시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
3 초 128 MB 65 10 8 14.815%

문제

한 달 가까이 구사과의 이상한 말들을 받아주느라 너무나 힘들었던 캇카흐는, 이제 대담한 복수를 하려고 합니다. 그 복수는 아니나 다를까, 멕카시나의 걸작, 후르츠 치킨을 구사과의 집으로 주문하는 것이죠!

구사과가 사는 곳은 매우 특이한 구조를 가지고 있습니다. 이 곳은 N개의 도시와 (N-1)개의 양방향 도로로 이루어져 있으며, 모든 도시 쌍 간에 그 두 도시를 잇는 경로가 존재합니다. 동쪽에 있는 도시들에는 멕카시나 가게들이 있고, 서쪽에 있는 도시들에는 구사과의 집들(맞아요, 구사과는 집이 여러 채 있는 부자에요!)이 있습니다. 물론 멕카시나도, 구사과의 집도 없는 도시도 있습니다.

그리고 이 곳에는 한 가지 더 특이한 점이 있습니다. 멕카시나가 있는 도시에서 구사과의 집으로 향하는 모든 경로는 어떤 특정한 도로를 지나도록 되어있습니다. 그 도로가 잇는 두 도시에는 멕카시나도, 구사과의 집도 없습니다.

캇카흐는 각 가게의 배달원들에게 연락하여, 그들이 어떻게 움직여야 하는지를 명령하려고 합니다. 구사과에게 들키지 않기 위해, 한 도로에 두 명 이상의 배달원(즉 둘 이상의 후르츠 치킨)이 동시에 있어서는 안 됩니다. 하지만 한 도시에 여러 명의 배달원이 대기하는 것은 가능합니다. 각각의 배달원들은 도로가 겹치지만 않는다면 동시에 이동이 가능합니다. 모든 도로를 지나는 데에는 1만큼의 시간이 걸립니다.

구사과에게 최대한 큰 정신적인 타격을 주기 위해서, 캇카흐는 후르츠 치킨이 서로 다른 구사과의 집으로 배달되기를 원합니다. 즉 어떤 두 치킨이 같은 집으로 배달되어서는 안 됩니다.

결전의 날이 왔습니다. 캇카흐는 모든 멕카시나 가게에 전화를 걸어, 오늘 영업하는 멕카시나 가게의 목록을 알아냈습니다. 캇카흐는 모든 후르츠 치킨이 배달되는 데에 필요한 시간을 최소화하고자 합니다. 구사과의 동네의 구조를 바탕으로, 치킨이 모두 배달되는 최소 시간을 구해주세요!

입력

입력의 첫 번째 줄에는 도시의 수 N, 멕카시나의 가게의 수 W, 그리고 구사과의 집의 수 Z가 주어집니다. (1 ≤ N, W, Z ≤ 106) 도시는 1부터 N까지의 번호가 붙어있으며, 멕카시나 가게가 있는 도시는 1번부터 W번까지이고, 구사과의 집이 있는 도시는 (N-Z+1)번부터 N번까지입니다.

그 뒤의 (N-1)개의 줄에는 구사과의 동네의 구조에 대한 설명이 주어집니다. 각각의 줄에는 1 이상 N 이하의 정수 a, b가 주어집니다. 이는 a번 도시와 b번 도시를 잇는 도로가 있다는 것을 나타냅니다.

그 다음 줄은 오늘 영업중인 멕카시나 가게의 수를 나타내는 1 이상 W 이하의 정수 P (1 ≤ p ≤ min(W, Z))가 주어집니다. 다음 줄에는 1 이상 W 이하의 서로 다른 P개의 정수가 주어집니다. 각각의 정수는 오늘 영업하는 멕카시나 가게가 있는 도시의 번호를 나타냅니다.

출력

첫 번째 줄에 모든 후르츠 치킨이 배달되는 데에 필요한 최소 시간을 출력하세요.

예제 입력 1

9 2 3
1 3
2 3
4 3
4 5
4 6
7 4
5 8
9 6
2
1 2

예제 출력 1

4

힌트

화살표는 치킨의 배달 과정을 나타냅니다. 제자리로 돌아오는 화살표는 배달원이 도로를 이용하기 위해 1의 시간만큼 기다렸음을 나타냅니다.

