨져 있다. 이 분기점들은 $N - 1$개의 양방향 도로로 연결되어 있고, 0부터 $N - 2$로 번호가 매겨져 있다. 서로 다른 두 분기점을 어떻게 고르더라도 이 둘을 잇는 유일한 경로가 있다. 도로 $i$ ($0 \le i \le N - 2$)는 분기점 $U[i]$와 $V[i]$를 연결한다.

환경 문제에 대한 경각심을 높이기 위해서 수라바야 시의 시장 김 박사는 자동차 없는 날을 지정하려고 한다. 자동차 없는 날 행사로, 김 박사는 도로를 폐쇄하려고 한다. 폐쇄할 도로는 다음과 같이 정해진다. 김 박사는 먼저 음이 아닌 정수 $k$를 고르고, 모든 분기점에 $k$개 이하의 폐쇄되지 않은 도로가 직접 연결되어 있도록 한다. 도로 $i$를 폐쇄하는 비용은 $W[i]$이다.

김 박사를 도와서 가능한 음이 아닌 정수 $k$ ($0 \le k \le N - 1$) 각각에 대해 조건을 만족하게 도로를 폐쇄하는 최소 비용을 구하자.

구현

다음 함수를 구현해야 한다.

int64[] minimum_closure_costs(int N, int[] U, int[] V, int[] W)
  • $N$: 수라바야의 분기점 수
  • $U$, $V$ : 길이 $N - 1$인 배열로, 분기점 $U[i]$와 $V[i]$는 도로 $i$로 연결되어 있다.
  • $W$: 길이 $N - 1$인 배열로, $W[i]$는 도로 $i$를 폐쇄하는데 드는 비용이다.
  • 이 함수는 하나의 배열 $N$을 리턴해야 한다. 각각 $k$마다 ($0 \le k \le N - 1$), 이 배열의 $k$번째 원소는 모든 분기점이 직접 연결된 폐쇄되지 않은 도로가 최대 $k$개가 되도록 도로를 폐쇄하는 최소 비용이다.
  • 이 함수는 정확하게 한 번 호출된다.

예제 1

다음 호출을 생각해보자.

minimum_closure_costs(5, [0, 0, 0, 2], [1, 2, 3, 4], [1, 4, 3, 2])

이는 총 5개의 분기점이 있고, 이를 잇는 도로 4개가 (0, 1), (0, 2), (0, 3), (2, 4)을 잇고, 이 도로를 폐쇄하는 비용은 각각 1, 4, 3, 2라는 뜻이다.

최소 비용을 구하기 위해서는 다음과 같다.

  • 김 박사가 $k = 0$으로 고르면, 모든 도로가 폐쇄되어야 하므로 총 비용은 1 + 4 + 3 + 2 = 10이다.
  • 김 박사가 $k = 1$로 고르면, 도로 0과 도로 1을 폐쇄하면 총 비용 1 + 4 = 5가 된다.
  • 김 박사가 $k = 2$로 고르면, 도로 0을 폐쇄하면 총 비용 1이 된다.
  • 김 박사가 $k = 3$ 또는 $k = 4$를 고르면, 어느 도로도 폐쇄하지 않아도 된다.

따라서, minimum_closure_costs의 리턴값은 [10, 5, 1, 0, 0]이다.

예제 2

다음 호출을 생각해 보자.

minimum_closure_costs(4, [0, 2, 0], [1, 0, 3], [5, 10, 5])

이는 총 4개의 분기점이 있고, 이를 잇는 도로 3개가 (0, 1), (2, 0), (0, 3)을 잇고, 이 도로를 폐쇄하는 비용은 각각 5, 10, 5라는 뜻이다.

최소 비용을 구하기 위해서는 다음과 같다.

  • 김 박사가 $k = 0$으로 고르면, 모든 도로가 폐쇄되어야 하므로 총 비용은 5 + 10 + 5 = 20이다.
  • 김 박사가 $k = 1$로 고르면, 도로 0과 도로 2을 폐쇄하면 총 비용 5 + 5 = 10이 된다.
  • 김 박사가 $k = 2$로 고르면, 도로 0 또는 도로 2을 폐쇄하면 총 비용 5가 된다.
  • 김 박사가 $k = 3$을 고르면, 어느 도로도 폐쇄하지 않아도 된다.

