문제
$N$개의 도시와 $N-1$개의 도로로 이루어진 국가가 있다. 도시에는 1ドル$부터 $N$까지의 번호가 붙어 있고, 도로에도 1ドル$부터 $N-1$의 번호가 붙어 있다. $i$번 도로는 $A_i$번 도시와 $B_i$번 도시를 양방향으로 연결하고, 이동 시에는 $W_i$의 비용이 든다. 임의의 두 도시를 고르더라도 둘 사이를 하나 이상의 도로를 사용하여 왕복할 수 있음이 보장된다.
두 도시 사이의 거리를 한 도시에서 출발하여 하나 이상의 도로를 거쳐 다른 도시로 갈 때 필요한 최소 비용으로 정의하자.
당신은 도로 회사의 사장으로, 명절을 맞아 할인 행사를 진행하려고 한다. 할인 행사를 위한 총 $Q$개의 계획이 있다. $i$번째 계획에서는 $X_i$번 도시에서 출발하여 $Y_i$번 도시로 가는 최단 경로에 속하는 모든 도로들에 할인을 적용하여 비용을 0으로 만들 것이다. 각 할인 행사 계획에 대해, 두 도시 사이 거리의 최댓값을 출력하라.
출력
총 $Q$개의 줄에 걸쳐 답을 출력한다. $i$번째 줄에는 $i$번째 계획에 대한 답을 출력해야 한다.
제한
2ドル\le N\le 100,円 000$
1ドル\le A_i,B_i\le N$ (1ドル\le i\le N-1$)
$A_i\neq B_i$ (1ドル\le i\le N-1$)
1ドル\le W_i\le 10^9$ (1ドル\le i\le N-1$)
입력으로 주어지는 나라의 구조는 올바른 트리를 이룬다.
1ドル\le Q\le 100,円 000$
1ドル\le X_i,Y_i\le N$ (1ドル\le i\le Q$)
$X_i\neq Y_i$ (1ドル\le i\le Q$)
서브태스크 번호 배점 제한 1 10 $N, Q \le 2,000円$
2 24 $X_i=1$ (1ドル \le i \le Q$)
3 27 $Q=N-1$; $X_i = A_i$; $Y_i = B_i$ (1ドル \le i \le N-1$)
4 39 추가적인 제약 조건이 없다.
예제 출력 3
복사
13
13
16
16
13
16
15
예제 출력 4
복사
12
11
11
12
7
11
[{"problem_id":"31818","problem_lang":"0","title":"Discount Event","description":"<p>$N$\uac1c\uc758 \ub3c4\uc2dc\uc640 $N-1$\uac1c\uc758 \ub3c4\ub85c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uad6d\uac00\uac00 \uc788\ub2e4. \ub3c4\uc2dc\uc5d0\ub294 $1$\ubd80\ud130 $N$\uae4c\uc9c0\uc758 \ubc88\ud638\uac00 \ubd99\uc5b4 \uc788\uace0, \ub3c4\ub85c\uc5d0\ub3c4 $1$\ubd80\ud130 $N-1$\uc758 \ubc88\ud638\uac00 \ubd99\uc5b4 \uc788\ub2e4. $i$\ubc88 \ub3c4\ub85c\ub294 $A_i$\ubc88 \ub3c4\uc2dc\uc640 $B_i$\ubc88 \ub3c4\uc2dc\ub97c \uc591\ubc29\ud5a5\uc73c\ub85c \uc5f0\uacb0\ud558\uace0, \uc774\ub3d9 \uc2dc\uc5d0\ub294 $W_i$\uc758 \ube44\uc6a9\uc774 \ub4e0\ub2e4. \uc784\uc758\uc758 \ub450 \ub3c4\uc2dc\ub97c \uace0\ub974\ub354\ub77c\ub3c4 \ub458 \uc0ac\uc774\ub97c \ud558\ub098 \uc774\uc0c1\uc758 \ub3c4\ub85c\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc655\ubcf5\ud560 \uc218 \uc788\uc74c\uc774 \ubcf4\uc7a5\ub41c\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ub3c4\uc2dc \uc0ac\uc774\uc758 \uac70\ub9ac\ub97c \ud55c \ub3c4\uc2dc\uc5d0\uc11c \ucd9c\ubc1c\ud558\uc5ec \ud558\ub098 \uc774\uc0c1\uc758 \ub3c4\ub85c\ub97c \uac70\uccd0 \ub2e4\ub978 \ub3c4\uc2dc\ub85c \uac08 \ub54c \ud544\uc694\ud55c \ucd5c\uc18c \ube44\uc6a9\uc73c\ub85c \uc815\uc758\ud558\uc790.