시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

인도네시아에는 N 개의 도시가 있고, 0부터 N - 1까지 번호가 매겨져 있다. 또 M 개의 양방향 도로가 있는데, 0 부터 M - 1까지 번호가 매겨져 있다. 각 도로는 두 개의 서로 다른 도시를 연결한다. i 번 도로는 U[i] 번 도시와 V[i] 번 도시를 연결하고, 자동차로 여행하려면 휘발유 W[i] 만큼이 필요하다. 어떤 두 도시도 서로 오갈 수 있도록 도로망이 구축되어 있다.

앞으로 Q 일 동안, 매일매일 한 쌍의 도시가 자매 도시 관계를 맺으려고 한다. 구체적으로는, j번째 날, X[j] 번 도시는 Y[j] 번 도시와 자매 도시 관계를 맺으려고 한다. 이러려면, X[j] 번 도시는 대표단을 자동차를 이용해서 Y[j] 번 도시로 보낸다. 비슷하게, Y[j] 번 도시도 대표단을 자동차를 이용해서 X[j] 번 도시로 보낸다.  

혼잡을 막기 위해서, 두 자동차는 어느 순간에도 만나면 안된다. 보다 구체적으로는, 두 자동차가 동시에 같은 도시에 있으면 안된다. 또, 같은 도로를 동시에 서로 반대 방향으로 여행해도 안된다. 추가로, 어떤 도로를 여행하는 자동차는 이 도로를 끝까지 가서 목적지에 도착해야 한다. (다른 말로 하면, 도로 중간에서 유턴할 수 없다.) 그렇지만, 자동차는 같은 도시 또는 같은 도로를 한 번 이상 방문할 수 있다. 또, 자동차는 언제든지 어떤 도시에서든지 대기할 수 있다.   

연료 탱크가 큰 자동차는 비싸기 때문에, 두 도시는 사용할 두 자동차의 연료 탱크의 최대 용량을 최소화하는 경로를 택하고 싶다. 각각의 도시에는 무한히 많은 휘발유가 있는 주유소가 있기 때문에, 자동차가 필요한 연료 탱크의 최대 용량은 자동차가 이용할 모든 도로에서 최대로 필요한 휘발유의 양이다.  

할 일

다음 init와 getMinimumFuelCapacity 함수를 구현해야 한다.  

  • init(N, M, U, V, W) - 이 함수는  getMinimumFuelCapacity 함수를 호출하기 전에 정확히 한 번 호출된다.  
    • N: 도시의 수를 나타내는 정수.
    • M: 도로의 수를 나타내는 정수.  
    • U: 길이 M인 정수의 배열로 도로의 한 쪽 끝을 나타낸다. 
    • V: 길이 M인 정수의 배열로 도로의 다른 쪽 끝을 나타낸다. 
    • W: 길이 M인 정수의 배열로 각 도로를 여행하는데 필요한 휘발유의 양을 나타낸다.
  • getMinimumFuelCapacity(X, Y) - 이 함수는 그레이더가 정확히 Q 번 호출한다.  
    • X: 첫번째 도시를 나타내는 정수.  
    • Y: 두번째 도시를 나타내는 정수.
    • 이 함수는 X번 도시의 대표단이 Y번 도시로, Y번 도시의 대표단이 X번 도시로 위에서 설명한 규칙을 따라 여행할 때 두 자동차가 필요한 연료 탱크의 최대 용량의 최소값을 리턴한다.  만약 규칙을 따라 여행하는 것이 불가능하다면, -1을 리턴한다.  

예제

첫번째 예제에서, N = 5, M = 6, U = [0, 0, 1, 1, 1, 2], V = [1, 2, 2, 3, 4, 3], W = [4, 4, 1, 2, 10, 3], Q = 3, X = [1, 2, 0], Y = [2, 4, 1]이다. 이 예제는 다음 그림과 같다.

그레이더는 처음에 init(5, 6, [0, 0, 1, 1, 1, 2], [1, 2, 2, 3, 4, 3], [4, 4, 1, 2, 10, 3])를 호출한다. 그 후, 그레이더는 다음 일들을 한다.

