找出有向图中两个节点之间是否存在路由

Question

我尝试使用DFS解决此问题。我的代码如下：

public static void main(String[] args){
    // building a graph g. g has a method getNodes() that can return all the nodes in the graph.
    // ...
    for(GraphNode n : g.getNodes())
        n.state = State.Unvistied;
    node1.state = State.Visiting;
    isRoute(g, node1, node2);
}

public boolean isRoute(Graph g, GraphNode start, GraphNode end){
    for(GraphNode gn : start.getAdjacent()){
        if(gn.state != State.Visited){
            if(gn == end)
                return true;
            else {
                gn.state = State.Visiting;
                if(isRoute(g, gn, end))
                    return true;    
            }
        }               
    }
    start.state = State.Visited;
    return false;
}

class GraphNode {
    private GraphNode adjacent[];
    private String vertex;
    public State state;

    public GraphNode(String vertex, int adjacentLength) {
        this.vertex = vertex;
        adjacent = new GraphNode[adjacentLength];
    }

    public GraphNode[] getAdjacent() {
        return adjacent;
    }

    public String getVertex() {
        return vertex;
    }
}

public enum State {

    Unvistied, Visited, Visiting;

}

我试图用一个示例图表在纸上运行这个算法，看起来是正确的。 然而，我不知道如何确定，即证明这个算法，特别是当它是递归的并且不容易运行测试用例时，如图中所示，是正确的。你们可以吗？给我一些见解？谢谢！