学步园

1 Unweighted Graphs 

For unweighted Graphs, a minimum  spanning tree(MST) means that a graph with minimum number of edges to connect all the vertices.

the number of edges E in a minimum spanning tree is always one less than the number of vertices V: E = V – 1.

The path of the
DFS(depth-first search) through the graph must be a minimum spanning tree.

1.1 Java implement 

   public void mst()  // minimum spanning tree (depth first)
      {                                  // start at 0
      vertexList[0].wasVisited = true;   // mark it
      theStack.push(0);                  // push it

      while( !theStack.isEmpty() )       // until stack empty
         {                               // get stack top
         int currentVertex = theStack.peek();
         // get next unvisited neighbor
         int v = getAdjUnvisitedVertex(currentVertex);
         if(v == -1)                     // if no more neighbors
            theStack.pop();              //    pop it away
         else                            // got a neighbor
            {
            vertexList[v].wasVisited = true;  // mark it
            theStack.push(v);                 // push it
                                         // display edge
            displayVertex(currentVertex);     // from currentV
            displayVertex(v);                 // to v
            System.out.print(" ");
            }
         }  // end while(stack not empty)

         // stack is empty, so we're done
         for(int j=0; j<nVerts; j++)          // reset flags
            vertexList[j].wasVisited = false;
      }  // end mst()