  • getMinimumFuelCapacity(1, 2). 먼저, 1번 도시에서 출발한 자동차는 3번 도시로 이동한다. 다음, 2번 도시에서 출발한 자동차는 1번 도시로 이동하고, 3번 도시에 있던 자동차는 2번 도시로 이동한다. 따라서 두 자동차가 필요한 연료 용량의 최대값은 3이다. (3번 도시에서 2번 도시로 이동하는데 필요) 이보다 적은 연료 용량으로 갈 수 있는 경로가 없기 때문에, 이 함수의 리턴값은 3이어야 한다.
  • getMinimumFuelCapacity(2, 4). 4번 도시에서 오거나 4번 도시로 가는 자동차는 연료가 10만큼 필요하기 때문에, 이 함수의 리턴값은 10이어야 한다.
  • getMinimumFuelCapacity(0, 1). 이 함수는 4를 리턴해야 한다.

두번째 예제에서는, N = 3, M = 2, U = [0, 0], V = [1, 2], W = [5, 5], Q = 1, X = [1], Y = [2]이다. 이 예제는 다음 그림과 같다.

그레이더는 처음에 init(3, 2, [0, 0], [1, 2], [5, 5])를 호출한다. 그 후, 그레이더는 다음 일을 한다.  

  • getMinimumFuelCapacity(1, 2). 자동차가 1번 도시에서 2번 도시로 이동하는 과정에서 다른 자동차를 만나지 않는 것은 불가능하기 때문에, 이 함수는 -1을 리턴해야 한다.

제한

  • 2 ≤ N ≤ 100000.
  • N − 1 ≤ M ≤ 200000.
  • 0 ≤ U[i] < V[i] < N.
  • 두 도시를 잇는 도로는 최대 1개이다.  
  • 어떤 두 도시도 하나 또는 둘 이상의 도로를 이용하여 오갈 수 있다.  
  • 1 ≤ W[i] ≤ 109.
  • 1 ≤ Q ≤ 200000.
  • 0 ≤ X[j] < Y[j] < N.

서브태스크 1 (6점)

  • 각 도시는 최대 2개의 도로의 끝점이다.

서브태스크 2 (7점)

  • M = N − 1.
  • U[i] = 0.

서브태스크 3 (17점)

  • Q ≤ 5.
  • N ≤ 1000.
  • M ≤ 2000.

서브태스크 4 (20점)

  • Q ≤ 5.

서브태스크 5 (23점)

  • M = N - 1.

서브태스크 6 (27점)