<\/p>\r\n\r\n<p>\ub2f9\uc2e0\uc740 \ub3c4\ub85c \ud68c\uc0ac\uc758 \uc0ac\uc7a5\uc73c\ub85c, \uba85\uc808\uc744 \ub9de\uc544 \ud560\uc778 \ud589\uc0ac\ub97c \uc9c4\ud589\ud558\ub824\uace0 \ud55c\ub2e4. \ud560\uc778 \ud589\uc0ac\ub97c \uc704\ud55c \ucd1d $Q$\uac1c\uc758 \uacc4\ud68d\uc774 \uc788\ub2e4. $i$\ubc88\uc9f8 \uacc4\ud68d\uc5d0\uc11c\ub294 $X_i$\ubc88 \ub3c4\uc2dc\uc5d0\uc11c \ucd9c\ubc1c\ud558\uc5ec $Y_i$\ubc88 \ub3c4\uc2dc\ub85c \uac00\ub294 \ucd5c\ub2e8 \uacbd\ub85c\uc5d0 \uc18d\ud558\ub294 \ubaa8\ub4e0 \ub3c4\ub85c\ub4e4\uc5d0 \ud560\uc778\uc744 \uc801\uc6a9\ud558\uc5ec \ube44\uc6a9\uc744 0\uc73c\ub85c \ub9cc\ub4e4 \uac83\uc774\ub2e4. \uac01 \ud560\uc778 \ud589\uc0ac \uacc4\ud68d\uc5d0 \ub300\ud574, \ub450 \ub3c4\uc2dc \uc0ac\uc774 \uac70\ub9ac\uc758 \ucd5c\ub313\uac12\uc744 \ucd9c\ub825\ud558\ub77c.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \ub3c4\uc2dc\uc758 \uc218\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218 $N$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c $N-1$\uac1c\uc758 \uc904 \uc911 $i$\ubc88\uc9f8 \uc904\uc5d0\ub294 \uc138 \uc815\uc218 $A_i$, $B_i$, $W_i$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub4e4\uc740 $i$\ubc88\uc9f8 \ub3c4\ub85c\uac00 \uc5f0\uacb0\ud558\ub294 \ub450 \ub3c4\uc2dc\uc758 \ubc88\ud638\uc640 \ub3c4\ub85c\uc758 \uc774\ub3d9 \ube44\uc6a9\uc744 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc904\uc5d0 \uacc4\ud68d\uc758 \uc218\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218 $Q$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c $Q$\uac1c\uc758 \uc904 \uc911 $i$\ubc88\uc9f8 \uc904\uc5d0\ub294 \ub450 \uc815\uc218 $X_i$\uc640 $Y_i$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub4e4\uc740 $i$\ubc88\uc9f8 \uacc4\ud68d\uc744 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n","output":"<p>\ucd1d $Q$\uac1c\uc758 \uc904\uc5d0 \uac78\uccd0 \ub2f5\uc744 \ucd9c\ub825\ud55c\ub2e4. $i$\ubc88\uc9f8 \uc904\uc5d0\ub294 $i$\ubc88\uc9f8 \uacc4\ud68d\uc5d0 \ub300\ud55c \ub2f5\uc744 \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$2\\le N\\le 100\\, 000$<\/li>\r\n\t<li>$1\\le A_i,B_i\\le N$ ($1\\le i\\le N-1$)<\/li>\r\n\t<li>$A_i\\neq B_i$ ($1\\le i\\le N-1$)<\/li>\r\n\t<li>$1\\le W_i\\le 10^9$ ($1\\le i\\le N-1$)<\/li>\r\n\t<li>\uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c0\ub294 \ub098\ub77c\uc758 \uad6c\uc870\ub294 \uc62c\ubc14\ub978 \ud2b8\ub9ac\ub97c \uc774\ub8ec\ub2e4.<\/li>\r\n\t<li>$1\\le Q\\le 100\\, 000$<\/li>\r\n\t<li>$1\\le X_i,Y_i\\le N$ ($1\\le i\\le Q$)<\/li>\r\n\t<li>$X_i\\neq Y_i$ ($1\\le i\\le Q$)<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N, Q \\le 2\\,000$<\/p>\r\n","subtask2":"<p>$X_i=1$ ($1 \\le i \\le Q$)<\/p>\r\n","subtask3":"<p>$Q=N-1$; $X_i = A_i$; $Y_i = B_i$ ($1 \\le i \\le N-1$)<\/p>\r\n","subtask4":"<p>\ucd94\uac00\uc801\uc778 \uc81c\uc57d \uc870\uac74\uc774 \uc5c6\ub2e4.