codeforces 839 C Journey

C. Journey

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

There are n cities and n - 1 roads in the Seven Kingdoms, each road connects two cities and we can reach any city from any other by the roads.

Theon and Yara Greyjoy are on a horse in the first city, they are starting traveling through the roads. But the weather is foggy, so they can’t see where the horse brings them. When the horse reaches a city (including the first one), it goes to one of the cities connected to the current city. But it is a strange horse, it only goes to cities in which they weren't before. In each such city, the horse goes with equal probabilities and it stops when there are no such cities.

Let the length of each road be 1. The journey starts in the city1. What is the expected length (expected value of length) of their journey? You can read about expected (average) value by the linkhttps://en.wikipedia.org/wiki/Expected_value.

Input

The first line contains a single integer n (1 ≤ n ≤ 100000) — number of cities.

Then n - 1 lines follow. The i-th line of these lines contains two integers u_i and v_i (1 ≤ u_i, v_i ≤ n,u_i ≠ v_i) — the cities connected by thei-th road.

It is guaranteed that one can reach any city from any other by the roads.

Output

Print a number — the expected length of their journey. The journey starts in the city1.

Your answer will be considered correct if its absolute or relative error does not exceed10^- 6.

Namely: let's assume that your answer is a, and the answer of the jury isb. The checker program will consider your answer correct, if.

Examples

Input

41 21 32 4

Output

1.500000000000000

Input

51 21 33 42 5

Output

2.000000000000000

Note

In the first sample, their journey may end in cities 3 or4 with equal probability. The distance to city 3 is 1 and to city 4 is2, so the expected length is 1.5.

In the second sample, their journey may end in city 4 or5. The distance to the both cities is 2, so the expected length is 2.

题目：http://codeforces.com/contest/839/problem/C 
大致题意： 

给出一颗树，求从根节点出发，走到叶子节点经过的路径长度的数学期望。父节点到所有相邻子节点是等概率的。
解法： 
直接深搜可以得出答案。

代码：

#include <iostream>#include <vector>#include <iomanip>using namespace std;bool used[100005]{false};double dfs(vector<vector<int>> &vec,int src,unsigned long long dis){double rtn = 0;used[src] = true;int num = 0;for(auto dsc:vec[src]){if(!used[dsc]) {rtn +=dfs(vec,dsc,dis+1);num++;}}used[src] = false;if(num == 0){return dis;}else return rtn/num;}int main(){int n;cin >> n;vector<vector<int> > vec(n);for(int i = 0 ; i < n-1 ; i++){int src,dsc;cin >> src >> dsc;vec[src-1].push_back(dsc-1);vec[dsc-1].push_back(src-1);}int num = 0;double res = dfs(vec,0,0);cout << fixed << setprecision(16) <<res << endl;return 0;}