[{"problem_id":"7993","problem_lang":"0","title":"\ud6c4\ub974\uce20 \uce58\ud0a8","description":"<p>\ud55c \ub2ec \uac00\uae4c\uc774 \uad6c\uc0ac\uacfc\uc758 \uc774\uc0c1\ud55c \ub9d0\ub4e4\uc744 \ubc1b\uc544\uc8fc\ub290\ub77c \ub108\ubb34\ub098 \ud798\ub4e4\uc5c8\ub358 \uce87\uce74\ud750\ub294, \uc774\uc81c \ub300\ub2f4\ud55c \ubcf5\uc218\ub97c \ud558\ub824\uace0 \ud569\ub2c8\ub2e4. \uadf8 \ubcf5\uc218\ub294 \uc544\ub2c8\ub098 \ub2e4\ub97c\uae4c, \uba55\uce74\uc2dc\ub098\uc758 \uac78\uc791,&nbsp;\ud6c4\ub974\uce20 \uce58\ud0a8\uc744 \uad6c\uc0ac\uacfc\uc758 \uc9d1\uc73c\ub85c \uc8fc\ubb38\ud558\ub294 \uac83\uc774\uc8e0!<\/p>\r\n\r\n<p>\uad6c\uc0ac\uacfc\uac00 \uc0ac\ub294 \uacf3\uc740 \ub9e4\uc6b0 \ud2b9\uc774\ud55c \uad6c\uc870\ub97c \uac00\uc9c0\uace0 \uc788\uc2b5\ub2c8\ub2e4. \uc774 \uacf3\uc740&nbsp;N\uac1c\uc758 \ub3c4\uc2dc\uc640 (N-1)\uac1c\uc758 \uc591\ubc29\ud5a5 \ub3c4\ub85c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uc73c\uba70, \ubaa8\ub4e0 \ub3c4\uc2dc \uc30d \uac04\uc5d0 \uadf8 \ub450 \ub3c4\uc2dc\ub97c \uc787\ub294 \uacbd\ub85c\uac00 \uc874\uc7ac\ud569\ub2c8\ub2e4. \ub3d9\ucabd\uc5d0 \uc788\ub294 \ub3c4\uc2dc\ub4e4\uc5d0\ub294&nbsp;\uba55\uce74\uc2dc\ub098&nbsp;\uac00\uac8c\ub4e4\uc774 \uc788\uace0, \uc11c\ucabd\uc5d0 \uc788\ub294 \ub3c4\uc2dc\ub4e4\uc5d0\ub294 \uad6c\uc0ac\uacfc\uc758 \uc9d1\ub4e4(\ub9de\uc544\uc694, \uad6c\uc0ac\uacfc\ub294 \uc9d1\uc774 \uc5ec\ub7ec \ucc44 \uc788\ub294 \ubd80\uc790\uc5d0\uc694!)\uc774 \uc788\uc2b5\ub2c8\ub2e4. \ubb3c\ub860 \uba55\uce74\uc2dc\ub098\ub3c4, \uad6c\uc0ac\uacfc\uc758 \uc9d1\ub3c4 \uc5c6\ub294 \ub3c4\uc2dc\ub3c4 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\uadf8\ub9ac\uace0 \uc774 \uacf3\uc5d0\ub294 \ud55c \uac00\uc9c0 \ub354 \ud2b9\uc774\ud55c \uc810\uc774 \uc788\uc2b5\ub2c8\ub2e4. \uba55\uce74\uc2dc\ub098\uac00 \uc788\ub294 \ub3c4\uc2dc\uc5d0\uc11c \uad6c\uc0ac\uacfc\uc758 \uc9d1\uc73c\ub85c \ud5a5\ud558\ub294 \ubaa8\ub4e0 \uacbd\ub85c\ub294 \uc5b4\ub5a4 \ud2b9\uc815\ud55c \ub3c4\ub85c\ub97c \uc9c0\ub098\ub3c4\ub85d \ub418\uc5b4\uc788\uc2b5\ub2c8\ub2e4. \uadf8 \ub3c4\ub85c\uac00 \uc787\ub294 \ub450 \ub3c4\uc2dc\uc5d0\ub294 \uba55\uce74\uc2dc\ub098\ub3c4, \uad6c\uc0ac\uacfc\uc758 \uc9d1\ub3c4 \uc5c6\uc2b5\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\uce87\uce74\ud750\ub294 \uac01 \uac00\uac8c\uc758 \ubc30\ub2ec\uc6d0\ub4e4\uc5d0\uac8c \uc5f0\ub77d\ud558\uc5ec, \uadf8\ub4e4\uc774 \uc5b4\ub5bb\uac8c \uc6c0\uc9c1\uc5ec\uc57c \ud558\ub294\uc9c0\ub97c \uba85\ub839\ud558\ub824\uace0 \ud569\ub2c8\ub2e4. \uad6c\uc0ac\uacfc\uc5d0\uac8c \ub4e4\ud0a4\uc9c0 \uc54a\uae30 \uc704\ud574, \ud55c \ub3c4\ub85c\uc5d0 \ub450 \uba85 \uc774\uc0c1\uc758 \ubc30\ub2ec\uc6d0(\uc989 \ub458 \uc774\uc0c1\uc758 \ud6c4\ub974\uce20 \uce58\ud0a8)\uc774 \ub3d9\uc2dc\uc5d0 \uc788\uc5b4\uc11c\ub294 \uc548 \ub429\ub2c8\ub2e4. \ud558\uc9c0\ub9cc \ud55c \ub3c4\uc2dc\uc5d0 \uc5ec\ub7ec \uba85\uc758 \ubc30\ub2ec\uc6d0\uc774 \ub300\uae30\ud558\ub294 \uac83\uc740 \uac00\ub2a5\ud569\ub2c8\ub2e4. \uac01\uac01\uc758 \ubc30\ub2ec\uc6d0\ub4e4\uc740 \ub3c4\ub85c\uac00 \uacb9\uce58\uc9c0\ub9cc \uc54a\ub294\ub2e4\uba74 \ub3d9\uc2dc\uc5d0 \uc774\ub3d9\uc774 \uac00\ub2a5\ud569\ub2c8\ub2e4. \ubaa8\ub4e0 \ub3c4\ub85c\ub97c \uc9c0\ub098\ub294 \ub370\uc5d0\ub294 1\ub9cc\ud07c\uc758 \uc2dc\uac04\uc774 \uac78\ub9bd\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\uad6c\uc0ac\uacfc\uc5d0\uac8c \ucd5c\ub300\ud55c \ud070 \uc815\uc2e0\uc801\uc778 \ud0c0\uaca9\uc744 \uc8fc\uae30 \uc704\ud574\uc11c, \uce87\uce74\ud750\ub294 \ud6c4\ub974\uce20 \uce58\ud0a8\uc774 \uc11c\ub85c \ub2e4\ub978&nbsp;\uad6c\uc0ac\uacfc\uc758 \uc9d1\uc73c\ub85c \ubc30\ub2ec\ub418\uae30\ub97c \uc6d0\ud569\ub2c8\ub2e4.&nbsp;\uc989 \uc5b4\ub5a4 \ub450 \uce58\ud0a8\uc774 \uac19\uc740 \uc9d1\uc73c\ub85c \ubc30\ub2ec\ub418\uc5b4\uc11c\ub294 \uc548 \ub429\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\uacb0\uc804\uc758 \ub0a0\uc774 \uc654\uc2b5\ub2c8\ub2e4. \uce87\uce74\ud750\ub294 \ubaa8\ub4e0 \uba55\uce74\uc2dc\ub098 \uac00\uac8c\uc5d0 \uc804\ud654\ub97c \uac78\uc5b4, \uc624\ub298 \uc601\uc5c5\ud558\ub294 \uba55\uce74\uc2dc\ub098 \uac00\uac8c\uc758 \ubaa9\ub85d\uc744 \uc54c\uc544\ub0c8\uc2b5\ub2c8\ub2e4. \uce87\uce74\ud750\ub294 \ubaa8\ub4e0 \ud6c4\ub974\uce20 \uce58\ud0a8\uc774 \ubc30\ub2ec\ub418\ub294 \ub370\uc5d0 \ud544\uc694\ud55c \uc2dc\uac04\uc744 \ucd5c\uc18c\ud654\ud558\uace0\uc790 \ud569\ub2c8\ub2e4. \uad6c\uc0ac\uacfc\uc758 \ub3d9\ub124\uc758 \uad6c\uc870\ub97c \ubc14\ud0d5\uc73c\ub85c, \uce58\ud0a8\uc774 \ubaa8\ub450 \ubc30\ub2ec\ub418\ub294 \ucd5c\uc18c \uc2dc\uac04\uc744 \uad6c\ud574\uc8fc\uc138\uc694!<\/p>\r\n","input":"<p>\uc785\ub825\uc758 \uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 \ub3c4\uc2dc\uc758 \uc218 N, \uba55\uce74\uc2dc\ub098\uc758 \uac00\uac8c\uc758 \uc218 W, \uadf8\ub9ac\uace0 \uad6c\uc0ac\uacfc\uc758 \uc9d1\uc758 \uc218 Z\uac00 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. (1 &le; N, W, Z &le; 10<sup>6<\/sup>) \ub3c4\uc2dc\ub294 1\ubd80\ud130 N\uae4c\uc9c0\uc758 \ubc88\ud638\uac00 \ubd99\uc5b4\uc788\uc73c\uba70,&nbsp;\uba55\uce74\uc2dc\ub098 \uac00\uac8c\uac00 \uc788\ub294 \ub3c4\uc2dc\ub294&nbsp;1\ubc88\ubd80\ud130 W\ubc88\uae4c\uc9c0\uc774\uace0, \uad6c\uc0ac\uacfc\uc758 \uc9d1\uc774 \uc788\ub294 \ub3c4\uc2dc\ub294 (N-Z+1)\ubc88\ubd80\ud130 N\ubc88\uae4c\uc9c0\uc785\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\uadf8 \ub4a4\uc758 (N-1)\uac1c\uc758 \uc904\uc5d0\ub294 \uad6c\uc0ac\uacfc\uc758 \ub3d9\ub124\uc758 \uad6c\uc870\uc5d0 \ub300\ud55c \uc124\uba85\uc774 