시간 제한메모리 제한제출정답맞힌 사람정답 비율
2 초 128 MB5551767524.671%

문제

학생들은 선생님들과 조교들이 스타를 하러 간 사이에 여러 방에 들어가 신나게 놀고 있었다. 그리고 시간이 되어 놀던 방에서 자려고 했지만 각 방에서 잘 수 있는 사람의 수가 정해져 있어서 불가피하게 몇몇 학생들은 방을 옮겨 자야한다. 하지만 학생들이 옮기는 시간 중에 스타를 끝내고 오신 원장선생님과 마주치게 되면 안되기 때문에 고민에 빠져있다. 결국 최대한 빠른 시간에 모든 학생들이 방에 잘 수 있는 제한 수를 넘지 않으면서 적당한 방에 숨어 자려고 한다.

F개의 방에 학생들이 현재 숨어 있고, 이 방들을 연결하는 P개의 통로가 있다. 통로의 폭은 넓기 때문에 동시에 한 통로에 지나가는 학생 수의 제한은 없고 양방으로 통행 가능하다.

모든 방의 제한이 넘지 않도록 학생들이 이동해야 하는 최소 시간을 출력하는 것이 문제이다. 물론 몇몇 학생들은 현재 방에 있을 수 있다. (근데, 아마 이 시간보다 스타가 빨리 끝날듯..)

입력

첫 번째 줄에 F(1≤F≤200), P(1≤P≤1,500)가 주어진다. 2번째 줄부터 F개의 줄까지 i번째 줄에는 i-1번째 방에 현재 있는 학생 수와 그 방에 잘 수 있는 학생 수가 빈칸으로 구분되어 주어진다. 두 수 모두 0 이상 1000 이하의 수이다. 다음 P개의 줄에는 한 통로가 연결되는 두 방과 그 통로를 통과하는데 걸리는 시간(≤1,000,000,000)이 주어진다.

출력

학생들이 이동해야 하는 최소 시간을 출력한다. 불가능할 경우 -1을 출력한다.

예제 입력 1

3 4
7 2
0 4
2 6
1 2 40
3 2 70
2 3 90
1 3 120

예제 출력 1

110

힌트

1번 방에 있는 학생 중 2명은 이 방에 남고 4명은 2번 방에 이동하며, 남은 1명은 3번 방으로 가면 총 110의 시간이 소요된다.

