Electrification Plan MST

Electrification Plan

Time Limit:500MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

Submit Status Practice URAL 1982

Description

Some country has n cities. The government has decided to electrify all these cities. At first, power stations in k different cities were built. The other cities should be connected with the power stations via power lines. For any cities i, j it is possible to build a power line between them in c_ij roubles. The country is in crisis after a civil war, so the government decided to build only a few power lines. Of course from every city there must be a path along the lines to some city with a power station. Find the minimum possible cost to build all necessary power lines.

Input

The first line contains integers n and k (1 ≤ k ≤ n ≤ 100). The second line contains k different integers that are the numbers of the cities with power stations. The next n lines contain an n × n table of integers { c_ij} (0 ≤ c_ij ≤ 10 ⁵). It is guaranteed that c_ij = c_ji, c_ij > 0 for i ≠ j,c_ii = 0.

Output

Output the minimum cost to electrify all the cities.

Sample Input

input	output
4 2 1 4 0 2 4 3 2 0 5 2 4 5 0 1 3 2 1 0	3

int n,m;
struct Edge
{
    int from,to,cost;
};

int p[maxn];
int find(int x)
{
    if(x == p[x])
        return x;
    else
    {
        p[x] = find(p[x]);
        return p[x];
    }
}

vector<Edge> edges; 
bool cmp(Edge e1,Edge e2)
{
    return e1.cost < e2.cost;
}


int kruskal()
{
    int ans = 0;
    rep(i,0,edges.size())
    {
        int x = find(edges[i].from);
        int y = find(edges[i].to);
        if(x != y)
        {
            p[x] = y;
            ans += edges[i].cost;
        }
    }
    return ans;
}
int main() 
{
    //freopen("in.txt","r",stdin);
    while(cin>>n>>m)
    {
        int b;
        cin>>b;
        repf(i,1,n)
            p[i] = i;
        
        repf(i,2,m)
        {
            int a;
            scanf("%d",&a);
            p[a] = b;
        }
        edges.clear();
        repf(i,1,n)
            repf(j,1,n)
            {
                int a;
                scanf("%d",&a);
                if(i < j)
                    edges.push_back((Edge){i,j,a});
            }
    
        sort(edges.begin(),edges.end(),cmp);
        
        cout<<kruskal()<<endl;
    }
    return 0;
}