따라서, minimum_closure_costs의 리턴값은 [20, 10, 5, 0]이다.

제한

  • $2 \le N \le 100\,000$
  • $0 \le U[i], V[i] \le N - 1$ (모든 $0 \le i \le N - 2$)
  • 어떤 두 분기점도 하나 또는 그 이상의 도로를 통해서 연결되어 있다.
  • $1 \le W[i] \le 10^9$ (모든 $0 \le i \le N - 2$)

서브태스크

번호 배점 제한
1 5

$U[i] = 0$ (모든 $0 \le i \le N - 2$)

2 7

$U[i] = i$, $V[i] = i + 1$ (모든 $0 \le i \le N - 2$)

3 14

$N \le 200$

4 10

$N \le 2000$

5 17

$W[i] = 1$ (모든 $0 \le i \le N - 2$)

6 25

$W[i] \le 10$ (모든 $0 \le i \le N - 2$)

7 22

추가적인 제약 조건이 없다.

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\ubc15\uc0ac\ub294 \uc790\ub3d9\ucc28 \uc5c6\ub294 \ub0a0\uc744 \uc9c0\uc815\ud558\ub824\uace0 \ud55c\ub2e4. \uc790\ub3d9\ucc28 \uc5c6\ub294 \ub0a0 \ud589\uc0ac\ub85c, \uae40 \ubc15\uc0ac\ub294 \ub3c4\ub85c\ub97c \ud3d0\uc1c4\ud558\ub824\uace0 \ud55c\ub2e4. \ud3d0\uc1c4\ud560 \ub3c4\ub85c\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\ud574\uc9c4\ub2e4. \uae40 \ubc15\uc0ac\ub294 \uba3c\uc800 \uc74c\uc774 \uc544\ub2cc \uc815\uc218 $k$\ub97c \uace0\ub974\uace0, \ubaa8\ub4e0 \ubd84\uae30\uc810\uc5d0 $k$\uac1c \uc774\ud558\uc758 \ud3d0\uc1c4\ub418\uc9c0 \uc54a\uc740 \ub3c4\ub85c\uac00 \uc9c1\uc811 \uc5f0\uacb0\ub418\uc5b4 \uc788\ub3c4\ub85d \ud55c\ub2e4. \ub3c4\ub85c $i$\ub97c \ud3d0\uc1c4\ud558\ub294 \ube44\uc6a9\uc740 $W[i]$\uc774\ub2e4.<\/p>\r\n\r\n<p>\uae40 \ubc15\uc0ac\ub97c \ub3c4\uc640\uc11c \uac00\ub2a5\ud55c \uc74c\uc774 \uc544\ub2cc \uc815\uc218 $k$ ($0 \\le k \\le N - 1$) \uac01\uac01\uc5d0 \ub300\ud574 \uc870\uac74\uc744 \ub9cc\uc871\ud558\uac8c \ub3c4\ub85c\ub97c \ud3d0\uc1c4\ud558\ub294 \ucd5c\uc18c \ube44\uc6a9\uc744 \uad6c\ud558\uc790.<\/p>\r\n","input":"","output":"","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$2 \\le N \\le 100\\,000$<\/li>\r\n\t<li>$0 \\le U[i], V[i] \\le N - 1$ (\ubaa8\ub4e0 $0 \\le i \\le N - 2$)<\/li>\r\n\t<li>\uc5b4\ub5a4 \ub450 \ubd84\uae30\uc810\ub3c4 \ud558\ub098 \ub610\ub294 \uadf8 \uc774\uc0c1\uc758 \ub3c4\ub85c\ub97c \ud1b5\ud574\uc11c \uc5f0\uacb0\ub418\uc5b4 \uc788\ub2e4.<\/li>\r\n\t<li>$1 \\le W[i] \\le 10^9$&nbsp;(\ubaa8\ub4e0 $0 \\le i \\le N - 2$)<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$U[i] = 0$ (\ubaa8\ub4e0 $0 \\le i \\le N - 2$)<\/p>\r\n","subtask2":"<p>$U[i] = i$, $V[i] = i + 1$ (\ubaa8\ub4e0 $0 \\le i \\le N - 2$)<\/p>\r\n","subtask3":"<p>$N \\le 200$<\/p>\r\n","subtask4":"<p>$N \\le 2000$<\/p>\r\n","subtask5":"<p>$W[i] = 1$ (\ubaa8\ub4e0 $0 \\le i \\le N - 2$)<\/p>\r\n","subtask6":"<p>$W[i] \\le 10$ (\ubaa8\ub4e0 $0 \\le i \\le N - 2$)<\/p>\r\n","subtask7":"<p>\ucd94\uac00\uc801\uc778 \uc81c\uc57d \uc870\uac74\uc774 \uc5c6\ub2e4.