시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 117 9 9 23.684%

문제

서울 내의 고속도로 도로망의 이용 요금이 빠르게 증가하고 있다. 때문에 최적의 경로를 찾는 것이 실제 문제로 제기되고 있다. 고속도로 도로망은 두 도시간의 양방향 도로들로 구성되어 있다. 각각의 도로에 대해 도로 이용요금과 도로를 지나가는데 걸리는 시간이 알려져 있다.

경로는 여행하는데 이용하는 도로들을 나열한 것을 의미한다. 경로상의 총 이동시간은 경로상의 도로들을 지나가는데 걸리는 시간의 합을 의미한다. 또한 경로상의 총 요금은 이동하는 도로들의 이용요금의 총합을 말한다. 그리고 경로상의 총 이용시간이 적을수록, 이용요금이 적을수록 더 좋은 경로가 된다. 즉, 어떤 경로가 다른 경로보다 좋다는 말은 이 경로가 다른 경로보다 빠르고 이용요금이 적다는 것을 의미한다. 우리는 어떠한 경로가 다른 어떤 경로보다도 좋은 경로일 때 이를 최적의 경로라 부른다. 하지만 항상 이러한 최적의 경로가 존재하는 것은 아니다.

예를 들어, 아래의 그림과 같은 고속도로 도로망이 있다고 하자. 각각의 도로는 요금과 이동하는데 걸리는 시간을 나타내는 한 쌍의 숫자로 구성되어진다,

그리고 도시 1에서 도시 4로 가는데는 총 4가지 경로가 존재한다. 4가지 경로에 대해 총 이동시간과 요금을 계산하여 보면 1-2-4(요금 4, 시간 5), 1-3-4(요금 4, 시간 5), 1-2-3-4(요금 6, 시간 4), 1-3-2-4(요금 4, 비용 10)이 된다.

그리고 여기서 경로 1-3-4와 1-2-4가 경로 1-3-2-4보다 좋은 것을 알 수 있다. 이 도로망에서는 효율적인 요금-시간 쌍이 두 가지 존재한다. 요금 4, 시간 5(경로 1-2-4, 1-3-4), 요금 6, 시간 4(경로 1-2-3-4). 만약 요금을 많이 내더라도 빠른 길을 원한다면 경로 1-2-3-4를 선택하면 되고 반대로 시간은 조금 더 걸리더라도 요금을 적게 내고 싶으면 경로 1-3-4 또는 1-2-4를 선택하면 된다.

문제는 고속도로 도로망에 대한 정보가 주어지면 시작 도시에서 끝 도시까지 연결하는 효율적인 경로를 계산하는 것이다. 우리는 단지 서로 다른 효율적인 비용-시간 쌍의 개수만 출력하면 된다.

문제는 지역들이 노드로 구성된 그래프가 주어졌을 때 원샘이 원하는 지역 간의 거리를 신속히 알려주는 것이다.

입력

첫째 줄에 도시의 개수 n(1≤n≤100), 도로의 개수 m(1≤m≤300), 시작 도시 s, 도착 도시 e가 주어진다. (1≤s,e≤n, s≠e) 그 다음부터 m개의 줄에 도로에 대한 정보가 주어지는데 한 줄에 한 도로의 양 끝점 p, r(1≤p,r≤n, p≠r)과 요금 c(0≤c≤100), 그리고 시간 t(0≤t≤100)이 주어진다. 두 개 도시 사이에는 한 개 이상의 도로가 존재할 수 있다.

출력

첫 줄에 서로 다른 효율적인 비용-시간 쌍의 개수를 출력한다.