[{"problem_id":"1745","problem_lang":"0","title":"\uc228\uae30","description":"<p>\ud559\uc0dd\ub4e4\uc740 \uc120\uc0dd\ub2d8\ub4e4\uacfc \uc870\uad50\ub4e4\uc774 \uc2a4\ud0c0\ub97c \ud558\ub7ec \uac04 \uc0ac\uc774\uc5d0 \uc5ec\ub7ec \ubc29\uc5d0 \ub4e4\uc5b4\uac00 \uc2e0\ub098\uac8c \ub180\uace0 \uc788\uc5c8\ub2e4. \uadf8\ub9ac\uace0 \uc2dc\uac04\uc774 \ub418\uc5b4 \ub180\ub358 \ubc29\uc5d0\uc11c \uc790\ub824\uace0 \ud588\uc9c0\ub9cc \uac01 \ubc29\uc5d0\uc11c \uc798 \uc218 \uc788\ub294 \uc0ac\ub78c\uc758 \uc218\uac00 \uc815\ud574\uc838 \uc788\uc5b4\uc11c \ubd88\uac00\ud53c\ud558\uac8c \uba87\uba87 \ud559\uc0dd\ub4e4\uc740 \ubc29\uc744 \uc62e\uaca8 \uc790\uc57c\ud55c\ub2e4. \ud558\uc9c0\ub9cc \ud559\uc0dd\ub4e4\uc774 \uc62e\uae30\ub294 \uc2dc\uac04 \uc911\uc5d0 \uc2a4\ud0c0\ub97c \ub05d\ub0b4\uace0 \uc624\uc2e0 \uc6d0\uc7a5\uc120\uc0dd\ub2d8\uacfc \ub9c8\uc8fc\uce58\uac8c \ub418\uba74 \uc548\ub418\uae30 \ub54c\ubb38\uc5d0 \uace0\ubbfc\uc5d0 \ube60\uc838\uc788\ub2e4. \uacb0\uad6d \ucd5c\ub300\ud55c \ube60\ub978 \uc2dc\uac04\uc5d0  \ubaa8\ub4e0 \ud559\uc0dd\ub4e4\uc774 \ubc29\uc5d0 \uc798 \uc218 \uc788\ub294 \uc81c\ud55c \uc218\ub97c \ub118\uc9c0 \uc54a\uc73c\uba74\uc11c \uc801\ub2f9\ud55c \ubc29\uc5d0 \uc228\uc5b4 \uc790\ub824\uace0 \ud55c\ub2e4.  <\/p>\r\n\r\n<p>F\uac1c\uc758 \ubc29\uc5d0 \ud559\uc0dd\ub4e4\uc774 \ud604\uc7ac \uc228\uc5b4 \uc788\uace0, \uc774 \ubc29\ub4e4\uc744 \uc5f0\uacb0\ud558\ub294 P\uac1c\uc758 \ud1b5\ub85c\uac00 \uc788\ub2e4. \ud1b5\ub85c\uc758 \ud3ed\uc740 \ub113\uae30 \ub54c\ubb38\uc5d0 \ub3d9\uc2dc\uc5d0 \ud55c \ud1b5\ub85c\uc5d0 \uc9c0\ub098\uac00\ub294 \ud559\uc0dd \uc218\uc758 \uc81c\ud55c\uc740 \uc5c6\uace0 \uc591\ubc29\uc73c\ub85c \ud1b5\ud589 \uac00\ub2a5\ud558\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \ubc29\uc758 \uc81c\ud55c\uc774 \ub118\uc9c0 \uc54a\ub3c4\ub85d \ud559\uc0dd\ub4e4\uc774 \uc774\ub3d9\ud574\uc57c \ud558\ub294 \ucd5c\uc18c \uc2dc\uac04\uc744 \ucd9c\ub825\ud558\ub294 \uac83\uc774 \ubb38\uc81c\uc774\ub2e4. \ubb3c\ub860 \uba87\uba87 \ud559\uc0dd\ub4e4\uc740 \ud604\uc7ac \ubc29\uc5d0 \uc788\uc744 \uc218 \uc788\ub2e4. (\uadfc\ub370, \uc544\ub9c8 \uc774 \uc2dc\uac04\ubcf4\ub2e4 \uc2a4\ud0c0\uac00 \ube68\ub9ac \ub05d\ub0a0\ub4ef..)<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 F(1&le;F&le;200), P(1&le;P&le;1,500)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. 2\ubc88\uc9f8 \uc904\ubd80\ud130 F\uac1c\uc758 \uc904\uae4c\uc9c0 i\ubc88\uc9f8 \uc904\uc5d0\ub294 i-1\ubc88\uc9f8 \ubc29\uc5d0 \ud604\uc7ac \uc788\ub294 \ud559\uc0dd \uc218\uc640 \uadf8 \ubc29\uc5d0 \uc798 \uc218 \uc788\ub294 \ud559\uc0dd \uc218\uac00 \ube48\uce78\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. \ub450 \uc218 \ubaa8\ub450 0 \uc774\uc0c1 1000 \uc774\ud558\uc758 \uc218\uc774\ub2e4. \ub2e4\uc74c P\uac1c\uc758 \uc904\uc5d0\ub294 \ud55c \ud1b5\ub85c\uac00 \uc5f0\uacb0\ub418\ub294 \ub450 \ubc29\uacfc \uadf8 \ud1b5\ub85c\ub97c \ud1b5\uacfc\ud558\ub294\ub370 \uac78\ub9ac\ub294 \uc2dc\uac04(&le;1,000,000,000)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\ud559\uc0dd\ub4e4\uc774 \uc774\ub3d9\ud574\uc57c \ud558\ub294 \ucd5c\uc18c \uc2dc\uac04\uc744 \ucd9c\ub825\ud55c\ub2e4. \ubd88\uac00\ub2a5\ud560 \uacbd\uc6b0 -1\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>1\ubc88 \ubc29\uc5d0 \uc788\ub294 \ud559\uc0dd \uc911 2\uba85\uc740 \uc774 \ubc29\uc5d0 \ub0a8\uace0 4\uba85\uc740 2\ubc88 \ubc29\uc5d0 \uc774\ub3d9\ud558\uba70, \ub0a8\uc740 1\uba85\uc740 3\ubc88 \ubc29\uc73c\ub85c \uac00\uba74 \ucd1d 110\uc758 \uc2dc\uac04\uc774 \uc18c\uc694\ub41c\ub2e4.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"1745","problem_lang":"1","title":"Ombrophobic Bovines","description":"<p>FJ&#39;s cows really hate getting wet so much that the mere thought of getting caught in the rain makes them shake in their hooves. They have decided to put a rain siren on the farm to let them know when rain is approaching. They intend to create a rain evacuation plan so that all the cows can get to shelter before the rain begins. Weather forecasting is not always correct, though. In order to minimize false alarms, they want to sound the siren as late as possible while still giving enough time for all the cows to get to some shelter.<\/p>\r\n\r\n<p>The farm has F (1 &lt;= F &lt;= 200) fields on which the cows graze. A set of P (1 &lt;= P &lt;= 1500) paths connects them. The paths are wide, so that any number of cows can traverse a path in either direction.<\/p>\r\n\r\n<p>Some of the farm&#39;s fields have rain shelters under which the cows can shield themselves. These shelters are of limited size, so a single shelter might not be able to hold all the cows. Fields are small compared to the paths and require no time for cows to traverse.<\/p>\r\n\r\n<p>Compute the minimum amount of time before rain starts that the siren must be sounded so that every cow can get to some shelter.<\/p>\r\n","input":"<ul>\r\n\t<li>Line 1: Two space-separated integers: F and P<\/li>\r\n\t<li>Lines 2..F+1: Two space-separated integers that describe a field. The first integer (range: 0..1000) is the number of cows in that field. The second integer (range: 0..1000) is the number of cows the shelter in that field can hold. Line i+1 describes field i.<\/li>\r\n\t<li>Lines F+2..F+P+1: Three space-separated integers that describe a path. The first and second integers (both range 1..F) tell the fields connected by the path. The third integer (range: 1..1,000,000,000) is how long any cow takes to traverse it.<\/li>\r\n<\/ul>\r\n","output":"<ul>\r\n\t<li>Line 1: The minimum amount of time required for all cows to get under a shelter, presuming they plan their routes optimally. If it not possible for the all the cows to get under a shelter, output &quot;-1&quot;.<\/li>\r\n<\/ul>\r\n","hint":"<p>In 110 time units, two cows from field 1 can get under the shelter in that field, four cows from field 1 can get under the shelter in field 2, and one cow can get to field 3 and join the cows from that field under the shelter in field 3. Although there are other plans that will get all the cows under a shelter, none will do it in fewer than 110 time units.<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

Olympiad > USA Computing Olympiad > 2004-2005 Season > USACO March 2005 Contest > Gold 1번

  • 문제를 번역한 사람: author6