<\/p>\r\n","custom_implementation":"<p>\ub2e4\uc74c \ud568\uc218\ub97c \uad6c\ud604\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<pre>\r\nint64[] minimum_closure_costs(int N, int[] U, int[] V, int[] W)<\/pre>\r\n\r\n<ul>\r\n\t<li>$N$: \uc218\ub77c\ubc14\uc57c\uc758 \ubd84\uae30\uc810 \uc218<\/li>\r\n\t<li>$U$, $V$ : \uae38\uc774 $N - 1$\uc778 \ubc30\uc5f4\ub85c, \ubd84\uae30\uc810 $U[i]$\uc640 $V[i]$\ub294 \ub3c4\ub85c $i$\ub85c \uc5f0\uacb0\ub418\uc5b4 \uc788\ub2e4.<\/li>\r\n\t<li>$W$: \uae38\uc774 $N - 1$\uc778 \ubc30\uc5f4\ub85c, $W[i]$\ub294 \ub3c4\ub85c $i$\ub97c \ud3d0\uc1c4\ud558\ub294\ub370 \ub4dc\ub294 \ube44\uc6a9\uc774\ub2e4.<\/li>\r\n\t<li>\uc774 \ud568\uc218\ub294 \ud558\ub098\uc758 \ubc30\uc5f4 $N$\uc744 \ub9ac\ud134\ud574\uc57c \ud55c\ub2e4. \uac01\uac01 $k$\ub9c8\ub2e4 ($0 \\le k \\le N -&nbsp;1$), \uc774 \ubc30\uc5f4\uc758 $k$\ubc88\uc9f8 \uc6d0\uc18c\ub294 \ubaa8\ub4e0 \ubd84\uae30\uc810\uc774 \uc9c1\uc811 \uc5f0\uacb0\ub41c \ud3d0\uc1c4\ub418\uc9c0 \uc54a\uc740 \ub3c4\ub85c\uac00 \ucd5c\ub300 $k$\uac1c\uac00 \ub418\ub3c4\ub85d \ub3c4\ub85c\ub97c \ud3d0\uc1c4\ud558\ub294 \ucd5c\uc18c \ube44\uc6a9\uc774\ub2e4.<\/li>\r\n\t<li>\uc774 \ud568\uc218\ub294 \uc815\ud655\ud558\uac8c \ud55c \ubc88 \ud638\ucd9c\ub41c\ub2e4.<\/li>\r\n<\/ul>\r\n","custom_example1":"<p>\ub2e4\uc74c \ud638\ucd9c\uc744 \uc0dd\uac01\ud574\ubcf4\uc790.<\/p>\r\n\r\n<pre>\r\nminimum_closure_costs(5, [0, 0, 0, 2], [1, 2, 3, 4], [1, 4, 3, 2])<\/pre>\r\n\r\n<p>\uc774\ub294 \ucd1d 5\uac1c\uc758 \ubd84\uae30\uc810\uc774 \uc788\uace0, \uc774\ub97c \uc787\ub294 \ub3c4\ub85c 4\uac1c\uac00 (0, 1), (0, 2), (0, 3), (2, 4)\uc744 \uc787\uace0, \uc774 \ub3c4\ub85c\ub97c \ud3d0\uc1c4\ud558\ub294 \ube44\uc6a9\uc740 \uac01\uac01 1, 4, 3, 2\ub77c\ub294 \ub73b\uc774\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/6b48ea03-f585-4b9e-b35c-38080aa2a8b3\/-\/preview\/\" \/><\/p>\r\n\r\n<p>\ucd5c\uc18c \ube44\uc6a9\uc744 \uad6c\ud558\uae30 \uc704\ud574\uc11c\ub294 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uae40 \ubc15\uc0ac\uac00 $k = 0$\uc73c\ub85c \uace0\ub974\uba74, \ubaa8\ub4e0 \ub3c4\ub85c\uac00 \ud3d0\uc1c4\ub418\uc5b4\uc57c \ud558\ubbc0\ub85c \ucd1d \ube44\uc6a9\uc740 1 + 4 + 3 + 2 = 10\uc774\ub2e4.<\/li>\r\n\t<li>\uae40 \ubc15\uc0ac\uac00 $k = 1$\ub85c \uace0\ub974\uba74, \ub3c4\ub85c 0\uacfc \ub3c4\ub85c 1\uc744 \ud3d0\uc1c4\ud558\uba74 \ucd1d \ube44\uc6a9 1 + 4 = 5\uac00 \ub41c\ub2e4.<\/li>\r\n\t<li>\uae40 \ubc15\uc0ac\uac00 $k = 2$\ub85c \uace0\ub974\uba74, \ub3c4\ub85c 0\uc744 \ud3d0\uc1c4\ud558\uba74 \ucd1d \ube44\uc6a9 1\uc774 \ub41c\ub2e4.<\/li>\r\n\t<li>\uae40 \ubc15\uc0ac\uac00 $k = 3$ \ub610\ub294 $k = 4$\ub97c \uace0\ub974\uba74, \uc5b4\ub290 \ub3c4\ub85c\ub3c4 \ud3d0\uc1c4\ud558\uc9c0 \uc54a\uc544\ub3c4 \ub41c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ub530\ub77c\uc11c, <code>minimum_closure_costs<\/code>\uc758 \ub9ac\ud134\uac12\uc740 [10, 5, 1, 0, 0]\uc774\ub2e4.