// relax edge e
private void relax(DirectedEdge e)
{
int v = e.from(), w = e.to();
if (distTo[w] > distTo[v] + e.Weight())
{
distTo[w] = distTo[v] + e.Weight();
edgeTo[w] = e;
}
}
// relax edge e and update pq if changed
private void relax(DirectedEdge e)
{
int v = e.from(), w = e.to();
if (distTo[w] > distTo[v] + e.Weight())
{
distTo[w] = distTo[v] + e.Weight();
edgeTo[w] = e;
if (pq.contains(w))
{
pq.decreaseKey(w, distTo[w]);
}
else
{
pq.insert(w, distTo[w]);
}
}
}
void Start()
{
string[] lines = txt.text.Split(new char[] { '\n' });
// V currencies
int V = int.Parse(lines[0]);
string[] name = new string[V];
// create complete network
EdgeWeightedDigraph G = new EdgeWeightedDigraph(V);
for (int v = 0; v < V; v++)
{
string[] lineStrs = lines[v + 1].Split(new char[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
name[v] = lineStrs[0];
for (int w = 0; w < V; w++)
{
double rate = double.Parse(lineStrs[w + 1]);
DirectedEdge e = new DirectedEdge(v, w, -Math.Log(rate));
G.addEdge(e);
}
}
// find negative cycle
BellmanFordSP spt = new BellmanFordSP(G, 0);
if (spt.hasNegativeCycle())
{
double stake = 1000.0;
foreach (DirectedEdge e in spt.negativeCycle())
{
string str = (stake + " " + name[e.from()] + " ");
stake *= Math.Exp(-e.Weight());
str += ("= " + stake + " " + name[e.to()] + "\n");
print(str);
}
print("以1000元为本金，该负权重环一圈套利" + (stake - 1000));
}
else
{
print("No arbitrage opportunity");
}
}
// check optimality conditions: either
// (i) there exists a negative cycle reacheable from s
// or
// (ii) for all edges e = v->w: distTo[w] <= distTo[v] + e.weight()
// (ii') for all edges e = v->w on the SPT: distTo[w] == distTo[v] + e.weight()
private bool check(EdgeWeightedDigraph G, int s)
{
// has a negative cycle
if (hasNegativeCycle())
{
double weight = 0.0;
foreach (DirectedEdge e in negativeCycle())
{
weight += e.Weight();
}
if (weight >= 0.0)
{
throw new System.Exception("error: weight of negative cycle = " + weight);
return false;
}
}
// no negative cycle reachable from source
else
{
// check that distTo[v] and edgeTo[v] are consistent
if (distTo[s] != 0.0 || edgeTo[s] != null)
{
throw new System.Exception("distanceTo[s] and edgeTo[s] inconsistent");
return false;
}
for (int v = 0; v < G.V(); v++)
{
if (v == s) continue;
if (edgeTo[v] == null && distTo[v] != double.PositiveInfinity)
{
throw new System.Exception("distTo[] and edgeTo[] inconsistent");
return false;
}
}
// check that all edges e = v->w satisfy distTo[w] <= distTo[v] + e.weight()
for (int v = 0; v < G.V(); v++)
{
foreach (DirectedEdge e in G.Adj(v))
{
int w = e.to();
if (distTo[v] + e.Weight() < distTo[w])
{
throw new System.Exception("edge " + e + " not relaxed");
return false;
}
}
}
// check that all edges e = v->w on SPT satisfy distTo[w] == distTo[v] + e.weight()
for (int w = 0; w < G.V(); w++)
{
if (edgeTo[w] == null) continue;
DirectedEdge e = edgeTo[w];
int v = e.from();
if (w != e.to()) return false;
if (distTo[v] + e.Weight() != distTo[w])
{
throw new System.Exception("edge " + e + " on shortest path not tight");
return false;
}
}
}
print("Satisfies optimality conditions");
return true;
}
private bool Check(EdgeWeightedDigraph G, int s)
{
// check that edge weights are nonnegative
foreach (DirectedEdge e in G.edges())
{
if (e.Weight() < 0)
{
throw new System.Exception("negative edge weight detected");
return(false);
}
}
// check that distTo[v] and edgeTo[v] are consistent
if (distTo[s] != 0.0 || edgeTo[s] != null)
{
throw new System.Exception("distTo[s] and edgeTo[s] inconsistent");
return(false);
}
for (int v = 0; v < G.V(); v++)
{
if (v == s)
{
continue;
}
if (edgeTo[v] == null && distTo[v] != double.PositiveInfinity)
{
throw new System.Exception("distTo[] and edgeTo[] inconsistent");
return(false);
}
}
// check that all edges e = v->w satisfy distTo[w] <= distTo[v] + e.weight()
for (int v = 0; v < G.V(); v++)
{
foreach (DirectedEdge e in G.Adj(v))
{
int w = e.to();
if (distTo[v] + e.Weight() < distTo[w])
{
throw new System.Exception("edge " + e + " not relaxed");
return(false);
}
}
}
// check that all edges e = v->w on SPT satisfy distTo[w] == distTo[v] + e.weight()
for (int w = 0; w < G.V(); w++)
{
if (edgeTo[w] == null)
{
continue;
}
DirectedEdge e = edgeTo[w];
int v = e.from();
if (w != e.to())
{
return(false);
}
if (distTo[v] + e.Weight() != distTo[w])
{
throw new System.Exception("edge " + e + " on shortest path not tight");
return(false);
}
}
return(true);
}