  • 추가적인 제약 조건이 없다.
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(\ub2e4\ub978 \ub9d0\ub85c \ud558\uba74, \ub3c4\ub85c \uc911\uac04\uc5d0\uc11c \uc720\ud134\ud560 \uc218 \uc5c6\ub2e4.) \uadf8\ub807\uc9c0\ub9cc, \uc790\ub3d9\ucc28\ub294 \uac19\uc740 \ub3c4\uc2dc \ub610\ub294 \uac19\uc740 \ub3c4\ub85c\ub97c \ud55c \ubc88 \uc774\uc0c1 \ubc29\ubb38\ud560 \uc218 \uc788\ub2e4. \ub610, \uc790\ub3d9\ucc28\ub294 \uc5b8\uc81c\ub4e0\uc9c0 \uc5b4\ub5a4 \ub3c4\uc2dc\uc5d0\uc11c\ub4e0\uc9c0&nbsp;\ub300\uae30\ud560 \uc218 \uc788\ub2e4.&nbsp;&nbsp;&nbsp;<\/p>\r\n\r\n<p>\uc5f0\ub8cc \ud0f1\ud06c\uac00 \ud070 \uc790\ub3d9\ucc28\ub294&nbsp;\ube44\uc2f8\uae30 \ub54c\ubb38\uc5d0, \ub450 \ub3c4\uc2dc\ub294 \uc0ac\uc6a9\ud560 \ub450 \uc790\ub3d9\ucc28\uc758 \uc5f0\ub8cc \ud0f1\ud06c\uc758 \ucd5c\ub300 \uc6a9\ub7c9\uc744 \ucd5c\uc18c\ud654\ud558\ub294 \uacbd\ub85c\ub97c \ud0dd\ud558\uace0 \uc2f6\ub2e4. \uac01\uac01\uc758 \ub3c4\uc2dc\uc5d0\ub294 \ubb34\ud55c\ud788 \ub9ce\uc740 \ud718\ubc1c\uc720\uac00 \uc788\ub294 \uc8fc\uc720\uc18c\uac00 \uc788\uae30 \ub54c\ubb38\uc5d0, \uc790\ub3d9\ucc28\uac00 \ud544\uc694\ud55c&nbsp;\uc5f0\ub8cc \ud0f1\ud06c\uc758 \ucd5c\ub300 \uc6a9\ub7c9\uc740 \uc790\ub3d9\ucc28\uac00 \uc774\uc6a9\ud560 \ubaa8\ub4e0 \ub3c4\ub85c\uc5d0\uc11c&nbsp;<strong>\ucd5c\ub300<\/strong>\ub85c \ud544\uc694\ud55c \ud718\ubc1c\uc720\uc758 \uc591\uc774\ub2e4.&nbsp;&nbsp;<\/p>\r\n","input":"","output":"","hint":"","original":"1","problem_lang_code":"\ud55c\uad6d\uc5b4","limit":"<ul>\r\n\t<li>2 &le; <em>N<\/em> &le; 100000.<\/li>\r\n\t<li><em>N<\/em> &minus; 1 &le; <em>M<\/em> &le; 200000.<\/li>\r\n\t<li>0 &le; <em>U<\/em>[<em>i<\/em>] &lt; <em>V<\/em>[<em>i<\/em>] &lt; <em>N<\/em>.<\/li>\r\n\t<li>\ub450 \ub3c4\uc2dc\ub97c \uc787\ub294 \ub3c4\ub85c\ub294 \ucd5c\ub300 1\uac1c\uc774\ub2e4.&nbsp;&nbsp;<\/li>\r\n\t<li>\uc5b4\ub5a4 \ub450 \ub3c4\uc2dc\ub3c4 \ud558\ub098 \ub610\ub294 \ub458 \uc774\uc0c1\uc758 \ub3c4\ub85c\ub97c \uc774\uc6a9\ud558\uc5ec \uc624\uac08 \uc218 \uc788\ub2e4.&nbsp;&nbsp;<\/li>\r\n\t<li>1 &le; <em>W<\/em>[<em>i<\/em>] &le; 10<sup>9<\/sup>.<\/li>\r\n\t<li>1 &le; <em>Q<\/em> &le; 200000.<\/li>\r\n\t<li>0 &le; <em>X<\/em>[<em>j<\/em>] &lt; <em>Y<\/em>[<em>j<\/em>] &lt; N.<\/li>\r\n<\/ul>\r\n","subtask1":"<ul>\r\n\t<li>\uac01 \ub3c4\uc2dc\ub294 \ucd5c\ub300 2\uac1c\uc758 \ub3c4\ub85c\uc758 \ub05d\uc810\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n","subtask2":"<ul>\r\n\t<li><em>M<\/em> = <em>N<\/em>&nbsp;&minus; 1.<\/li>\r\n\t<li><em>U<\/em>[<em>i<\/em>] = 0.<\/li>\r\n<\/ul>\r\n","subtask3":"<ul>\r\n\t<li><em>Q<\/em> &le; 5.<\/li>\r\n\t<li><em>N<\/em>&nbsp;&le; 1000.<\/li>\r\n\t<li><em>M<\/em> &le; 2000.<\/li>\r\n<\/ul>\r\n","subtask4":"<ul>\r\n\t<li><em>Q<\/em> &le; 5.<\/li>\r\n<\/ul>\r\n","subtask5":"<ul>\r\n\t<li><em>M<\/em> = <em>N<\/em> - 1.<\/li>\r\n<\/ul>\r\n","subtask6":"<ul>\r\n\t<li>\ucd94\uac00\uc801\uc778 \uc81c\uc57d \uc870\uac74\uc774 \uc5c6\ub2e4.<\/li>\r\n<\/ul>\r\n","custom_task":"<p>\ub2e4\uc74c&nbsp;<code>init<\/code>\uc640&nbsp;<code>getMinimumFuelCapacity<\/code>&nbsp;\ud568\uc218\ub97c \uad6c\ud604\ud574\uc57c \ud55c\ub2e4.