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. \uac01\uac01\uc758 \uc904\uc5d0\ub294 1 \uc774\uc0c1 N \uc774\ud558\uc758 \uc815\uc218 a, b\uac00 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. \uc774\ub294 a\ubc88 \ub3c4\uc2dc\uc640 b\ubc88 \ub3c4\uc2dc\ub97c \uc787\ub294 \ub3c4\ub85c\uac00 \uc788\ub2e4\ub294 \uac83\uc744 \ub098\ud0c0\ub0c5\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\uadf8 \ub2e4\uc74c \uc904\uc740 \uc624\ub298 \uc601\uc5c5\uc911\uc778 \uba55\uce74\uc2dc\ub098 \uac00\uac8c\uc758 \uc218\ub97c \ub098\ud0c0\ub0b4\ub294 1 \uc774\uc0c1 W \uc774\ud558\uc758 \uc815\uc218 P (1 &le; p &le;&nbsp;min(W, Z))\uac00 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. \ub2e4\uc74c \uc904\uc5d0\ub294 1 \uc774\uc0c1 W \uc774\ud558\uc758 \uc11c\ub85c \ub2e4\ub978 P\uac1c\uc758 \uc815\uc218\uac00 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. \uac01\uac01\uc758 \uc815\uc218\ub294 \uc624\ub298 \uc601\uc5c5\ud558\ub294 \uba55\uce74\uc2dc\ub098 \uac00\uac8c\uac00 \uc788\ub294 \ub3c4\uc2dc\uc758 \ubc88\ud638\ub97c \ub098\ud0c0\ub0c5\ub2c8\ub2e4.<\/p>\r\n","output":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \ubaa8\ub4e0 \ud6c4\ub974\uce20 \uce58\ud0a8\uc774 \ubc30\ub2ec\ub418\ub294 \ub370\uc5d0 \ud544\uc694\ud55c \ucd5c\uc18c \uc2dc\uac04\uc744 \ucd9c\ub825\ud558\uc138\uc694.<\/p>\r\n","hint":"<p>\ud654\uc0b4\ud45c\ub294 \uce58\ud0a8\uc758 \ubc30\ub2ec \uacfc\uc815\uc744 \ub098\ud0c0\ub0c5\ub2c8\ub2e4. \uc81c\uc790\ub9ac\ub85c \ub3cc\uc544\uc624\ub294 \ud654\uc0b4\ud45c\ub294 \ubc30\ub2ec\uc6d0\uc774 \ub3c4\ub85c\ub97c \uc774\uc6a9\ud558\uae30 \uc704\ud574 1\uc758 \uc2dc\uac04\ub9cc\ud07c \uae30\ub2e4\ub838\uc74c\uc744 \ub098\ud0c0\ub0c5\ub2c8\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/7993\/1.png\" style=\"height:223px; width:400px\" \/><\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"7993","problem_lang":"1","title":"East-West","description":"<p>International agreements signed by the Awfully Vast State impose on it transit obligations - it has to enable the transport of nuclear waste from its eastern neighbours power plants to recycling facilities in the West, by means of its railway system. Ecological reasons impose such traffic organization, that the waste-carrying trains leave the territory of the state as quickly as possible.<\/p>\r\n\r\n<p>The railway network in this country has a very peculiar structure. It consists of n cities - railway junctions and n-1 two-way railway track segments, connecting the junctions. Transport is possible between each pair of cities. Furthermore, there is a section of the railway track, whose ends are not border cities and every connection from the eastern to the western border has to lead through that very section.