Practice-It

Write a method named isConnected that accepts a Graph<String, String> parameter and returns true if a path can be made from every vertex to any other vertex, or false if there is any vertex cannot be reached by a path from some other vertex. An empty graph is defined as being connected. (You can just check every pair of vertices to see if they can reach each other, though this is not an ideal algorithm in terms of runtime.)

You are allowed to call methods on the graph but you should not modify its state. The graph passed to your method implements the following interface:

public interface Graph<V, E> {
    public void addEdge(V v1, V v2);
    public void addEdge(V v1, V v2, E e);
    public void addEdge(V v1, V v2, int weight);
    public void addEdge(V v1, V v2, E e, int weight);
    public void addVertex(V v);
    public void clear();
    public void clearEdges();
    public boolean containsEdge(E e);
    public boolean containsEdge(V v1, V v2);
    public boolean containsPath(List<V> path);
    public boolean containsVertex(V v);
    public int cost(List<V> path);
    public int degree(V v);
    public E edge(V v1, V v2);
    public int edgeCount();
    public Collection<E> edges();
    public int edgeWeight(V v1, V v2);
    public int inDegree(V v);
    public Set<V> inverseNeighbors(V v);
    public boolean isDirected();
    public boolean isEmpty();
    public boolean isReachable(V v1, V v2);         // depth-first search
    public boolean isWeighted();
    public List<V> minimumWeightPath(V v1, V v2);   // Dijkstra's algorithm
    public Set<V> neighbors(V v);
    public int outDegree(V v);
    public void removeEdge(E e);
    public void removeEdge(V v1, V v2);
    public void removeVertex(V v);
    public List<V> shortestPath(V v1, V v2);        // breadth-first search
    public String toString();
    public int vertexCount();
    public Set<V> vertices();
}