/// <summary>
/// Finds the shortest, weighted path between two vertices, if one exists. Assumes there are no negative-weight edges in the graph.
/// </summary>
/// <param name="from">The start of the path.</param>
/// <param name="to">The end of the path.</param>
/// <param name="path">The path that was found. <code>null</code> if there is no path.</param>
/// <returns><code>true</code> if there is a path; <code>false</code> otherwise.</returns>
public bool Dijkstra(uint from, uint to, out Path path)
{
path = null;
DMinHeap<int, uint> fringe = new DMinHeap<int, uint>();
Dictionary<uint, uint> parents = new Dictionary<uint, uint>();
Dictionary<uint, int> dist = new Dictionary<uint, int>();
this.DijkstraInit(from, dist, fringe);
uint current;
while (fringe.Count > 0)
{
current = fringe.Extract();
if (current == to)
{
path = Path.FromParents(from, to, parents, this);
return true;
}
this.DijkstraRelax(current, dist, parents, fringe);
}
return false;
}
/// <summary>
/// Finds the shortest, weighted path between two vertices, if one exists. Assumes there are no negative-weight edges in the graph.
/// </summary>
/// <param name="from">The start of the path.</param>
/// <param name="to">The end of the path.</param>
/// <param name="path">The path that was found. <code>null</code> if there is no path.</param>
/// <returns><code>true</code> if there is a path; <code>false</code> otherwise.</returns>
public bool Dijkstra(uint from, uint to, out Path path)
{
path = null;
DMinHeap <int, uint> fringe = new DMinHeap <int, uint>();
Dictionary <uint, uint> parents = new Dictionary <uint, uint>();
Dictionary <uint, int> dist = new Dictionary <uint, int>();
this.DijkstraInit(from, dist, fringe);
uint current;
while (fringe.Count > 0)
{
current = fringe.Extract();
if (current == to)
{
path = Path.FromParents(from, to, parents, this);
return(true);
}
this.DijkstraRelax(current, dist, parents, fringe);
}
return(false);
}
private void DijkstraInit(uint from, Dictionary<uint, int> dist, DMinHeap<int, uint> fringe)
{
foreach (uint v in this.Vertices.Keys)
{
if (v == from)
dist[v] = 0;
else
dist[v] = int.MaxValue;
fringe.Add(v, dist[v]);
}
}
/// <summary>
/// Find the shortest, weighted paths from a given vertex to all other vertices. Assumes there are no negative-weight edges in the graph.
/// </summary>
/// <param name="from">The vertex to calculate the shortest paths from.</param>
/// <param name="lengths">The lengths of the shortest paths to all vertices.</param>
/// <param name="parents">The parent-pointers for the paths to all vertices.</param>
public void Dijkstra(uint from, out Dictionary<uint, int> lengths, out Dictionary<uint, uint> parents)
{
DMinHeap<int, uint> fringe = new DMinHeap<int, uint>();
parents = new Dictionary<uint, uint>();
lengths = new Dictionary<uint, int>();
this.DijkstraInit(from, lengths, fringe);
uint current;
while (fringe.Count > 0)
{
current = fringe.Extract();
this.DijkstraRelax(current, lengths, parents, fringe);
}
}
private void DijkstraInit(uint from, Dictionary <uint, int> dist, DMinHeap <int, uint> fringe)
{
foreach (uint v in this.Vertices.Keys)
{
if (v == from)
{
dist[v] = 0;
}
else
{
dist[v] = int.MaxValue;
}
fringe.Add(v, dist[v]);
}
}
private void DijkstraRelax(uint current, Dictionary<uint, int> dist, Dictionary<uint, uint> parents, DMinHeap<int, uint> fringe)
{
foreach (Edge e in this.Vertices[current].Neighbours.Values)
{
if (!fringe.ContainsValue(e.To))
continue;
int newDist = dist[current] + e.Weight;
if (newDist < dist[e.To])
{
dist[e.To] = newDist;
parents[e.To] = current;
fringe.ChangeKey(e.To, newDist);
}
}
}
/// <summary>
/// Find the shortest, weighted paths from a given vertex to all other vertices. Assumes there are no negative-weight edges in the graph.