&nbsp;&nbsp;<\/p>\r\n\r\n<ul>\r\n\t<li><code>init(N, M, U, V, W)<\/code>&nbsp;- \uc774 \ud568\uc218\ub294&nbsp;&nbsp;<code>getMinimumFuelCapacity&nbsp;<\/code>\ud568\uc218\ub97c \ud638\ucd9c\ud558\uae30 \uc804\uc5d0 \uc815\ud655\ud788 \ud55c \ubc88 \ud638\ucd9c\ub41c\ub2e4.&nbsp;&nbsp;\r\n\r\n\t<ul>\r\n\t\t<li><em>N<\/em>: \ub3c4\uc2dc\uc758 \uc218\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218.<\/li>\r\n\t\t<li><em>M<\/em>: \ub3c4\ub85c\uc758 \uc218\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218.&nbsp;&nbsp;<\/li>\r\n\t\t<li><em>U<\/em>: \uae38\uc774&nbsp;<em>M<\/em>\uc778 \uc815\uc218\uc758 \ubc30\uc5f4\ub85c \ub3c4\ub85c\uc758 \ud55c \ucabd \ub05d\uc744 \ub098\ud0c0\ub0b8\ub2e4.&nbsp;<\/li>\r\n\t\t<li><em>V<\/em>: \uae38\uc774&nbsp;<em>M<\/em>\uc778 \uc815\uc218\uc758 \ubc30\uc5f4\ub85c \ub3c4\ub85c\uc758 \ub2e4\ub978&nbsp;\ucabd \ub05d\uc744 \ub098\ud0c0\ub0b8\ub2e4.&nbsp;<\/li>\r\n\t\t<li><em>W<\/em>: \uae38\uc774 <em>M<\/em>\uc778 \uc815\uc218\uc758 \ubc30\uc5f4\ub85c \uac01 \ub3c4\ub85c\ub97c \uc5ec\ud589\ud558\ub294\ub370 \ud544\uc694\ud55c \ud718\ubc1c\uc720\uc758 \uc591\uc744 \ub098\ud0c0\ub0b8\ub2e4.<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n\t<li><code>getMinimumFuelCapacity(X, Y)<\/code>&nbsp;- \uc774 \ud568\uc218\ub294 \uadf8\ub808\uc774\ub354\uac00 \uc815\ud655\ud788&nbsp;<em>Q<\/em> \ubc88 \ud638\ucd9c\ud55c\ub2e4.&nbsp;&nbsp;\r\n\t<ul>\r\n\t\t<li><em>X<\/em>: \uccab\ubc88\uc9f8 \ub3c4\uc2dc\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218.&nbsp;&nbsp;<\/li>\r\n\t\t<li><em>Y<\/em>: \ub450\ubc88\uc9f8 \ub3c4\uc2dc\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218.<\/li>\r\n\t\t<li>\uc774 \ud568\uc218\ub294&nbsp;<em>X<\/em>\ubc88 \ub3c4\uc2dc\uc758 \ub300\ud45c\ub2e8\uc774 <em>Y<\/em>\ubc88 \ub3c4\uc2dc\ub85c, <em>Y<\/em>\ubc88 \ub3c4\uc2dc\uc758 \ub300\ud45c\ub2e8\uc774 <em>X<\/em>\ubc88 \ub3c4\uc2dc\ub85c \uc704\uc5d0\uc11c \uc124\uba85\ud55c \uaddc\uce59\uc744 \ub530\ub77c \uc5ec\ud589\ud560 \ub54c \ub450 \uc790\ub3d9\ucc28\uac00 \ud544\uc694\ud55c&nbsp;\uc5f0\ub8cc \ud0f1\ud06c\uc758 \ucd5c\ub300 \uc6a9\ub7c9\uc758 \ucd5c\uc18c\uac12\uc744 \ub9ac\ud134\ud55c\ub2e4.&nbsp;&nbsp;\ub9cc\uc57d \uaddc\uce59\uc744 \ub530\ub77c \uc5ec\ud589\ud558\ub294 \uac83\uc774 \ubd88\uac00\ub2a5\ud558\ub2e4\uba74,&nbsp;-1\uc744 \ub9ac\ud134\ud55c\ub2e4.&nbsp;&nbsp;<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n<\/ul>\r\n","custom_example":"<p>\uccab\ubc88\uc9f8 \uc608\uc81c\uc5d0\uc11c,&nbsp;<em>N<\/em> = 5,&nbsp;<em>M<\/em> = 6,&nbsp;<em>U<\/em> = [0, 0, 1, 1, 1, 2],&nbsp;<em>V<\/em> = [1, 2, 2, 3, 4, 3], <em>W<\/em> = [4, 4, 1, 2, 10, 3],&nbsp;<em>Q<\/em> = 3,&nbsp;<em>X<\/em> = [1, 2, 0],&nbsp;<em>Y<\/em> = [2, 4, 1]\uc774\ub2e4. \uc774 \uc608\uc81c\ub294 \ub2e4\uc74c \uadf8\ub9bc\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/b2d9c304-c42d-4630-b10b-2c71ef99b61d\/-\/preview\/\" style=\"width: 268px; height: 