<\/p>\r\n"},{"problem_id":"31818","problem_lang":"1","title":"Discount Event","description":"<p>There is a country with $N$ cities and $N-1$ roads. Each city is labeled with integers from $1$ to $N$, and each road is labeled with integers from $1$ to $N-1$. The $i$-th road connects cities $A_i$ and $B_i$ bidirectionally, and has travel costs $W_i$. You can travel along any pair of cities using the roads.<\/p>\r\n\r\n<p>The distance between two cities is defined as the minimum cost of moving from one city to another.<\/p>\r\n\r\n<p>As the president of a road company, you are planning a discount event for the holidays. There are a total of $Q$ plans for the discount event. In the $i$-th plan, the discount is applied to all roads in the shortest path between cities $X_i$ and $Y_i$, and the travel costs of the road become zero. For each discount event plan, compute the maximum value of the distance between any two cities.<\/p>\r\n","input":"<p>The first line contains an integer $N$ &mdash; the number of cities.<\/p>\r\n\r\n<p>The $i$-th of the next $N-1$ lines contains three integers $A_i$, $B_i$, and $W_i$ separated by a space &mdash; the cities the $i$-th road connects and the road&rsquo;s travel cost.<\/p>\r\n\r\n<p>The next line contains an integer $Q$ &mdash; the number of plans.<\/p>\r\n\r\n<p>The $i$-th of the next $Q$ lines contains two integers $X_i$ and $Y_i$ separated by a space, describing the $i$-th plan.<\/p>\r\n","output":"<p>Print the answer along $Q$ lines. In the $i$-th line, you should print the answer for the $i$-th query.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$2\\le N\\le 100\\, 000$<\/li>\r\n\t<li>$1\\le A_i,B_i\\le N$ ($1\\le i\\le N-1$)<\/li>\r\n\t<li>$A_i\\neq B_i$ ($1\\le i\\le N-1$)<\/li>\r\n\t<li>$1\\le W_i\\le 10^9$ ($1\\le i\\le N-1$)<\/li>\r\n\t<li>It is possible to travel along any pair of cities using the roads.<\/li>\r\n\t<li>$1\\le Q\\le 100\\, 000$<\/li>\r\n\t<li>$1\\le X_i,Y_i\\le N$ ($1\\le i\\le Q$)<\/li>\r\n\t<li>$X_i\\neq Y_i$ ($1\\le i\\le Q$)<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N, Q \\le 2\\,000$<\/p>\r\n","subtask2":"<p>$X_i=1$ ($1 \\le i \\le Q$)<\/p>\r\n","subtask3":"<p>$Q=N-1$; $X_i = A_i$; $Y_i = B_i$ ($1 \\le i \\le N-1$)<\/p>\r\n","subtask4":"<p>No additional constraints.<\/p>\r\n"}]