<\/p>\r\n","custom_example2":"<p>\ub2e4\uc74c \ud638\ucd9c\uc744 \uc0dd\uac01\ud574 \ubcf4\uc790.<\/p>\r\n\r\n<pre>\r\nminimum_closure_costs(4, [0, 2, 0], [1, 0, 3], [5, 10, 5])<\/pre>\r\n\r\n<p>\uc774\ub294 \ucd1d 4\uac1c\uc758 \ubd84\uae30\uc810\uc774 \uc788\uace0, \uc774\ub97c \uc787\ub294 \ub3c4\ub85c 3\uac1c\uac00 (0, 1), (2, 0), (0, 3)\uc744 \uc787\uace0, \uc774 \ub3c4\ub85c\ub97c \ud3d0\uc1c4\ud558\ub294 \ube44\uc6a9\uc740 \uac01\uac01 5, 10, 5\ub77c\ub294 \ub73b\uc774\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/b1a20334-afb3-4f50-b645-56102bfeaf69\/-\/preview\/\" \/><\/p>\r\n\r\n<p>\ucd5c\uc18c \ube44\uc6a9\uc744 \uad6c\ud558\uae30 \uc704\ud574\uc11c\ub294 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uae40 \ubc15\uc0ac\uac00 $k = 0$\uc73c\ub85c \uace0\ub974\uba74, \ubaa8\ub4e0 \ub3c4\ub85c\uac00 \ud3d0\uc1c4\ub418\uc5b4\uc57c \ud558\ubbc0\ub85c \ucd1d \ube44\uc6a9\uc740 5 + 10 + 5 = 20\uc774\ub2e4.<\/li>\r\n\t<li>\uae40 \ubc15\uc0ac\uac00 $k = 1$\ub85c \uace0\ub974\uba74, \ub3c4\ub85c 0\uacfc \ub3c4\ub85c 2\uc744 \ud3d0\uc1c4\ud558\uba74 \ucd1d \ube44\uc6a9 5 + 5 = 10\uc774 \ub41c\ub2e4.<\/li>\r\n\t<li>\uae40 \ubc15\uc0ac\uac00 $k = 2$\ub85c \uace0\ub974\uba74, \ub3c4\ub85c 0 \ub610\ub294 \ub3c4\ub85c 2\uc744 \ud3d0\uc1c4\ud558\uba74 \ucd1d \ube44\uc6a9 5\uac00 \ub41c\ub2e4.<\/li>\r\n\t<li>\uae40 \ubc15\uc0ac\uac00 $k = 3$\uc744 \uace0\ub974\uba74, \uc5b4\ub290 \ub3c4\ub85c\ub3c4 \ud3d0\uc1c4\ud558\uc9c0 \uc54a\uc544\ub3c4 \ub41c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ub530\ub77c\uc11c, <code>minimum_closure_costs<\/code>\uc758 \ub9ac\ud134\uac12\uc740 [20, 10, 5, 0]\uc774\ub2e4.<\/p>\r\n","custom_grader":"<p>\uc0d8\ud50c \uadf8\ub808\uc774\ub354\ub294 \uc785\ub825\uc744 \ub2e4\uc74c \uc591\uc2dd\uc73c\ub85c \uc77d\ub294\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>line 1: $N$<\/li>\r\n\t<li>line 2 + $i$ ($0 \\le i \\le&nbsp;N - 2$): $U[i]$ $V[i]$ $W[i]$<\/li>\r\n<\/ul>\r\n\r\n<p>\uc0d8\ud50c \uadf8\ub808\uc774\ub354\ub294 <code>minimum_closure_costs<\/code>\uac00 \ub9ac\ud134\ud55c \ubc30\uc5f4\uc744 \ud55c \uc904\uc5d0 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","custom_attachment":"<ul>\r\n\t<li><a href=\"https:\/\/upload.acmicpc.net\/861aab94-18a4-4115-9305-fe0b2e643e07\/\">roads.zip<\/a><\/li>\r\n<\/ul>\r\n"},{"problem_id":"21853","problem_lang":"1","title":"Road Closures","description":"<p>In the city of Surabaya, there are $N$ junctions, numbered from $0$ to $N - 1$. These junctions are connected by $N - 1$ bidirectional roads, numbered from $0$ to $N - 2$, such that there is a unique path between any pair of junctions through the roads. Road $i$ ($0 \\le i \\le N - 2$) connects junction $U[i]$ and $V[i]$.