200px;\" \/><\/p>\r\n\r\n<p>\uadf8\ub808\uc774\ub354\ub294 \ucc98\uc74c\uc5d0&nbsp;<code>init(5, 6, [0, 0, 1, 1, 1, 2], [1, 2, 2, 3, 4, 3], [4, 4, 1, 2, 10, 3])<\/code>\ub97c \ud638\ucd9c\ud55c\ub2e4. \uadf8 \ud6c4, \uadf8\ub808\uc774\ub354\ub294 \ub2e4\uc74c \uc77c\ub4e4\uc744 \ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li><code>getMinimumFuelCapacity(1, 2)<\/code>. \uba3c\uc800, 1\ubc88 \ub3c4\uc2dc\uc5d0\uc11c \ucd9c\ubc1c\ud55c \uc790\ub3d9\ucc28\ub294 3\ubc88 \ub3c4\uc2dc\ub85c \uc774\ub3d9\ud55c\ub2e4. \ub2e4\uc74c, 2\ubc88 \ub3c4\uc2dc\uc5d0\uc11c \ucd9c\ubc1c\ud55c \uc790\ub3d9\ucc28\ub294 1\ubc88 \ub3c4\uc2dc\ub85c \uc774\ub3d9\ud558\uace0, 3\ubc88 \ub3c4\uc2dc\uc5d0 \uc788\ub358 \uc790\ub3d9\ucc28\ub294 2\ubc88 \ub3c4\uc2dc\ub85c \uc774\ub3d9\ud55c\ub2e4. \ub530\ub77c\uc11c \ub450 \uc790\ub3d9\ucc28\uac00 \ud544\uc694\ud55c \uc5f0\ub8cc \uc6a9\ub7c9\uc758 \ucd5c\ub300\uac12\uc740&nbsp;3\uc774\ub2e4.&nbsp;(3\ubc88 \ub3c4\uc2dc\uc5d0\uc11c 2\ubc88 \ub3c4\uc2dc\ub85c \uc774\ub3d9\ud558\ub294\ub370 \ud544\uc694) \uc774\ubcf4\ub2e4 \uc801\uc740 \uc5f0\ub8cc \uc6a9\ub7c9\uc73c\ub85c \uac08 \uc218 \uc788\ub294 \uacbd\ub85c\uac00 \uc5c6\uae30 \ub54c\ubb38\uc5d0, \uc774 \ud568\uc218\uc758 \ub9ac\ud134\uac12\uc740&nbsp;3\uc774\uc5b4\uc57c \ud55c\ub2e4.<\/li>\r\n\t<li><code>getMinimumFuelCapacity(2, 4)<\/code>. 4\ubc88 \ub3c4\uc2dc\uc5d0\uc11c \uc624\uac70\ub098 4\ubc88 \ub3c4\uc2dc\ub85c \uac00\ub294 \uc790\ub3d9\ucc28\ub294 \uc5f0\ub8cc\uac00&nbsp;10\ub9cc\ud07c \ud544\uc694\ud558\uae30 \ub54c\ubb38\uc5d0, \uc774 \ud568\uc218\uc758 \ub9ac\ud134\uac12\uc740&nbsp;10\uc774\uc5b4\uc57c \ud55c\ub2e4.<\/li>\r\n\t<li><code>getMinimumFuelCapacity(0, 1)<\/code>. \uc774 \ud568\uc218\ub294&nbsp;4\ub97c \ub9ac\ud134\ud574\uc57c \ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ub450\ubc88\uc9f8 \uc608\uc81c\uc5d0\uc11c\ub294,&nbsp;<em>N<\/em> = 3,&nbsp;<em>M<\/em> = 2,&nbsp;<em>U<\/em> = [0, 0],&nbsp;<em>V<\/em> = [1, 2],&nbsp;<em>W<\/em> = [5, 5],&nbsp;<em>Q<\/em> = 1,&nbsp;<em>X<\/em> = [1],&nbsp;<em>Y<\/em> = [2]\uc774\ub2e4. \uc774 \uc608\uc81c\ub294 \ub2e4\uc74c \uadf8\ub9bc\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/abad6b77-2e91-4129-b45e-dc103bdba8b2\/-\/preview\/\" style=\"width: 157px; height: 200px;\" \/><\/p>\r\n\r\n<p>\uadf8\ub808\uc774\ub354\ub294 \ucc98\uc74c\uc5d0&nbsp;<code>init(3, 2, [0, 0], [1, 2], [5, 5])<\/code>\ub97c \ud638\ucd9c\ud55c\ub2e4. \uadf8 \ud6c4, \uadf8\ub808\uc774\ub354\ub294 \ub2e4\uc74c \uc77c\uc744 \ud55c\ub2e4.&nbsp;&nbsp;<\/p>\r\n\r\n<ul>\r\n\t<li><code>getMinimumFuelCapacity(1, 2)<\/code>. \uc790\ub3d9\ucc28\uac00 1\ubc88 \ub3c4\uc2dc\uc5d0\uc11c 2\ubc88 \ub3c4\uc2dc\ub85c \uc774\ub3d9\ud558\ub294 \uacfc\uc815\uc5d0\uc11c \ub2e4\ub978 \uc790\ub3d9\ucc28\ub97c \ub9cc\ub098\uc9c0 \uc54a\ub294 \uac83\uc740 \ubd88\uac00\ub2a5\ud558\uae30 \ub54c\ubb38\uc5d0, \uc774 \ud568\uc218\ub294&nbsp;-1\uc744 \ub9ac\ud134\ud574\uc57c \ud55c\ub2e4.<\/li>\r\n<\/ul>\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<pre>\r\nN M\r\nU[0] V[0] W[0]\r\nU[1] V[1] W[1]\r\n.