시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

라인 제로 놀이 동산에 새로운 미로가 생겼다. 미로는 방 n개와 방을 연결하는 통로 m개로 이루어져 있다. 통로는 ci 색으로 색칠되어져 있다. 미로는 입구는 1번 방이고, 출구는 n번 방이다. 미로에 들어가려면 헬리콥터를 타고 1번 방으로 낙하해야 한다.

미로를 만든 선영이는 다음날 미로 탈출 대회를 개최하려고 한다. 참가자는 1번 방 에서 출발하고, n번 방에 도착할 때까지 지난 복도의 색상을 모두 종이에 적는다. 대회를 우승하려면 종이에 적은 숫자의 개수가 적어야 한다. 또, 종이에 적은 숫자의 개수가 같은 경우에는 가장 이상적인 경로인 사람이 우승하게 된다. 다른 경로보다 모두 사전 순으로 앞서는 경로를 이상적인 경로라고 한다.

미로의 정보가 주어졌을 때, 1번 방에서 n번 방으로 가는 가장 이상적인 경로를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 방의 수 n과 복도의 수 m이 주어진다. (2 ≤ n ≤ 100,000, 1 ≤ m ≤ 200,000) 다음 m개 줄에는 복도의 정보가 주어지며, 정보는 세 정수 ai, bi, ci로 이루어져 있다. ai와 bi는 복도가 연결하는 방의 번호이고, ci는 복도의 색상이다. (1 ≤ ai, bi ≤ n, 1 ≤ ci ≤ 109) 복도는 양방향이며, 두 방을 연결하는 복도의 개수는 1개보다 많을 수도 있다. 또, 자기 자신으로 되돌아오는 복도가 존재할 수도 있다. 항상 1번 방에서 n번 방으로 갈 수 있는 미로만 입력으로 주어진다.

출력

첫째 줄에 1번 방에서 n번 방으로 가는 최단 경로의 길이를 출력한다. 둘째 줄에는 가장 이상적인 경로의 색을 지나가는 순서대로 출력한다.

예제 입력 1

4 6
1 2 1
1 3 2
3 4 3
2 3 1
2 4 4
3 1 1

예제 출력 1

2
1 3

힌트

수열 (a1, a2, ..., ak)가 수열 (b1, b2, ..., bk)보다 사전 순으로 앞서러면, ai < bi와 모든 j<i에 대해서 aj = bj를 만족하는 i가 존재해야 한다.

