【CodeForces】444A - DZY Loves Physics（图论规律）

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A. DZY Loves Physics

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

DZY loves Physics, and he enjoys calculating density.

Almost everything has density, even a graph. We define the density of a non-directed graph (nodes and edges of the graph have some values) as follows:

where v is the sum of the values of the nodes, e is the sum of the values of the edges.

Once DZY got a graph G, now he wants to find a connected induced subgraph G' of the graph, such that the density of G' is as large as possible.

An induced subgraph G'(V', E') of a graph G(V, E) is a graph that satisfies:

;

• edge

if and only if

, and edge

;

• the value of an edge in G' is the same as the value of the corresponding edge in G, so as the value of a node.

Help DZY to find the induced subgraph with maximum density. Note that the induced subgraph you choose must be connected.

Input

The first line contains two space-separated integers n (1 ≤ n ≤ 500),

. Integer n represents the number of nodes of the graph G, m represents the number of edges.

The second line contains n space-separated integers xi (1 ≤ xi ≤ 106), where xi represents the value of the i-th node. Consider the graph nodes are numbered from 1 to n.

Each of the next m lines contains three space-separated integers ai, bi, ci (1 ≤ ai < bi ≤ n; 1 ≤ ci ≤ 103), denoting an edge between node ai and bi with value ci. The graph won't contain multiple edges.

Output

Output a real number denoting the answer, with an absolute or relative error of at most 10 - 9.

Examples

input

1 0
1

output

0.000000000000000

input

2 1
1 2
1 2 1

output

3.000000000000000

input

5 6
13 56 73 98 17
1 2 56
1 3 29
1 4 42
2 3 95
2 4 88
3 4 63

output

2.965517241379311

Note

In the first sample, you can only choose an empty subgraph, or the subgraph containing only node 1.

In the second sample, choosing the whole graph is optimal.

题意：求一个图的诱导子图，要求子图任意两点之间如果存在边，子图也必须存在边，求子图节点的和比上边的权值的最大值。

题解：根据图论的结论，结果应该为两个点组成的子图，可以证明如果是三个或三个以上的点那个最终的结果会小。

所以直接对于输入的每一组边计算更新ans就行了。

代码如下：

#include <cstdio>
#include <stack>
#include <queue>
#include <cmath>
#include <vector>
#include <cstring>
#include <algorithm>
using namespace std;
#define CLR(a,b) memset(a,b,sizeof(a))
#define INF 0x3f3f3f3f
#define LL long long
#define MAX 500
int main()
{
	int n,m;
	double v[MAX+5];
	while (~scanf ("%d %d",&n,&m))
	{
		for (int i = 1 ; i <= n ; i++)
			scanf ("%lf",&v[i]);
		double ans = 0;
		int x,y;
		double edge;
		while (m--)
		{
			scanf ("%d %d %lf",&x,&y,&edge);
			ans = max(ans , (v[x] + v[y]) / edge);
		}
		printf ("%.12lf\n",ans);
	}
	return 0;
}