/// <summary>
/// Dijkstra algorithm (shortest path) based on graph g for start vertice s. Positive cycles are allowed in shortest path algorithm
/// </summary>
/// <param name="g">Graph for search</param>
/// <param name="s">Start vertice</param>
public static PathStats ShortestPath(GraphBase g, int s)
{
var ps = new PathStats(g.V);
for (var i = 0; i < ps.Dist.Length; i++)
{
ps.Dist[i] = int.MaxValue;
ps.Prev[i] = -1;
}
ps.Dist[s] = 0;//start vertice
var pq = new IndexMinPQ<Distance>(ps.Dist.Length);
for (int i = 0; i < ps.Dist.Length; i++)
{
pq.Insert(i, new Distance { V = i, Dist = ps.Dist[i] });
}
while (!pq.IsEmpty())
{
var v = pq.DelRoot();
foreach (var e in g.Adjacent(v))
{
if (ps.Dist[e.V2] > ps.Dist[v] + e.Weight)
{
ps.Dist[e.V2] = ps.Dist[v] + e.Weight;
ps.Prev[e.V2] = v;
pq.ChangeKey(e.V2, new Distance { V = e.V2, Dist = ps.Dist[e.V2] });
}
}
}
return ps;
}
public static DfsStats DepthFirstSearch(GraphBase g)
{
var ds = new DfsStats(g.V);
for (var i = 0; i < g.V; i++)
ds.Visited[i] = false;
for (var i = 0; i < g.V; i++)
if (!ds.Visited[i])
{
ds.ComponentCount++;
Explore(g, i, ds);
}
return ds;
}
public static void Explore(GraphBase g, int v, DfsStats dfsStats)
{
PreVisitVertice(v, dfsStats);
foreach (var e in g.Adjacent(v))
{
if (!dfsStats.Visited[e.V2])
{
Explore(g, e.V2, dfsStats);
}
//else if (e < v)
//only directed graph has 'back edge'
else if (g is DirectedGraph && e.V2 < v)//e < v is not right
{
dfsStats.BackEdges.Add(new Edge { V1 = v, V2 = e.V2 });
}
}
PostVisitVertice(v, dfsStats);
}
public static LinkedList<int> GetLinearization(GraphBase g)
{
return DepthFirstSearch(g).Linearization;
}
private static PathStats GetPathStats(GraphBase g, int s, bool isShortest)
{
var ps = new PathStats(g.V);
for (var i = 0; i < ps.Dist.Length; i++)
{
ps.Dist[i] = isShortest ? int.MaxValue : int.MinValue;
ps.Prev[i] = -1;
}
ps.Dist[s] = 0;//start vertice
var pq = isShortest ? new MinPQ<Distance>(ps.Dist.Length) : new MaxPQ<Distance>(ps.Dist.Length);
pq.Insert(new Distance { Dist = 0, V = s });
while (!pq.IsEmpty())
{
var v = pq.DelRoot();
foreach (var e in g.Adjacent(v.V))
{
if ((isShortest && ps.Dist[e.V2] > ps.Dist[v.V] + e.Weight) || //shortest path
(!isShortest && ps.Dist[e.V2] < ps.Dist[v.V] + e.Weight)) //longest path
{
ps.Dist[e.V2] = ps.Dist[v.V] + e.Weight;
ps.Prev[e.V2] = v.V;
pq.Insert(new Distance { V = e.V2, Dist = ps.Dist[e.V2] });
}
}
}
return ps;
}
