private void visit(EdgeWightedGraph g, Int32 v) { marked[v] = true; foreach (Edge e in g.Adj(v)) { int w = e.Other(v); if (marked[w]) { continue;//访问过了 } if (e.Weight < disTo[w]) { //从MST到w的距离变短了。最佳边变成e edgeTo[w] = e; disTo[w] = e.Weight; if (pq.Contains(w)) { pq.Change(w, disTo[w]); } else { pq.Insert(w, disTo[w]); } } } }
private Chapter2.SortDemos.IndexPriorityQueue <Double> pq; //始终有最短的边 /// <summary> /// 构造函数 /// </summary> /// <param name="graph">有向加权非负权图</param> /// <param name="s">起点</param> public DijkstraSP(DirectedWeightedGraph graph, int s) { edgeTo = new DirectedEdge[graph.V]; disTo = new Double[graph.V]; pq = new Chapter2.SortDemos.IndexPriorityQueue <double>(graph.V); for (Int32 v = 0; v < graph.V; ++v) { disTo[v] = Double.PositiveInfinity; } disTo[s] = 0.0;//自己到自己为0 pq.Insert(s, 0.0); while (!pq.IsEmpty()) { Relax(graph, pq.DeleteMin());//放松节点,找到到某个点的最短的距离 } }
private Chapter2.SortDemos.IndexPriorityQueue <Double> pq; //保存最小边的最小堆 public PrimMST(EdgeWightedGraph g) { pq = new Chapter2.SortDemos.IndexPriorityQueue <double>(g.V, (Double s, Double b) => { return(s < b); });//允许的标号[0,g.V] edgeTo = new Edge[g.V]; marked = new Boolean[g.V]; disTo = new Double[g.V]; for (Int32 v = 0; v < g.V; ++v) { disTo[v] = Double.PositiveInfinity; //表示为正无穷 } pq.Insert(0, 0.0); disTo[0] = 0.0; while (!pq.IsEmpty()) { visit(g, pq.DeleteMin());//获取二叉堆中总是最小的索引 } }
private void Relax(DirectedWeightedGraph g, int v) { foreach (DirectedEdge edge in g.GetEdge(v)) { int w = edge.End; //如果存在放松的条件 if (disTo[w] > disTo[v] + edge.Weight) { //存在,需要更新 disTo[w] = disTo[v] + edge.Weight; edgeTo[w] = edge; //重新累计从 s 到某个点的最短距离。这个距离只有可能减小 if (pq.Contains(w)) { pq.Change(w, disTo[w]); } else { pq.Insert(w, disTo[w]); } } } }