<\/p>\r\n\r\n<p>To raise environmental awareness, Pak Dengklek, as the mayor of Surabaya, plans to hold a Car Free Day. To encourage the event, Pak Dengklek will organize road closures. Pak Dengklek will first choose a non-negative integer $k$, then close some of the roads such that each junction is directly connected to&nbsp;<strong>at most<\/strong>&nbsp;$k$ roads that are not closed. The cost to close road $i$ is $W[i]$.<\/p>\r\n\r\n<p>Help Pak Dengklek to find the minimum total cost to close the roads for each possible non-negative integer $k$ ($0 \\le k \\le N - 1$).<\/p>\r\n","input":"","output":"","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$2 \\le N \\le 100\\,000$<\/li>\r\n\t<li>$0 \\le U[i], V[i] \\le N - 1$ (for all $0 \\le i \\le N - 2$)<\/li>\r\n\t<li>It is possible to travel between any pair of junctions through the roads.<\/li>\r\n\t<li>$1 \\le W[i] \\le 10^9$&nbsp;(for all $0 \\le i \\le N - 2$)<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$U[i] = 0$ (for all $0 \\le i \\le N - 2$)<\/p>\r\n","subtask2":"<p>$U[i] = i$, $V[i] = i + 1$ (for all $0 \\le i \\le N - 2$)<\/p>\r\n","subtask3":"<p>$N \\le 200$<\/p>\r\n","subtask4":"<p>$N \\le 2000$<\/p>\r\n","subtask5":"<p>$W[i] = 1$ (for all $0 \\le i \\le N - 2$)<\/p>\r\n","subtask6":"<p>$W[i] \\le 10$ (for all $0 \\le i \\le N - 2$)<\/p>\r\n","subtask7":"<p>No additional constraints.<\/p>\r\n","custom_implementation":"<p>You should implement the following procedure:<\/p>\r\n\r\n<pre>\r\n<code>int64[] minimum_closure_costs(int N, int[] U, int[] V, int[] W)\r\n<\/code><\/pre>\r\n\r\n<ul>\r\n\t<li>$N$: the number of junctions in Surabaya.<\/li>\r\n\t<li>$U$ and $V$: arrays of size $N - 1$, where junctions $U[i]$ and $V[i]$ are connected by road $i$.<\/li>\r\n\t<li>$W$: an array of size $N - 1$, where $W[i]$ is the cost to close road $i$.<\/li>\r\n\t<li>This procedure should return a single array of size $N$. For each $k$ ($0 \\le k \\le N - 1$), the $k$-th element is the minimum total cost to close the roads such that each junction is directly connected to at most $k$ roads that are not closed.<\/li>\r\n\t<li>This procedure is called exactly once.<\/li>\r\n<\/ul>\r\n","custom_example1":"<p>Consider the following call:<\/p>\r\n\r\n<pre>\r\n<code>minimum_closure_costs(5, [0, 0, 0, 2], [1, 2, 3, 4], [1, 4, 3, 2])\r\n<\/code><\/pre>\r\n\r\n<p>This means there is a total of $5$ junctions and $4$ roads connecting the junction pairs $(0, 1)$, $(0, 2)$, $(0, 3)$, and $(2, 4)$ with closure costs $1$, $4$, $3$, and $2$, respectively.