예제 입력 1

4 5 1 4
2 1 2 1
3 4 3 1
2 3 1 2
3 1 1 4
2 4 2 4

예제 출력 1

2
[{"problem_id":"1702","problem_lang":"0","title":"\uace0\uc18d\ub3c4\ub85c","description":"<p>\uc11c\uc6b8 \ub0b4\uc758 \uace0\uc18d\ub3c4\ub85c \ub3c4\ub85c\ub9dd\uc758 \uc774\uc6a9 \uc694\uae08\uc774 \ube60\ub974\uac8c \uc99d\uac00\ud558\uace0 \uc788\ub2e4. \ub54c\ubb38\uc5d0 \ucd5c\uc801\uc758 \uacbd\ub85c\ub97c \ucc3e\ub294 \uac83\uc774 \uc2e4\uc81c \ubb38\uc81c\ub85c \uc81c\uae30\ub418\uace0 \uc788\ub2e4. \uace0\uc18d\ub3c4\ub85c \ub3c4\ub85c\ub9dd\uc740 \ub450 \ub3c4\uc2dc\uac04\uc758 \uc591\ubc29\ud5a5 \ub3c4\ub85c\ub4e4\ub85c \uad6c\uc131\ub418\uc5b4 \uc788\ub2e4. \uac01\uac01\uc758 \ub3c4\ub85c\uc5d0 \ub300\ud574 \ub3c4\ub85c \uc774\uc6a9\uc694\uae08\uacfc \ub3c4\ub85c\ub97c \uc9c0\ub098\uac00\ub294\ub370 \uac78\ub9ac\ub294 \uc2dc\uac04\uc774 \uc54c\ub824\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uacbd\ub85c\ub294 \uc5ec\ud589\ud558\ub294\ub370 \uc774\uc6a9\ud558\ub294 \ub3c4\ub85c\ub4e4\uc744 \ub098\uc5f4\ud55c \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4. \uacbd\ub85c\uc0c1\uc758 \ucd1d \uc774\ub3d9\uc2dc\uac04\uc740 \uacbd\ub85c\uc0c1\uc758 \ub3c4\ub85c\ub4e4\uc744 \uc9c0\ub098\uac00\ub294\ub370 \uac78\ub9ac\ub294 \uc2dc\uac04\uc758 \ud569\uc744 \uc758\ubbf8\ud55c\ub2e4. \ub610\ud55c&nbsp;\uacbd\ub85c\uc0c1\uc758 \ucd1d \uc694\uae08\uc740 \uc774\ub3d9\ud558\ub294 \ub3c4\ub85c\ub4e4\uc758 \uc774\uc6a9\uc694\uae08\uc758 \ucd1d\ud569\uc744 \ub9d0\ud55c\ub2e4. \uadf8\ub9ac\uace0 \uacbd\ub85c\uc0c1\uc758 \ucd1d \uc774\uc6a9\uc2dc\uac04\uc774 \uc801\uc744\uc218\ub85d, \uc774\uc6a9\uc694\uae08\uc774 \uc801\uc744\uc218\ub85d \ub354 \uc88b\uc740 \uacbd\ub85c\uac00 \ub41c\ub2e4. \uc989, \uc5b4\ub5a4 \uacbd\ub85c\uac00 \ub2e4\ub978 \uacbd\ub85c\ubcf4\ub2e4 \uc88b\ub2e4\ub294 \ub9d0\uc740 \uc774 \uacbd\ub85c\uac00 \ub2e4\ub978 \uacbd\ub85c\ubcf4\ub2e4 \ube60\ub974\uace0 \uc774\uc6a9\uc694\uae08\uc774 \uc801\ub2e4\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4. \uc6b0\ub9ac\ub294 \uc5b4\ub5a0\ud55c \uacbd\ub85c\uac00 \ub2e4\ub978 \uc5b4\ub5a4 \uacbd\ub85c\ubcf4\ub2e4\ub3c4 \uc88b\uc740 \uacbd\ub85c\uc77c \ub54c \uc774\ub97c \ucd5c\uc801\uc758 \uacbd\ub85c\ub77c \ubd80\ub978\ub2e4. \ud558\uc9c0\ub9cc \ud56d\uc0c1 \uc774\ub7ec\ud55c \ucd5c\uc801\uc758 \uacbd\ub85c\uac00 \uc874\uc7ac\ud558\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, \uc544\ub798\uc758 \uadf8\ub9bc\uacfc \uac19\uc740 \uace0\uc18d\ub3c4\ub85c \ub3c4\ub85c\ub9dd\uc774 \uc788\ub2e4\uace0 \ud558\uc790. \uac01\uac01\uc758 \ub3c4\ub85c\ub294 \uc694\uae08\uacfc \uc774\ub3d9\ud558\ub294\ub370 \uac78\ub9ac\ub294 \uc2dc\uac04\uc744 \ub098\ud0c0\ub0b4\ub294 \ud55c \uc30d\uc758 \uc22b\uc790\ub85c \uad6c\uc131\ub418\uc5b4\uc9c4\ub2e4,<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/JudgeOnline\/upload\/201005\/gragra.PNG\" style=\"height:143px; width:276px\" \/><\/p>\r\n\r\n<p>\uadf8\ub9ac\uace0 \ub3c4\uc2dc 1\uc5d0\uc11c \ub3c4\uc2dc 4\ub85c \uac00\ub294\ub370\ub294 \ucd1d 4\uac00\uc9c0 \uacbd\ub85c\uac00 \uc874\uc7ac\ud55c\ub2e4. 