Breadth-first search

given a graph G  and a distinguished source vertex s, breadth-first
search systematically explores the edges of G to “discover” every vertex that is
reachable from s.

To keep track of progress, breadth-first search colors each vertex white, gray, or
black. All vertices start out white and may later become gray and then black. A
vertex is discovered the first time it is encountered during the search, at which time
it becomes nonwhite. Gray and black vertices, therefore, have been discovered, but
breadth-first search distinguishes between them to ensure that the search proceeds
in a breadth-first manner

 package element_graph;

 import java.util.Iterator;
 import java.util.LinkedList;
 import java.util.List;

 import edu.princeton.cs.algs4.Queue;

 public class breadth_first_search {
     private static class vertex{
         private LinkedList<vertex> link;
         private String name;
         private String color;
         private vertex p;
         private int d;
         public vertex(String na,LinkedList<vertex> lin){
             name = na;
             link = lin;
             color = "white";
             p = null;
             d = 9999;
         }
     }
     public static void BFS(vertex s){
         s.color = "grey";
         s.d = 0;
         Queue<vertex> q = new Queue<vertex>();
         q.enqueue(s);
         while(!q.isEmpty()){
             vertex u = q.dequeue();
             for (vertex v : u.link) {  //every adj
                 if(v.color == "white"){
                     v.color = "gray";
                     v.d = v.d + 1;
                     v.p = u;
                     q.enqueue(v);
                 }
             }
             u.color = "black";
             }

     }
     public static void printpath(vertex s,vertex v){
         if(v == s){
             System.out.println(s.name);
         }
         else if(v.p == null){  //will not get s
             System.out.println("no way");
         }
         else{
             printpath(s,v.p);
             System.out.println(v.name);
         }
     }

      public static void main(String[] args) {
             LinkedList<vertex> sl = new LinkedList<vertex>();

             LinkedList<vertex> rl = new LinkedList<vertex>();

             LinkedList<vertex> vl = new LinkedList<vertex>();

             LinkedList<vertex> wl = new LinkedList<vertex>();

             LinkedList<vertex> tl = new LinkedList<vertex>();

             LinkedList<vertex> xl = new LinkedList<vertex>();

             LinkedList<vertex> ul = new LinkedList<vertex>();

             LinkedList<vertex> yl = new LinkedList<vertex>();

             vertex sv = new vertex("s",sl);
             vertex rv = new vertex("r",rl);
             vertex vv = new vertex("v",vl);
             vertex wv = new vertex("w",wl);
             vertex tv = new vertex("t",tl);
             vertex xv = new vertex("x",xl);
             vertex uv = new vertex("u",ul);
             vertex yv = new vertex("y",yl);
             sl.add(rv);
             sl.add(wv);
             rl.add(sv);
             rl.add(vv);
             vl.add(rv);
             wl.add(xv);
             wl.add(tv);
             wl.add(sv);
             tl.add(xv);
             tl.add(uv);
             tl.add(wv);
             xl.add(tv);
             xl.add(uv);
             xl.add(yv);
             xl.add(wv);
             xl.add(tv);
             xl.add(xv);
             xl.add(yv);
             xl.add(uv);
             xl.add(xv);
              BFS(sv);
              printpath(sv,tv);

         }
 }