[{"problem_id":"3526","problem_lang":"0","title":"\uc774\uc0c1\uc801\uc778 \uacbd\ub85c","description":"<p>\ub77c\uc778 \uc81c\ub85c \ub180\uc774 \ub3d9\uc0b0\uc5d0 \uc0c8\ub85c\uc6b4 \ubbf8\ub85c\uac00 \uc0dd\uacbc\ub2e4. \ubbf8\ub85c\ub294 \ubc29 n\uac1c\uc640 \ubc29\uc744 \uc5f0\uacb0\ud558\ub294 \ud1b5\ub85c m\uac1c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \ud1b5\ub85c\ub294 c<sub>i<\/sub> \uc0c9\uc73c\ub85c \uc0c9\uce60\ub418\uc5b4\uc838 \uc788\ub2e4. \ubbf8\ub85c\ub294 \uc785\uad6c\ub294 1\ubc88 \ubc29\uc774\uace0, \ucd9c\uad6c\ub294 n\ubc88 \ubc29\uc774\ub2e4. \ubbf8\ub85c\uc5d0 \ub4e4\uc5b4\uac00\ub824\uba74 \ud5ec\ub9ac\ucf65\ud130\ub97c \ud0c0\uace0 1\ubc88 \ubc29\uc73c\ub85c \ub099\ud558\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ubbf8\ub85c\ub97c \ub9cc\ub4e0 \uc120\uc601\uc774\ub294 \ub2e4\uc74c\ub0a0 \ubbf8\ub85c \ud0c8\ucd9c \ub300\ud68c\ub97c \uac1c\ucd5c\ud558\ub824\uace0 \ud55c\ub2e4. \ucc38\uac00\uc790\ub294 1\ubc88 \ubc29 \uc5d0\uc11c \ucd9c\ubc1c\ud558\uace0, n\ubc88 \ubc29\uc5d0 \ub3c4\ucc29\ud560 \ub54c\uae4c\uc9c0 \uc9c0\ub09c \ubcf5\ub3c4\uc758 \uc0c9\uc0c1\uc744 \ubaa8\ub450 \uc885\uc774\uc5d0 \uc801\ub294\ub2e4. \ub300\ud68c\ub97c \uc6b0\uc2b9\ud558\ub824\uba74 \uc885\uc774\uc5d0 \uc801\uc740 \uc22b\uc790\uc758 \uac1c\uc218\uac00 \uc801\uc5b4\uc57c \ud55c\ub2e4. \ub610, \uc885\uc774\uc5d0 \uc801\uc740 \uc22b\uc790\uc758 \uac1c\uc218\uac00 \uac19\uc740 \uacbd\uc6b0\uc5d0\ub294 \uac00\uc7a5 \uc774\uc0c1\uc801\uc778 \uacbd\ub85c\uc778 \uc0ac\ub78c\uc774 \uc6b0\uc2b9\ud558\uac8c \ub41c\ub2e4. \ub2e4\ub978 \uacbd\ub85c\ubcf4\ub2e4 \ubaa8\ub450 \uc0ac\uc804 \uc21c\uc73c\ub85c \uc55e\uc11c\ub294 \uacbd\ub85c\ub97c \uc774\uc0c1\uc801\uc778 \uacbd\ub85c\ub77c\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ubbf8\ub85c\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, 1\ubc88 \ubc29\uc5d0\uc11c n\ubc88 \ubc29\uc73c\ub85c \uac00\ub294 \uac00\uc7a5 \uc774\uc0c1\uc801\uc778 \uacbd\ub85c\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ubc29\uc758 \uc218 n\uacfc \ubcf5\ub3c4\uc758 \uc218 m\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (2 &le; n &le; 100,000, 1 &le; m &le; 200,000) \ub2e4\uc74c m\uac1c \uc904\uc5d0\ub294 \ubcf5\ub3c4\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c0\uba70, \uc815\ubcf4\ub294 \uc138 \uc815\uc218 a<sub>i<\/sub>, b<sub>i<\/sub>, c<sub>i<\/sub>\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. a<sub>i<\/sub>\uc640 b<sub>i<\/sub>\ub294 \ubcf5\ub3c4\uac00 \uc5f0\uacb0\ud558\ub294 \ubc29\uc758 \ubc88\ud638\uc774\uace0, c<sub>i<\/sub>\ub294 \ubcf5\ub3c4\uc758 \uc0c9\uc0c1\uc774\ub2e4. (1 &le; a<sub>i<\/sub>, b<sub>i<\/sub> &le; n, 1 &le; c<sub>i<\/sub> &le; 10<sup>9<\/sup>) \ubcf5\ub3c4\ub294 \uc591\ubc29\ud5a5\uc774\uba70, \ub450 \ubc29\uc744 \uc5f0\uacb0\ud558\ub294 \ubcf5\ub3c4\uc758 \uac1c\uc218\ub294 1\uac1c\ubcf4\ub2e4 \ub9ce\uc744 \uc218\ub3c4 \uc788\ub2e4. \ub610, \uc790\uae30 \uc790\uc2e0\uc73c\ub85c \ub418\ub3cc\uc544\uc624\ub294 \ubcf5\ub3c4\uac00 \uc874\uc7ac\ud560 \uc218\ub3c4 \uc788\ub2e4. \ud56d\uc0c1 1\ubc88 \ubc29\uc5d0\uc11c n\ubc88 \ubc29\uc73c\ub85c \uac08 \uc218 \uc788\ub294 \ubbf8\ub85c\ub9cc \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 1\ubc88 \ubc29\uc5d0\uc11c n\ubc88 \ubc29\uc73c\ub85c \uac00\ub294 \ucd5c\ub2e8 \uacbd\ub85c\uc758 \uae38\uc774\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub458\uc9f8 \uc904\uc5d0\ub294 \uac00\uc7a5 \uc774\uc0c1\uc801\uc778 \uacbd\ub85c\uc758 \uc0c9\uc744 \uc9c0\ub098\uac00\ub294 \uc21c\uc11c\ub300\ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uc218\uc5f4 (a<sub>1<\/sub>, a<sub>2<\/sub>, ..., a<sub>k<\/sub>)\uac00 \uc218\uc5f4 (b<sub>1<\/sub>, b<sub>2<\/sub>, ..., b<sub>k<\/sub>)\ubcf4\ub2e4 \uc0ac\uc804 \uc21c\uc73c\ub85c \uc55e\uc11c\ub7ec\uba74, a<sub>i<\/sub> &lt; b<sub>i<\/sub>\uc640 \ubaa8\ub4e0 j&lt;i\uc5d0 \ub300\ud574\uc11c a<sub>j<\/sub> = b<sub>j<\/sub>\ub97c \ub9cc\uc871\ud558\ub294 i\uac00 \uc874\uc7ac\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3526","problem_lang":"1","title":"Ideal Path","description":"<p>New labyrinth attraction is open in New Lostland amusement park. The labyrinth consists of n rooms connected by m passages. Each passage is colored into some color c<sub>i<\/sub>. Visitors of the labyrinth are dropped from the helicopter to the room number 1 and their goal is to get to the labyrinth exit located in the room number n.<\/p>\r\n\r\n<p>Labyrinth owners are planning to run a contest tomorrow. Several runners will be dropped to the room number 1. They will run to the room number n writing down colors of passages as they run through them. The contestant with the shortest sequence of colors is the winner of the contest. If there are several contestants with the same sequence length, the one with the ideal path is the winner. The path is the ideal path if its color sequence is the lexicographically smallest among shortest paths.<\/p>\r\n\r\n<p>Andrew is preparing for the contest. He took a helicopter tour above New Lostland and made a picture of the labyrinth. Your task is to help him find the ideal path from the room number 1 to the room number n that would allow him to win the contest.<\/p>\r\n","input":"<p>The first line of the input contains integers n and m - the number of rooms and passages, respectively (2 &le; n &le; 100 000, 1 &le; m &le; 200 000). The following m lines describe passages, each passage is described with three integer numbers: a<sub>i<\/sub>, b<sub>i<\/sub>, and c<sub>i<\/sub> - the numbers of rooms it connects and its color (1 &le; a<sub>i<\/sub>, b<sub>i<\/sub> &le; n, 1 &le; c<sub>i<\/sub> &le; 10<sup>9<\/sup>). Each passage can be passed in either direction. Two rooms can be connected with more than one passage, there can be a passage from a room to itself. It is guaranteed that it is possible to reach the room number n from the room number 1.<\/p>\r\n","output":"<p>The first line of the output must contain k - the length of the shortest path from the room number 1 to the room number n. The second line must contain k numbers - the colors of passages in the order they must be passed in the ideal path.<\/p>\r\n","hint":"<p>A sequence (a<sub>1<\/sub>, a<sub>2<\/sub>, ... , a<sub>k<\/sub>) is lexicographically smaller than a sequence (b<sub>1<\/sub>, b<sub>2<\/sub>, ... , b<sub>k<\/sub>) if there exists i such that a<sub>i<\/sub> &lt; b<sub>i<\/sub>, and a<sub>j<\/sub> = b<sub>j<\/sub> for all j &lt; i.<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > Europe > Northeastern European Regional Contest > NEERC 2010 I번

  • 문제를 번역한 사람: baekjoon
  • 잘못된 번역을 찾은 사람: sgc109