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  • Codeforces444A_DZY Loves Physics

    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 Gm 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.

    Sample test(s)
    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.

    解题报告

    这题的优先策略是仅仅选一条边。

    (v+a)/(e+b)  <=  v/e

    #include<cstdio>
    #include<cmath>
    #include<cstring>
    #include<queue>
    #include<iostream>
    #include<algorithm>
    using namespace std;
    int n,m,num[550];
    int main()
    {
        int u,v,w,i,j;
        while(cin>>n>>m)
        {
            memset(num,0,sizeof(num));
            double maxx=0;
            for(i=1;i<=n;i++)
            {
                cin>>num[i];
            }
            for(i=0;i<m;i++)
            {
                cin>>u>>v>>w;
                maxx=max(maxx,(num[u]+num[v])/(double)w);
            }
            printf("%.15lf
    ",maxx);
        }
    }
    


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  • 原文地址:https://www.cnblogs.com/yjbjingcha/p/7244126.html
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