void shortestPaths(int sourceVertex,T* distanceFromSource, int* predecessor)
      {
       //predecessor[i]保存从源定点到达顶点i的路径中前面的那个顶点
       // Find shortest paths from sourceVertex.
       // Return shortest distances in distanceFromSource.
       // Return predecessor information in predecessor.
         if (sourceVertex < 1 || sourceVertex > n)
            throw illegalParameterValue("Invalid source vertex");

         if (!weighted())
            throw undefinedMethod
            ("adjacencyWDigraph::shortestPaths() not defined for unweighted graphs");
         //使用无序链表保存可到达的顶点
         graphChain<int> newReachableVertices;

         // initialize
         //所有邻接于源顶点的顶点i,令predecessor[i] = sourceVertex
         //对所有其他顶点predecessor[i] = -1且predecessor[sourceVertex] = 0
         //创建表newReachableVertices存储所有predecessor[i]>0的顶点（即邻接于源顶点的点）
         for (int i = 1; i <= n; i++)
         {
            distanceFromSource[i] = a[sourceVertex][i];
            if (distanceFromSource[i] == noEdge)
               predecessor[i] = -1;
            else
            {
               predecessor[i] = sourceVertex; 
               newReachableVertices.insert(0, i);
            }
         }
         distanceFromSource[sourceVertex] = 0;
         predecessor[sourceVertex] = 0;  // source vertex has no predecessor

         // update distanceFromSource and predecessor
         while (!newReachableVertices.empty())
         {// more paths exist
            // find unreached vertex v with least distanceFromSource
            chain<int>::iterator iNewReachableVertices
                                 = newReachableVertices.begin();
            chain<int>::iterator theEnd = newReachableVertices.end();
            int v = *iNewReachableVertices;
            iNewReachableVertices++;
            //寻找表中路径最短的边
            while (iNewReachableVertices != theEnd)
            {
               int w = *iNewReachableVertices;
               iNewReachableVertices++;
               if (distanceFromSource[w] < distanceFromSource[v])
                  v = w;
            }

            // next shortest path is to vertex v, delete v from
            // newReachableVertices and update distanceFromSource
            newReachableVertices.eraseElement(v);
            for (int j = 1; j <= n; j++)
            {
               //发现新路径时，更新最短路径。
               if (a[v][j] != noEdge && (predecessor[j] == -1 ||
               distanceFromSource[j] > distanceFromSource[v] + a[v][j]))
               {
                  // distanceFromSource[j] decreases
                  distanceFromSource[j] = distanceFromSource[v] + a[v][j];
                  // add j to newReachableVertices
                  if (predecessor[j] == -1)
                     // not reached before 没在表中时要加入Reach
                     newReachableVertices.insert(0, j);
                  predecessor[j] = v;//保存路径
               }
            }
         }
      }