/// <summary>
/// 松弛图g中的顶点v
/// </summary>
/// <param name="g"></param>
/// <param name="v"></param>
private void relax(EdgeDirectedWeightedDirgraph g, int v)
{
IEnumerator ie = g.adj(v).GetEnumerator();
while (ie.MoveNext())
{
EdgeDirected e = (EdgeDirected)ie.Current;
// 获取到该边的终点w
int w = e.to();
// 通过松弛技术，判断从起点s到顶点w的最短路径是否需要先从顶点s到顶点v，然后再由定点v到顶点w
if (this.distTo(v) + e.weight() < this.distTo(w))
{
this.distToDouble[w] = this.distToDouble[v] + e.weight();
this.edgeTo[w] = e;
// 判断pq中是否已经存在在顶点w，如果存在，则更新新权重，如果不存在则直接添加
if (this.pq.contains(w))
{
this.pq.changeItem(w, this.distTo(w));
}
else
{
this.pq.insert(w, distTo(w));
}
}
}
}
/// <summary>
/// 最短路径
/// </summary>
private static void DijksraSPTest()
{
// 创建加权有向图
EdgeDirectedWeightedDirgraph graph = new EdgeDirectedWeightedDirgraph(8);
graph.addEdge(new EdgeDirected(4, 5, 0.35f));
graph.addEdge(new EdgeDirected(5, 4, 0.35f));
graph.addEdge(new EdgeDirected(4, 7, 0.37f));
graph.addEdge(new EdgeDirected(5, 7, 0.28f));
graph.addEdge(new EdgeDirected(7, 5, 0.28f));
graph.addEdge(new EdgeDirected(5, 1, 0.32f));
graph.addEdge(new EdgeDirected(0, 4, 0.38f));
graph.addEdge(new EdgeDirected(0, 2, 0.26f));
graph.addEdge(new EdgeDirected(7, 3, 0.39f));
graph.addEdge(new EdgeDirected(1, 3, 0.29f));
graph.addEdge(new EdgeDirected(2, 7, 0.34f));
graph.addEdge(new EdgeDirected(6, 2, 0.40f));
graph.addEdge(new EdgeDirected(3, 6, 0.52f));
graph.addEdge(new EdgeDirected(6, 0, 0.58f));
graph.addEdge(new EdgeDirected(6, 4, 0.93f));
// 创建 DijksraSP 对象 查找最短路径
int start = 0;
DijksraSP dijksra = new DijksraSP(graph, start);
// 查找最短路径 0->6
int end = 6;
QueueList <EdgeDirected> allEdges = dijksra.pathTo(end);
// 遍历打印
if (allEdges == null)
{
Console.WriteLine("not path to " + end);
}
else
{
IEnumerator ie = allEdges.GetEnumerator();
while (ie.MoveNext())
{
EdgeDirected e = (EdgeDirected)ie.Current;
Console.WriteLine(e.from() + " -> " + e.to() + " : " + e.weight().ToString("F2"));
}
}
}
/// <summary>
/// 根据加权有向图g和顶点s创建一个计算顶点为s的最短路径树对象
/// </summary>
/// <param name="g"></param>
/// <param name="s"></param>
public DijksraSP(EdgeDirectedWeightedDirgraph g, int s)
{
// 初始化 edgeTo
this.edgeTo = new EdgeDirected[g.countV()];
// 初始化 distToDouble
this.distToDouble = new double[g.countV()];
for (int i = 0; i < this.distToDouble.Length; i++)
{
this.distToDouble[i] = Double.PositiveInfinity;
}
// 初始化 pq
this.pq = new IndexMinPriorityQueue <double>(g.countV());
// 找到图g中顶点s为起点的最短路径树
// 默认让顶点s进入到最短路径树中
this.distToDouble[s] = 0.0f;
this.pq.insert(s, 0.0f);
// 遍历pq
while (!this.pq.isEmpty())
{
relax(g, this.pq.delMinIndex());
}
}