/// </summary>
/// <param name="from">The vertex to calculate the shortest paths from.</param>
/// <param name="lengths">The lengths of the shortest paths to all vertices.</param>
/// <param name="parents">The parent-pointers for the paths to all vertices.</param>
public void Dijkstra(uint from, out Dictionary <uint, int> lengths, out Dictionary <uint, uint> parents)
{
DMinHeap <int, uint> fringe = new DMinHeap <int, uint>();
parents = new Dictionary <uint, uint>();
lengths = new Dictionary <uint, int>();
this.DijkstraInit(from, lengths, fringe);
uint current;
while (fringe.Count > 0)
{
current = fringe.Extract();
this.DijkstraRelax(current, lengths, parents, fringe);
}
}
public static T[] PatienceSort(T[] input, int start, int length)
{
CheckArguments(input, start, length);
List <Stack <T> > stacks = new List <Stack <T> >();
for (int i = start; i < start + length; i++)
{
Stack <T> stack = new Stack <T>();
stack.Push(input[i]);
int index = stacks.BinarySearch(stack);
if (index < 0)
{
index = ~index;
}
if (index != stacks.Count)
{
stacks[index].Push(input[i]);
}
else
{
stacks.Add(stack);
}
}
DMinHeap <T, Stack <T> > heap = new DMinHeap <T, Stack <T> >(3);
foreach (Stack <T> s in stacks)
{
heap.Add(s, s.Peek());
}
for (int i = start; i < start + length; i++)
{
Stack <T> stack = heap.Extract();
input[i] = stack.Pop();
if (stack.Count != 0)
{
heap.Add(stack, stack.Peek());
}
}
return(input);
}
/// <summary>
/// Returns <code>true</code> if there is a path between two given nodes in the given, weighted graph; <code>false</code> otherwise.
/// </summary>
/// <param name="graph">The graph to find the path in.</param>
/// <param name="start">The start of the path.</param>
/// <param name="end">The end of the path.</param>
/// <param name="path">A list containing the edges of the path that was found, in order. Empty if there is no path.</param>
/// <returns><code>true</code> if there is a path; <code>false</code> otherwise.</returns>
public static bool ShortestPath(IGraph <IWeightedGraphEdge> graph, IGraphNode <IWeightedGraphEdge> start, IGraphNode <IWeightedGraphEdge> end, out List <IWeightedGraphEdge> path)
{
path = new List <IWeightedGraphEdge>();
DMinHeap <DijkstraNode> open = new DMinHeap <DijkstraNode>();
open.Add(new DijkstraNode(start, null, null));
HashSet <uint> closed = new HashSet <uint>();
closed.Add(start.ID);
DijkstraNode node;
while (open.Count > 0)
{
node = open.Extract();
foreach (IWeightedGraphEdge e in node.Node.Neighbours)
{
if (closed.Contains(e.To))
{
continue;
}
else if (e.To == end.ID)
{
path.Add(e);
while (node.Parent != null)
{
path.Add(node.Edge);
node = node.Parent;
}
path.Reverse();
return(true);
}
open.Add(new DijkstraNode(graph.Nodes[e.To], e, node));
}
}
return(false);
}
private void DijkstraRelax(uint current, Dictionary <uint, int> dist, Dictionary <uint, uint> parents, DMinHeap <int, uint> fringe)
{
foreach (Edge e in this.Vertices[current].Neighbours.Values)
{
if (!fringe.ContainsValue(e.To))
{
continue;
}
int newDist = dist[current] + e.Weight;
if (newDist < dist[e.To])
{
dist[e.To] = newDist;
parents[e.To] = current;
fringe.ChangeKey(e.To, newDist);
}
}
}