CF~Good Bye 2014 D. New Year Santa Network

D. New Year Santa Network
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
New Year is coming in Tree World! In this world, as the name implies, there are n cities connected by n - 1 roads, and for any two distinct cities there always exists a path between them. The cities are numbered by integers from 1 to n, and the roads are numbered by integers from 1 to n - 1. Let's define d(u, v) as total length of roads on the path between city u and city v.
As an annual event, people in Tree World repairs exactly one road per year. As a result, the length of one road decreases. It is already known that in the i-th year, the length of the ri-th road is going to become wi, which is shorter than its length before. Assume that the current year is year 1.
Three Santas are planning to give presents annually to all the children in Tree World. In order to do that, they need some preparation, so they are going to choose three distinct cities c1, c2, c3 and make exactly one warehouse in each city. The k-th (1 ≤ k ≤ 3) Santa will take charge of the warehouse in city ck.
It is really boring for the three Santas to keep a warehouse alone. So, they decided to build an only-for-Santa network! The cost needed to build this network equals to d(c1, c2) + d(c2, c3) + d(c3, c1) dollars. Santas are too busy to find the best place, so they decided to choose c1, c2, c3 randomly uniformly over all triples of distinct numbers from 1 to n. Santas would like to know the expected value of the cost needed to build the network.
However, as mentioned, each year, the length of exactly one road decreases. So, the Santas want to calculate the expected after each length change. Help them to calculate the value.
Input
The first line contains an integer n (3 ≤ n ≤ 105) — the number of cities in Tree World.
Next n - 1 lines describe the roads. The i-th line of them (1 ≤ i ≤ n - 1) contains three space-separated integers ai, bi, li (1 ≤ ai, bi ≤ n,ai ≠ bi, 1 ≤ li ≤ 103), denoting that the i-th road connects cities ai and bi, and the length of i-th road is li.
The next line contains an integer q (1 ≤ q ≤ 105) — the number of road length changes.
Next q lines describe the length changes. The j-th line of them (1 ≤ j ≤ q) contains two space-separated integers rj, wj (1 ≤ rj ≤ n - 1, 1 ≤ wj ≤ 103). It means that in the j-th repair, the length of the rj-th road becomes wj. It is guaranteed that wj is smaller than the current length of the rj-th road. The same road can be repaired several times.
Output
Output q numbers. For each given change, print a line containing the expected cost needed to build the network in Tree World. The answer will be considered correct if its absolute and relative error doesn't exceed 10 - 6.
Sample test(s)
input

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

output

14.0000000000
12.0000000000
8.0000000000
6.0000000000
4.0000000000

input

6
1 5 3
5 3 2
6 1 7
1 4 4
5 2 3
5
1 2
2 1
3 5
4 1
5 2

output

19.6000000000
18.6000000000
16.6000000000
13.6000000000
12.6000000000

Note
Consider the first sample. There are 6 triples: (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1). Because n = 3, the cost needed to build the network is always d(1, 2) + d(2, 3) + d(3, 1) for all the triples. So, the expected cost equals to d(1, 2) + d(2, 3) + d(3, 1).
제목: n각점, n-1조변전연통, 제i조변유권치Wi;그 중에서 a, b, c 세 가지를 골라서 디스(a, b)+디스(b, c)+디스(a, c)의 기대치를 묻는다.q차 도로 보수가 있어 i조 권한치를 바꾸고 q차 변경 후 원하는 기대치를 구합니다.
문제풀이: 임의의 두 점(a, b)에 대해 나머지 (n-2)점과 가능한 상황을 구성할 수 있다. 즉, 매 쌍(a, b)마다 화해(n-2)를 구할 수 있다.기대 E=[(n-2)*sum length(a,b)]/[n*(n-1)*(n-2)/(3*2*1)]=6.0*sumlength(a,b)/n/(n-1) ;        
i변에 연결된 두 점(u, v)에 대해 u, v를 뿌리로 하는 서브트리는 각각treeu、tree_v개 점, 예: i조 모서리는sumlength 출항 횟수는treeu*tree_v ;알기 쉽게treev=(n-treeu) .

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <cctype>
#include <queue>
#include <stack>
#include <vector>
#define INF 0x7fffffff
#define maxn 987654321
#define sizeN 300009
#define eps (1e-9)
#define clearto(s,x) memset(s,x,sizeof(s))
using namespace std;
typedef long long llong;

int n,m,tot;
int length[sizeN]={0};
llong used[sizeN]={0};
typedef pair<int,int> node;
vector<node> vec[sizeN];

int dfs(int fa,int lst,int id)
{
    int szA=1;
    int chl,loc;
    for(int i=0;i<vec[fa].size();i++)
    {
        chl=vec[fa][i].first;
        loc=vec[fa][i].second;
        if(chl==lst)    continue;
        szA+=dfs(chl,fa,loc);
    }
    used[id]=(llong)szA*(n-szA)*2;    //     *2，    tmp    6.0；  WA，  
    return szA;
}
int main()
{
	//freopen("E:\DATA.txt","r",stdin);
	int i,j;
	int a,b,l;
	scanf("%d",&n);
	for(i=1;i<n;i++)
	{
	    scanf("%d %d %d",&a,&b,&l);
	    vec[a].push_back(make_pair(b,i));
	    vec[b].push_back(make_pair(a,i));
	    length[i]=l;
	}
	dfs(1,-1,0);
    llong sum=0;
    for(i=1;i<n;i++){
        sum=sum+length[i]*used[i];
        //cout<<sum<<' '<<length[i]<<' '<<used[i]<<endl;
    }
    double tmp= 3.0/n/(n-1);            //   3.0/(n*(n-1))     
    scanf("%d",&tot);
    while(tot--)
    {
        scanf("%d %d",&a,&b);
        sum=sum-(used[a]*(length[a]-b));
        printf("%.8lf
",(double)sum*tmp);
        length[a]=b;
    }
	return 0;
}