\r\n.\r\n.\r\nU[M-1] V[M-1] W[M-1]\r\nQ\r\nX[0] Y[0]\r\nX[1] Y[1]\r\n.\r\n.\r\n.\r\nX[Q-1] Y[Q-1]\r\n<\/pre>\r\n\r\n<p>\uc0d8\ud50c \uadf8\ub808\uc774\ub354\ub294&nbsp;<code>getMinimumFuelCapacity<\/code>&nbsp;\ud568\uc218\ub97c \ud638\ucd9c\ud560 \ub54c\ub9c8\ub2e4, \uc774 \ud568\uc218\uc758 \ub9ac\ud134\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","custom_attachment":"<p>\uacf5\uac1c\ub41c \uadf8\ub808\uc774\ub354, \uc608\uc81c \ucf00\uc774\uc2a4, \ubb38\uc81c\uc5d0 \ub300\ud55c \uae30\ubcf8 \ud30c\uc77c\uc740&nbsp;<a href=\"https:\/\/upload.acmicpc.net\/6939eef7-244a-4868-bb3a-d6d5d1a867f3\/\">\uc5ec\uae30<\/a>\uc5d0\uc11c \ubc1b\uc744 \uc218 \uc788\ub2e4.&nbsp;<\/p>\r\n"},{"problem_id":"19619","problem_lang":"1","title":"Swapping Cities","description":"<p>There are&nbsp;<em>N<\/em> cities in Indonesia, numbered from&nbsp;0&nbsp;to&nbsp;<em>N<\/em> - 1. There are also&nbsp;<em>M<\/em> two-way roads, numbered from&nbsp;0 to&nbsp;<em>M<\/em> - 1. Each road connects two different cities. The&nbsp;<em>i<\/em>-th road connects the <em>U<\/em>[<em>i<\/em>]-th city and the <em>V<\/em>[<em>i<\/em>]-th city and consumes <em>W<\/em>[<em>i<\/em>]&nbsp;units of gas when traversed by car. The cities are connected such that it is possible to travel between any pair of cities through the roads.<\/p>\r\n\r\n<p>For each of the next <em>Q<\/em>&nbsp;days, a pair of cities would like to establish a political relationship. In particular, on the&nbsp;<em>j<\/em>-th day, the <em>X<\/em>[<em>j<\/em>]-th city would like to establish a political relationship with the <em>Y<\/em>[<em>j<\/em>]-th city. In order to do this, the <em>X<\/em>[<em>j<\/em>]-th city should send a representative to go to the&nbsp;Y[j]Y[j]-th city by car. Similarly, the <em>Y<\/em>[<em>j<\/em>]-th city should also send a representative to go to the <em>X<\/em>[<em>j<\/em>]-th city by car.<\/p>\r\n\r\n<p>To avoid congestion, both cars should not meet at any point in time. In particular, both cars should not be in the same city at the same time. Also, both cars should not traverse the same road in the opposite direction at the same time. Additionally, cars that traverse the road must complete the road and go to the destination city (in other words, cars are not allowed to make a U-turn in the middle of a road). However, cars are allowed to visit the same city and road more than once. In addition, cars may also wait at any city at any point in time.<\/p>\r\n\r\n<p>Since cars with high fuel capacity are expensive, both cities would like to choose routes for both cars such that the maximum fuel capacity of the two cars is minimized. There are gas stations in each city with an infinite supply of gas, thus the fuel capacity required by a car is the&nbsp;<strong>maximum<\/strong>&nbsp;gas consumption among all roads traversed by the car.<\/p>\r\n","input":"","output":"","hint":"","original":"0","problem_lang_code":"\uc601\uc5b4","limit":"<ul>\r\n\t<li>2 &le; <em>N<\/em> &le; 100000.