4\uac00\uc9c0 \uacbd\ub85c\uc5d0 \ub300\ud574 \ucd1d \uc774\ub3d9\uc2dc\uac04\uacfc \uc694\uae08\uc744 \uacc4\uc0b0\ud558\uc5ec \ubcf4\uba74 1-2-4(\uc694\uae08 4, \uc2dc\uac04 5), 1-3-4(\uc694\uae08 4, \uc2dc\uac04 5), 1-2-3-4(\uc694\uae08 6, \uc2dc\uac04 4), 1-3-2-4(\uc694\uae08 4, \ube44\uc6a9 10)\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uadf8\ub9ac\uace0 \uc5ec\uae30\uc11c \uacbd\ub85c 1-3-4\uc640 1-2-4\uac00 \uacbd\ub85c 1-3-2-4\ubcf4\ub2e4 \uc88b\uc740 \uac83\uc744 \uc54c \uc218 \uc788\ub2e4. \uc774 \ub3c4\ub85c\ub9dd\uc5d0\uc11c\ub294 \ud6a8\uc728\uc801\uc778 \uc694\uae08-\uc2dc\uac04 \uc30d\uc774 \ub450 \uac00\uc9c0 \uc874\uc7ac\ud55c\ub2e4. \uc694\uae08 4, \uc2dc\uac04 5(\uacbd\ub85c 1-2-4, 1-3-4), \uc694\uae08 6, \uc2dc\uac04 4(\uacbd\ub85c 1-2-3-4). \ub9cc\uc57d \uc694\uae08\uc744 \ub9ce\uc774 \ub0b4\ub354\ub77c\ub3c4 \ube60\ub978 \uae38\uc744 \uc6d0\ud55c\ub2e4\uba74 \uacbd\ub85c 1-2-3-4\ub97c \uc120\ud0dd\ud558\uba74 \ub418\uace0 \ubc18\ub300\ub85c \uc2dc\uac04\uc740 \uc870\uae08 \ub354 \uac78\ub9ac\ub354\ub77c\ub3c4 \uc694\uae08\uc744 \uc801\uac8c \ub0b4\uace0 \uc2f6\uc73c\uba74 \uacbd\ub85c 1-3-4 \ub610\ub294 1-2-4\ub97c \uc120\ud0dd\ud558\uba74 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\ubb38\uc81c\ub294 \uace0\uc18d\ub3c4\ub85c \ub3c4\ub85c\ub9dd\uc5d0 \ub300\ud55c \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c0\uba74 \uc2dc\uc791 \ub3c4\uc2dc\uc5d0\uc11c \ub05d \ub3c4\uc2dc\uae4c\uc9c0 \uc5f0\uacb0\ud558\ub294 \ud6a8\uc728\uc801\uc778 \uacbd\ub85c\ub97c \uacc4\uc0b0\ud558\ub294 \uac83\uc774\ub2e4. \uc6b0\ub9ac\ub294 \ub2e8\uc9c0 \uc11c\ub85c \ub2e4\ub978 \ud6a8\uc728\uc801\uc778 \ube44\uc6a9-\uc2dc\uac04 \uc30d\uc758 \uac1c\uc218\ub9cc \ucd9c\ub825\ud558\uba74 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\ubb38\uc81c\ub294 \uc9c0\uc5ed\ub4e4\uc774 \ub178\ub4dc\ub85c \uad6c\uc131\ub41c \uadf8\ub798\ud504\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c \uc6d0\uc0d8\uc774 \uc6d0\ud558\ub294 \uc9c0\uc5ed \uac04\uc758 \uac70\ub9ac\ub97c \uc2e0\uc18d\ud788 \uc54c\ub824\uc8fc\ub294 \uac83\uc774\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub3c4\uc2dc\uc758 \uac1c\uc218 n(1&le;n&le;100), \ub3c4\ub85c\uc758 \uac1c\uc218 m(1&le;m&le;300), \uc2dc\uc791 \ub3c4\uc2dc s, \ub3c4\ucc29 \ub3c4\uc2dc e\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1&le;s,e&le;n, s&ne;e) \uadf8 \ub2e4\uc74c\ubd80\ud130 m\uac1c\uc758 \uc904\uc5d0 \ub3c4\ub85c\uc5d0 \ub300\ud55c \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c0\ub294\ub370 \ud55c \uc904\uc5d0 \ud55c \ub3c4\ub85c\uc758 \uc591 \ub05d\uc810 p, r(1&le;p,r&le;n, p&ne;r)\uacfc \uc694\uae08 c(0&le;c&le;100), \uadf8\ub9ac\uace0 \uc2dc\uac04 t(0&le;t&le;100)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub450 \uac1c \ub3c4\uc2dc \uc0ac\uc774\uc5d0\ub294 \ud55c \uac1c \uc774\uc0c1\uc758 \ub3c4\ub85c\uac00 \uc874\uc7ac\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n","output":"<p>\uccab \uc904\uc5d0 \uc11c\ub85c \ub2e4\ub978 \ud6a8\uc728\uc801\uc778 \ube44\uc6a9-\uc2dc\uac04 \uc30d\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"1702","problem_lang":"1","title":"Bicriterial routing","description":"<p>The network of pay highways in Byteland is growing up very rapidly. It has become so dense, that the choice of the best route is a real problem. The network of highways consists of bidirectional roads connecting cities. Each such road is characterized by the traveling time and the toll to be paid.