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/6b48ea03-f585-4b9e-b35c-38080aa2a8b3\/-\/preview\/\" \/><\/p>\r\n\r\n<p>To obtain the minimum costs:<\/p>\r\n\r\n<ul>\r\n\t<li>if Pak Dengklek chose $k = 0$, then all roads should be closed with a total cost of $1 + 4 + 3 + 2 = 10$;<\/li>\r\n\t<li>if Pak Dengklek chose $k = 1$, then road $0$ and road $1$ should be closed with a total cost of $1 + 4 = 5$;<\/li>\r\n\t<li>if Pak Dengklek chose $k = 2$, then road $0$ should be closed with a total cost of $1$;<\/li>\r\n\t<li>if Pak Dengklek chose $k = 3$ or $k = 4$, then no roads need to be closed.<\/li>\r\n<\/ul>\r\n\r\n<p>Therefore, the&nbsp;<code>minimum_closure_costs<\/code>&nbsp;procedure should return $[10, 5, 1, 0, 0]$.<\/p>\r\n","custom_example2":"<p>Consider the following call:<\/p>\r\n\r\n<pre>\r\n<code>minimum_closure_costs(4, [0, 2, 0], [1, 0, 3], [5, 10, 5])\r\n<\/code><\/pre>\r\n\r\n<p>This means there is a total of $4$ junctions and $3$ roads connecting the junction pairs $(0, 1)$, $(2, 0)$, and $(0, 3)$ with the closure costs $5$, $10$, and $5$ respectively.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/b1a20334-afb3-4f50-b645-56102bfeaf69\/-\/preview\/\" \/><\/p>\r\n\r\n<p>To obtain the minimum costs:<\/p>\r\n\r\n<ul>\r\n\t<li>if Pak Dengklek chose $k = 0$, then all roads should be closed with a total cost of $5 + 10 + 5 = 20$;<\/li>\r\n\t<li>if Pak Dengklek chose $k = 1$, then road $0$ and road $2$ should be closed with a total cost of $5 + 5 = 10$;<\/li>\r\n\t<li>if Pak Dengklek chose $k = 2$, then either road $0$ or road $2$ should be closed with a total cost of $5$;<\/li>\r\n\t<li>if Pak Dengklek chose $k = 3$, then no roads need to be closed.<\/li>\r\n<\/ul>\r\n\r\n<p>Therefore, the&nbsp;<code>minimum_closure_costs<\/code>&nbsp;procedure should return $[20, 10, 5, 0]$.<\/p>\r\n","custom_grader":"<p>The sample grader reads the input in the following format:<\/p>\r\n\r\n<ul>\r\n\t<li>line $1$: $N$<\/li>\r\n\t<li>line $2 + i$ ($0 \\le i \\le N - 2$): $U[i] \\; V[i] \\; W[i]$<\/li>\r\n<\/ul>\r\n\r\n<p>The sample grader prints a single line containing the array returned by&nbsp;<code>minimum_closure_costs<\/code>.<\/p>\r\n","custom_attachment":"<ul>\r\n\t<li><a href=\"https:\/\/upload.acmicpc.net\/861aab94-18a4-4115-9305-fe0b2e643e07\/\">roads.zip<\/a><\/li>\r\n<\/ul>\r\n"}]

샘플 그레이더

샘플 그레이더는 입력을 다음 양식으로 읽는다.

  • line 1: $N$
  • line 2 + $i$ ($0 \le i \le N - 2$): $U[i]$ $V[i]$ $W[i]$

샘플 그레이더는 minimum_closure_costs가 리턴한 배열을 한 줄에 출력한다.

첨부

제출할 수 있는 언어

C++17, C++14, C++20, C++14 (Clang), C++17 (Clang), C++20 (Clang)

채점 및 기타 정보

  • 예제는 채점하지 않는다.