<\/li>\r\n\t<li><em>N<\/em> &minus; 1 &le; <em>M<\/em> &le; 200000.<\/li>\r\n\t<li>0 &le; <em>U<\/em>[<em>i<\/em>] &lt; <em>V<\/em>[<em>i<\/em>] &lt; <em>N<\/em>.<\/li>\r\n\t<li>There is at most one road between each pair of cities.<\/li>\r\n\t<li>It is possible to travel between any pair of cities through the roads.<\/li>\r\n\t<li>1 &le; <em>W<\/em>[<em>i<\/em>] &le; 10<sup>9<\/sup>.<\/li>\r\n\t<li>1 &le; <em>Q<\/em> &le; 200000.<\/li>\r\n\t<li>0 &le; <em>X<\/em>[<em>j<\/em>] &lt; <em>Y<\/em>[<em>j<\/em>] &lt; N.<\/li>\r\n<\/ul>\r\n","subtask1":"<ul>\r\n\t<li>Each city is an endpoint of at most two roads.<\/li>\r\n<\/ul>\r\n","subtask2":"<ul>\r\n\t<li><em>M<\/em> = <em>N<\/em>&nbsp;&minus; 1.<\/li>\r\n\t<li><em>U<\/em>[<em>i<\/em>] = 0.<\/li>\r\n<\/ul>\r\n","subtask3":"<ul>\r\n\t<li><em>Q<\/em> &le; 5.<\/li>\r\n\t<li><em>N<\/em>&nbsp;&le; 1000.<\/li>\r\n\t<li><em>M<\/em> &le; 2000.<\/li>\r\n<\/ul>\r\n","subtask4":"<ul>\r\n\t<li><em>Q<\/em> &le; 5.<\/li>\r\n<\/ul>\r\n","subtask5":"<ul>\r\n\t<li><em>M<\/em> = <em>N<\/em> - 1.<\/li>\r\n<\/ul>\r\n","subtask6":"<ul>\r\n\t<li>No additional constraints.<\/li>\r\n<\/ul>\r\n","custom_task":"<p>You have to implement&nbsp;<code>init<\/code>&nbsp;and&nbsp;<code>getMinimumFuelCapacity<\/code>&nbsp;functions.<\/p>\r\n\r\n<ul>\r\n\t<li><code>init(N, M, U, V, W)<\/code>&nbsp;- This function will be called by the grader exactly once before any&nbsp;<code>getMinimumFuelCapacity<\/code>&nbsp;calls.\r\n\r\n\t<ul>\r\n\t\t<li><em>N<\/em>: An integer representing the number of cities.<\/li>\r\n\t\t<li><em>M<\/em>: An integer representing the number of roads.<\/li>\r\n\t\t<li><em>U<\/em>: An array of&nbsp;<em>M<\/em>&nbsp;integers representing the first endpoint of the roads.<\/li>\r\n\t\t<li><em>V<\/em>: An array of&nbsp;<em>M<\/em> integers representing the second endpoint of the roads.<\/li>\r\n\t\t<li><em>W<\/em>: An array of&nbsp;<em>M<\/em>&nbsp;integers representing the gas consumption of the roads.<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n\t<li><code>getMinimumFuelCapacity(X, Y)<\/code>&nbsp;- This function will be called by the grader exactly&nbsp;<em>Q<\/em> times.\r\n\t<ul>\r\n\t\t<li><em>X<\/em>: An integer representing the first city.<\/li>\r\n\t\t<li><em>Y<\/em>: An integer representing the second city.<\/li>\r\n\t\t<li>This function must return an integer representing the minimum unit of fuel capacity of the maximum fuel capacity of the two cars such that a representative from the <em>X<\/em>-th city can go to the&nbsp;<em>Y<\/em>-th city and a representative from the <em>Y<\/em>-th city can go to the&nbsp;<em>X<\/em>-th city following the rules explained in the problem statement, or&nbsp;-1&nbsp;if it is impossible to do so.