private void Dfs(EdgeWeightedDigraph G, int v)//(加权有向图)寻找相连的顶点
{
onStack[v] = true;
marked[v] = true;
foreach (DirectedEdge w in G.Adj(v))
{
if (this.HasCycle())
{
return;
}
else if (!marked[w.To()])
{
edgeTo[w.To()] = v;//存储最先到达w.To()点的v点
Dfs(G, w.To());
}
else if (onStack[w.To()])
{
cycle = new Stack <int>();
for (int x = v; x != w.To(); x = edgeTo[x])
{
cycle.Push(x);
}
cycle.Push(w.To());
cycle.Push(v);
}
}
onStack[v] = false;
}
public AcyclicLP(EdgeWeightedDigraph G)
{
edgeTo = new DirectedEdge[G.VNumber()];
distTo = new double[G.VNumber()];
for (int v = 0; v < G.VNumber(); v++)
{
distTo[v] = Double.NegativeInfinity;
}
Topological top = new Topological(G);
/*起先并不知道图的拓扑排序顺序，因此无法得知起点位置，
* 因此引入计数器n，判定拓扑排序起点，并将起点的distTo[]设置为0。
*/
int n = 0;
foreach (int v in top.Order())
{
if (n == 0)
{
distTo[v] = 0.0;
}
Relax(G, v);
n++;
}
}
public Topological(EdgeWeightedDigraph G)
{
DirectedCycle cycleFinder = new DirectedCycle(G);
if (!cycleFinder.HasCycle())
{
DepthFirstOrder dfs = new DepthFirstOrder(G);
order = dfs.ReversePost();
}
}
private void Relax(EdgeWeightedDigraph G, int v)
{
foreach (DirectedEdge e in G.Adj(v))
{
int w = e.To();
if (distTo[w] > distTo[v] + e.Weight())
{
distTo[w] = distTo[v] + e.Weight();
edgeTo[w] = e;
}
}
}
public DirectedCycle(EdgeWeightedDigraph G)
{
onStack = new bool[G.VNumber()];
edgeTo = new int[G.VNumber()];
marked = new bool[G.VNumber()];
for (int v = 0; v < G.VNumber(); v++)
{
if (!marked[v])
{
Dfs(G, v);
}
}
}
private void Dfs(EdgeWeightedDigraph G, int v)
{
pre.enqueue(v);
marked[v] = true;
foreach (DirectedEdge w in G.Adj(v))
{
if (!marked[w.To()])
{
Dfs(G, w.To());
}
}
post.enqueue(v);
reversePost.Push(v);
}
public DepthFirstOrder(EdgeWeightedDigraph G)
{
pre = new Queue <int>();
post = new Queue <int>();
reversePost = new Stack <int>();
marked = new bool[G.VNumber()];
for (int v = 0; v < G.VNumber(); v++)
{
if (!marked[v])
{
Dfs(G, v);
}
}
}
private void FindNegativeCycle()
{
int V = edgeTo.Length;
EdgeWeightedDigraph spt = new EdgeWeightedDigraph(V);
for (int v = 0; v < V; v++)
{
if (edgeTo[v] != null)
{
spt.AddEdge(edgeTo[v]);
}
}
DirectedCycle cf = new DirectedCycle(spt);
cycle = cf.Cycle();
}
public DijkstraSP(EdgeWeightedDigraph G, int s)
{
edgeTo = new DirectedEdge[G.VNumber()];
distTo = new double[G.VNumber()];
pq = new IndexMinPQ <double>(G.VNumber());
for (int v = 0; v < G.VNumber(); v++)
{
distTo[v] = Double.PositiveInfinity;
}
distTo[s] = 0.0;
pq.Insert(s, 0.0);
while (!pq.IsEmpty())
{
Relax(G, pq.DelMin());
}
}
private Stack <int> cycle; //edgeTo[]中的是否有负权重环
public BellmanFordSP(EdgeWeightedDigraph G, int s)
{
distTo = new double[G.VNumber()];
edgeTo = new DirectedEdge[G.VNumber()];
onQ = new bool[G.VNumber()];
queue = new Queue <int>();
for (int v = 0; v < G.VNumber(); v++)
{
distTo[v] = Double.PositiveInfinity;
}
distTo[s] = 0.0;
queue.enqueue(s);
onQ[s] = true;
while (!queue.IsEmpty() && !HasNegativeCycle())
{
int v = queue.dequeue();
onQ[v] = false;
Relax(G, v);
}
}
private void Relax(EdgeWeightedDigraph G, int v)
{
foreach (DirectedEdge e in G.Adj(v))
{// v->w e:v和w相连的边
int w = e.To();
if (distTo[w] > distTo[v] + e.Weight())
{// 起点到达w点的路径 > 起点到达v的路径+e的权重
distTo[w] = distTo[v] + e.Weight();
edgeTo[w] = e;
if (pq.Contains(w))
{
pq.Change(w, distTo[w]);
}
else
{
pq.Insert(w, distTo[w]);
}
}
}
}
private void Relax(EdgeWeightedDigraph G, int v)
{
foreach (DirectedEdge e in G.Adj(v))
{
int w = e.To();
if (distTo[w] > distTo[v] + e.Weight())
{
distTo[w] = distTo[v] + e.Weight();
edgeTo[w] = e;
if (!onQ[w])
{
queue.enqueue(w);
onQ[w] = true;
}
}
if (cost++ % G.VNumber() == 0)
{
FindNegativeCycle();//寻找有向图中是否有负权重环，以保证循环能够结束
}
}
}