<\/p>\r\n\r\n<p>The route is composed of consecutive roads to be traveled. The total time needed to travel the route is equal to the sum of traveling times of the roads constituting the route. The total fee for the route is equal to the sum of tolls for the roads of which the route consists. The faster one can travel the route and the lower the fee, the better the route. Strictly speaking, one route is better than the other if one can travel it faster and does not have to pay more, or vice versa: one can pay less and can travel it not slower than the other one. We will call a route connecting two cities minimal if there is no better route connecting these cities. Unfortunately, not always exists one minimal route &ndash; there can be several incomparable routes or there can be no route at all.<\/p>\r\n\r\n<p>The picture below presents an example network of highways. Each road is accompanied by a pair of numbers: the toll and the traveling time.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/high.png\" style=\"height:232px; width:489px\" \/><\/p>\r\n\r\n<p>Let us consider four different routes from city 1 to city 4, together with their fees and traveling times: 1 2 4 (fee 4, time 5), 1 3 4 (fee 4, time 5), 1 2 3 4 (fee 6, time 4) and 1 3 2 4 (fee 4, time 10).<\/p>\r\n\r\n<p>Routes 1 3 4 and 1 2 4 are better than 1 3 2 4. There are two minimal pairs fee time: fee 4, time 5 (roots 1 2 4 and 1 3 4) and fee 6, time 4 (root 1 2 3 4). When choosing the route we have to decide whether we prefer to travel faster but we must pay more (route 1 2 3 4), or we would rather travel slower but cheaper (route 1 3 4 or 1 2 4).<\/p>\r\n\r\n<p>Your task is to write a program, which:<\/p>\r\n\r\n<ul>\r\n\t<li>Reads the description of the highway network and starting and ending cities of the route form the text file bic.in.<\/li>\r\n\t<li>Computes the number of different minimal routes connecting the starting and ending city, however all the routes characterized by the same fee and traveling time count as just one route; we are interested just in the number of different minimal pairs fee time.<\/li>\r\n\t<li>Writes the result to the output file bic.out.<\/li>\r\n<\/ul>\r\n","input":"<p>There are four integers, separated by single spaces, in the first line of the text file bic.in: number of cities n (they are numbered from 1 to n), 1 &le; n &le; 100, number of roads m, 0 &le; m &le; 300, starting city s and ending city e of the route, 1 &le; s, e &le; n, s &ne; e. The consecutive m lines describe the roads, one road per line. Each of these lines contains four integers separated by single spaces: two ends of a road p and r, 1 &le; p, r &le; n, p &ne; r, the toll c, 0 &le; c &le; 100, and the traveling time t, 0 &le; t &le; 100. Two cities can be connected by more than one road.<\/p>\r\n","output":"<p>Your program should write one integer, number of different minimal pairs fee time for routes from s to e, in the first and only line of the text file bic.out.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

Olympiad > Baltic Olympiad in Informatics > BOI 2002 4번