<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n<\/ul>\r\n","custom_example":"<p>In the first example,&nbsp;<em>N<\/em> = 5,&nbsp;<em>M<\/em> = 6,&nbsp;<em>U<\/em> = [0, 0, 1, 1, 1, 2],&nbsp;<em>V<\/em> = [1, 2, 2, 3, 4, 3], <em>W<\/em> = [4, 4, 1, 2, 10, 3],&nbsp;<em>Q<\/em> = 3,&nbsp;<em>X<\/em> = [1, 2, 0],&nbsp;<em>Y<\/em> = [2, 4, 1]. The example is illustrated by the following image:<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/b2d9c304-c42d-4630-b10b-2c71ef99b61d\/-\/preview\/\" style=\"width: 268px; height: 200px;\" \/><\/p>\r\n\r\n<p>The grader will initially call&nbsp;<code>init(5, 6, [0, 0, 1, 1, 1, 2], [1, 2, 2, 3, 4, 3], [4, 4, 1, 2, 10, 3])<\/code>. After that, the grader will call the following:<\/p>\r\n\r\n<ul>\r\n\t<li><code>getMinimumFuelCapacity(1, 2)<\/code>. First, the car from the first city can go to the third city. Next, the car from the second city can go to the first city, and the car from the third city can go to the second city. Therefore, the maximum fuel capacity of the two cars is&nbsp;3&nbsp;units of fuel (required to go from the third city to the second city. There is no route that requires less fuel capacity, thus the function should return&nbsp;3.<\/li>\r\n\t<li><code>getMinimumFuelCapacity(2, 4)<\/code>. Any car that goes to or from the fourth city should require&nbsp;10 units of fuel capacity, thus the function should return&nbsp;10.<\/li>\r\n\t<li><code>getMinimumFuelCapacity(0, 1)<\/code>. The function should return&nbsp;4.<\/li>\r\n<\/ul>\r\n\r\n<p>In the second example,&nbsp;<em>N<\/em> = 3,&nbsp;<em>M<\/em> = 2,&nbsp;<em>U<\/em> = [0, 0],&nbsp;<em>V<\/em> = [1, 2],&nbsp;<em>W<\/em> = [5, 5],&nbsp;<em>Q<\/em> = 1,&nbsp;<em>X<\/em> = [1],&nbsp;<em>Y<\/em> = [2]. The example is illustrated by the following image:<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/abad6b77-2e91-4129-b45e-dc103bdba8b2\/-\/preview\/\" style=\"width: 157px; height: 200px;\" \/><\/p>\r\n\r\n<p>The grader will initially call&nbsp;<code>init(3, 2, [0, 0], [1, 2], [5, 5])<\/code>. After that, the grader will call the following:<\/p>\r\n\r\n<ul>\r\n\t<li><code>getMinimumFuelCapacity(1, 2)<\/code>. It is impossible for the car in the first city to go to the second city without meeting the other car at some time, thus the function should return&nbsp;-1.<\/li>\r\n<\/ul>\r\n","custom_grader":"<p>The sample grader reads the input in the following format:<\/p>\r\n\r\n<pre>\r\nN M\r\nU[0] V[0] W[0]\r\nU[1] V[1] W[1]\r\n.\r\n.\r\n.\r\nU[M-1] V[M-1] W[M-1]\r\nQ\r\nX[0] Y[0]\r\nX[1] Y[1]\r\n.\r\n.\r\n.\r\nX[Q-1] Y[Q-1]\r\n<\/pre>\r\n\r\n<p>For each&nbsp;<code>getMinimumFuelCapacity<\/code>&nbsp;call, the sample grader prints the value returned by the function.<\/p>\r\n","custom_attachment":"<p>The public grader, sample cases, and skeleton files for this problem is available&nbsp;<a href=\"https:\/\/upload.acmicpc.net\/6939eef7-244a-4868-bb3a-d6d5d1a867f3\/\">here<\/a>.<\/p>\r\n"}]

샘플 그레이더

샘플 그레이더는 입력을 다음 양식으로 읽는다.

N M
U[0] V[0] W[0]
U[1] V[1] W[1]
.
.
.
U[M-1] V[M-1] W[M-1]
Q
X[0] Y[0]
X[1] Y[1]
.
.
.
X[Q-1] Y[Q-1]

샘플 그레이더는 getMinimumFuelCapacity 함수를 호출할 때마다, 이 함수의 리턴값을 출력한다.

첨부

공개된 그레이더, 예제 케이스, 문제에 대한 기본 파일은 여기에서 받을 수 있다. 

제출할 수 있는 언어

C++14, Java, C++17, Java (OpenJDK), Java 11, C++2a, C++14 (Clang), C++17 (Clang), C++2a (Clang)

채점

  • 예제는 채점하지 않는다.