<\/p>\r\n\r\n<p>All waste-carrying trains arrive at the eastern border on the same day, before dawn, at distinct checkpoints, however. For safety reasons the trains only move during the day. Only a single waste-carrying train can move on a given track section at a time, but an unlimited amount of them can wait at a junction. It takes one day for a train to traverse a section of the track. The traffic has to be organized in such a way, that allows each waste-carrying train to reach a distinct destination on the western border.<\/p>\r\n\r\n<p>How many days, at least, do the waste-carrying trains have to spend on the territory of the Awfully Vast State?<\/p>\r\n\r\n<p>Your task is to write a programme which:<\/p>\r\n\r\n<ul>\r\n\t<li>reads from the standard input a description of the railway network and border checkpoints at which the waste-carrying trains have arrived,<\/li>\r\n\t<li>finds the minimal number of days the transit has to last,<\/li>\r\n\t<li>writes the solution to the standard output.<\/li>\r\n<\/ul>\r\n","input":"<p>The first line of the input contains three integers 1 &le; n, w, z &le; 10<sup>6<\/sup>, n &ge; w+z+2, separated by single spaces. n denotes the number of junctions (which are labelled with 1,&hellip;,n), while w and z denote the number of border checkpoints on the eastern and western border, respectively. The checkpoints on the eastern border are labelled with 1,&hellip;,w, while those on the western border with n-z+1,&hellip;,n.<\/p>\r\n\r\n<p>In the following n-1 lines there is a description of the railway network. Each line contains two distinct integers, 1 &le; a, b &le; n, separated by a single space. They denote junctions connected by a section of the railway.<\/p>\r\n\r\n<p>The (n+1)&rsquo;st line contains a single integer p, 1 &le; p &le; w, 1 &le; p &le; z, denoting the number of waste-carrying trains. In the next (and last) line of the input there are p distinct integers, all of which are not greater than w, separated by single spaces. These are the numbers of checkpoints on the eastern border, at which the waste-carrying trains have arrived.<\/p>\r\n","output":"<p>The first and only line of the output should contain exactly one integer, denoting the minimal amount of days the waste have to spend on the territory of the state.<\/p>\r\n","hint":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/7993\/1.png\" style=\"height:223px; width:400px\" \/><\/p>\r\n\r\n<p>The arrows denote the movement of the trains in consecutive days for one of the optimal organizations of the railway traffic - a loop means that on a given day the train waited at the junction.<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Olympiad > Polish Olympiad in Informatics > POI 2003/2004 > Stage 3 1번