广度优先搜索：需要多少个顶点状态？

Question

I am working on Breadth First Search and I tried to write BFS to print all the edges. The first version is adapted from Algorithm book in which a vertex has 3 states: NOT_VISIT (initial state), VISIT and PROCESSED. A vertex is 'VISIT' when you first see it. A vertex is 'PROCESSED' when all of its neighbors are visited. The second version is the one that I wrote, use only 2 states: Initial state and VISITED. Both work:

public static void BFS(Graph g, int start) {
    boolean[] visit = new boolean[g.size()];
    boolean[] process = new boolean[g.size()];
    List<Integer> queue = new ArrayList<Integer>();
    queue.add(start);
    visit[start] = true;
    while (!queue.isEmpty()) {
        int currentVertex = queue.remove(0);
        process[currentVertex] = true;
        List<Integer> adj = g.getAdjacents(currentVertex);
        if (adj != null) {
            for (Integer i : adj) {
                if (visit[i] == false) {
                    visit[i] = true;
                    queue.add(i);
                }
                if (process[i] == false) {
                    System.out.println(currentVertex + " --- "
                            + i);

                }
            }
        }
    }
}




public static int BFS2(Graph g, int start) {
    List<Integer> queue = new ArrayList<Integer>();
            boolean[] visited = new boolean[g.size()];
    queue.add(start);
    while (!queue.isEmpty()) {
        int v = queue.remove(0);
        visited[v] = true;// only mark visited[v] = true when processing all
                            // its neighbors
        List<Integer> adj = g.getAdjacents(v);
        if (adj != null) {
            for (Integer i : adj) {
                if (!visited[i]) {
                    queue.add(i);
                    System.out.println(v + " --- "
                            + i);
                }
            }
        }
      }
  }

My question is: When is it necessary to have 3 states for a vertex in BFS ? Can you give an example when we need 3 states ?

Answer 1

Usually you add the middle state ("Visit" in your case, commonly "Gray" when using colors to mark nodes) just to visualise how BFS is working. In standard implementation it is not necessary (you may switch to "Visited" without going through the middle state.)

You can see it yourself, try to follow BFS (even with paper and pencil you can do it). You will see that nodes in state "Visit" are equally distanced from source (with maximum difference of 1, to be specific). For educational purposes it is good to do the same with DFS then (so you can observe the difference between Breadth-First and Depth-First searching).