JAVA 8

public static long roadsAndLibraries(int vertices, int c_lib, int c_road, List> cities) { //base case if(c_lib

//arraylist for adjacency list
ArrayList<ArrayList<Integer>> arr = new ArrayList<>();
for(int i = 0;i<vertices;i++)
{
    arr.add(new ArrayList<Integer>());
}
//adding edges --> adjacency list
for(int i = 0;i<cities.size();i++)
{
    arr.get(cities.get(i).get(0)-1).add(cities.get(i).get(1)-1);
    arr.get(cities.get(i).get(1)-1).add(cities.get(i).get(0)-1);
}

boolean[] visited = new boolean[vertices];

long cost = (long)vertices*c_lib; 
long road = 0;

for(int i = 0;i<vertices;i++)
{
    if(!visited[i])
    {
        road += connectedRoads(i,arr,visited);
        long tempc = ((long)vertices - road)*(long)c_lib + road*(long)c_road;
        cost = Math.min(cost, tempc);
    }
} 
return cost;

}
private static long connectedRoads(int source,ArrayList<ArrayList<Integer>> arr, boolean[] visited) 
{
    long roads = 0;
    visited[source] = true;

    //using bfs
    Queue<Integer> q = new LinkedList();
    q.offer(source);

    while(!q.isEmpty())
    {
        int current = q.poll();
        for(int next : arr.get(current))
        {
            if(visited[next]!= true)
            {
                visited[next]=true;
                roads++;
                q.add(next);
            }
        }
    }
    return roads;
}