public static void Main(string[] args)
{
var N = Console.Read();
Console.ReadLine();
var G = new EdgeWeightedDigraph(2 * N + 2);
var s = 2 * N;
var t = 2 * N + 1;
for (int i = 0; i < N; i++)
{
var a = Console.ReadLine().Split(' ');
var duation = double.Parse(a[0]);
G.AddEdge(new DirectedEdge(i, i + N, duation));
G.AddEdge(new DirectedEdge(s, i, 0.0));
G.AddEdge(new DirectedEdge(i + N, t, 0.0));
for (int j = 1; j < a.Length; j++)
{
var successor = int.Parse(a[j]);
G.AddEdge(new DirectedEdge(i + N, successor, 0.0));
}
}
var lp = new AcyclicLP(G, s);
Console.WriteLine("Start times: ");
for (int i = 0; i < N; i++)
{
Console.Write("{0} : {1:f1}\n", i, lp.DistToW(i));
}
Console.WriteLine("Finish time: {0:f1}", lp.DistToW(t));
}
public DijkstraAllPairsSP(EdgeWeightedDigraph G)
{
all = new DijkstraSP[G.V];
for (int v = 0; v < G.V; v++)
{
all[v] = new DijkstraSP(G, v);
}
}
public Topological(EdgeWeightedDigraph G)
{
var cycleFinder = new DirectedCycle(G);
if (!cycleFinder.HasCycle())
{
var dfs = new DepthFirstOrder(G);
Order = dfs.ReversePost;
}
}
private void Relax(EdgeWeightedDigraph g, int v)
{
foreach (var e in g.adj[v])
{
var w = e.To();
if (DistTo[w] < DistTo[v] + e.Weight)
{
DistTo[w] = DistTo[v] + e.Weight;
EdgeTo[w] = e;
}
}
}
public EdgeWeightedCycleFinder(EdgeWeightedDigraph G)
{
marked = new bool[G.V];
OnStack = new bool[G.V];
EdgeTo = new DirectedEdge[G.V];
for (int v = 0; v < G.V; v++)
{
if (!marked[v])
{
DFS(G, v);
}
}
}
public DirectedCycle(EdgeWeightedDigraph G)
{
Marked = new bool[G.V];
EdgeTo = new int[G.V];
OnStack = new bool[G.V];
for (int v = 0; v < G.V; v++)
{
if (!Marked[v])
{
DFS(G, v);
}
}
}
private void DFS(EdgeWeightedDigraph g, int v)
{
Pre.Enqueue(v);
Marked[v] = true;
foreach (var 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.V];
for (int v = 0; v < G.V; v++)
{
if (!Marked[v])
{
DFS(G, v);
}
}
}
private void FindNegativeCycle()
{
var V = EdgeTo.Length;
var spt = new EdgeWeightedDigraph(V);
for (int v = 0; v < V; v++)
{
if (EdgeTo[v] != null)
{
spt.AddEdge(EdgeTo[v]);
}
}
var cf = new EdgeWeightedCycleFinder(spt);
Cycle = cf.Cycle;
}
public AcyclicLP(EdgeWeightedDigraph G, int s)
{
EdgeTo = new DirectedEdge[G.V];
DistTo = new double[G.V];
for (int v = 0; v < G.V; v++)
{
DistTo[v] = double.NegativeInfinity;
}
DistTo[s] = 0.0;
var top = new Topological(G);
foreach (var v in top.Order)
{
Relax(G, v);
}
}
public DijkstraSP(EdgeWeightedDigraph G, int s)
{
EdgeTo = new DirectedEdge[G.V];
DistTo = new double[G.V];
pq = new SortedDictionary <int, double>();
for (int v = 0; v < G.V; v++)
{
DistTo[v] = double.PositiveInfinity;
}
DistTo[0] = 0.0;
pq.Add(s, 0.0);
//核心就是每次选出权重最小点来继续搜索
while (pq.Count > 0)
{
var min = pq.Min();
Relax(G, min.Key);
}
}
private void Relax(EdgeWeightedDigraph g, int v)
{
foreach (var e in g.adj[v])
{
var w = e.To();
if (DistTo[w] > DistTo[v] + e.Weight)
{
DistTo[w] = DistTo[v] + e.Weight;
EdgeTo[w] = e;
if (pq.ContainsKey(w))
{
pq[w] = DistTo[w];
}
else
{
pq.Add(w, DistTo[w]);
}
}
}
}
public BellmanFordSP(EdgeWeightedDigraph G, int s)
{
DistTo = new double[G.V];
EdgeTo = new DirectedEdge[G.V];
OnQ = new bool[G.V];
queue = new Queue <int>();
for (int v = 0; v < G.V; v++)
{
DistTo[v] = double.PositiveInfinity;
}
this.s = s;
DistTo[s] = 0.0;
queue.Enqueue(s);
OnQ[s] = true;
while (queue.Count > 0 && !HasNegativeCycle())
{
var v = queue.Dequeue();
OnQ[v] = false;
Relax(G, v);
}
}
public static void Main(string[] args)
{
//using (var reader = new StreamReader("rates.txt")) {
using (var reader = new StreamReader(args[0])) {
var V = int.Parse(reader.ReadLine().Split(' ')[0]);
var name = new string[V];
var G = new EdgeWeightedDigraph(V);
for (int v = 0; v < V; v++)
{
var line = reader.ReadLine().Split(new char[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
name[v] = line[0];
for (int w = 0; w < V; w++)
{
var rate = double.Parse(line[w + 1]);
if (rate != 1)
{
var e = new DirectedEdge(v, w, -Math.Log(rate));
Console.WriteLine("{0}-->{1} : {2}", v, w, -Math.Log(rate));
G.AddEdge(e);
}
}
}
var spt = new BellmanFordSP(G, 0);
if (spt.HasNegativeCycle())
{
var stake = 1000.0;
foreach (var e in spt.NegativeCycle())
{
Console.Write("{0:f5} {1} ", stake, name[e.From()]);
stake *= Math.Exp(-e.Weight);
Console.WriteLine("= {0:f5} {1}", stake, name[e.To()]);
}
}
else
{
Console.WriteLine("No arbitrage opportunity");
}
//Console.Read();
}
}
private void Relax(EdgeWeightedDigraph G, int v)
{
foreach (var e in G.adj[v])
{
var 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;
}
}
//如果不存在从起点S可达的负权重环，算法会在进行v-1轮放松后结束，
//因为所有最短路含有的边数都不大于v-1，所以进行V轮后就可以检查一次负权重环
if (++cost % G.V == 0)
{
FindNegativeCycle();
}
}
}