/// <summary>
/// Retrieves the path distance from one node to another, or calculates
/// it if it has not yet been found and CalculateFully has not been called.
/// </summary>
/// <param name="a">The first graph node.</param>
/// <param name="b">The second graph node.</param>
/// <returns>The length of the path from a to b (equals the amount of edges
/// traversed).</returns>
/// <remarks>
/// If CalculateFully has been called and the nodes are not connected, 0 will be returned.
/// If CalculateFully has been called and the nodes were not both passed to it, a IndexOutOfRangeException will be thrown.
/// If CalculateFully has not been called and the nodes are not connected, a GraphNotConnectedException will be thrown.
/// </remarks>
public int this[GraphNode a, GraphNode b]
{
get
{
if (FullyCached)
{
return _distancesFast[a.DistancesIndex, b.DistancesIndex];
}
var index = GetIndex(a, b);
if (!_distances.ContainsKey(index))
{
Dijkstra(a, b);
}
return _distances[index];
}
}
public GraphEdge(GraphNode inside, GraphNode outside)
{
Inside = inside;
Outside = outside;
}
/// <summary>
/// Adds the distance and shortest path between from and to to the respectives
/// dictionarys if not already present.
/// </summary>
private void AddEdge(GraphNode from, GraphNode to, int distFromStart, IDictionary<ushort, ushort> predecessors)
{
var length = distFromStart + 1;
if (FullyCached)
{
var i1 = from.DistancesIndex;
var i2 = to.DistancesIndex;
if (_pathsFast[i1, i2] != null) return;
var path = length > 0 ? GenerateShortestPath(from.Id, to.Id, predecessors, length) : new ushort[0];
_distancesFast[i1, i2] = _distancesFast[i2, i1] = length;
_pathsFast[i1, i2] = _pathsFast[i2, i1] = path;
}
else
{
var index = GetIndex(from, to);
if (_distances.ContainsKey(index)) return;
var path = length > 0 ? GenerateShortestPath(from.Id, to.Id, predecessors, length) : new ushort[0];
_paths[index] = path;
_distances[index] = length;
}
}
/// <summary>
/// Uses a djikstra-like algorithm to flood the graph from the start
/// node until the target node is found (if specified) or until all marked nodes got checked.
/// </summary>
/// <param name="start">The starting node. (not null)</param>
/// <param name="target">The (optional) target node.</param>
/// <exception cref="GraphNotConnectedException">
/// If target node is not null and it could not be found.
/// </exception>
private void Dijkstra(GraphNode start, GraphNode target = null)
{
if (start == null) throw new ArgumentNullException("start");
AddEdge(start, start, -1, null);
if (start == target) return;
// The last newly found nodes.
var front = new HashSet<GraphNode>() { start };
// The already visited nodes.
var visited = new HashSet<GraphNode>() { start };
// The dictionary of the predecessors of the visited nodes.
var predecessors = new Dictionary<ushort, ushort>();
// The traversed distance from the starting node in edges.
var distFromStart = 0;
while (front.Count > 0)
{
var newFront = new HashSet<GraphNode>();
foreach (var node in front)
{
foreach (var adjacentNode in node.Adjacent)
{
if (visited.Contains(adjacentNode))
continue;
predecessors[adjacentNode.Id] = node.Id;
if (adjacentNode == target)
{
AddEdge(start, adjacentNode, distFromStart, predecessors);
return;
}
if (adjacentNode.DistancesIndex >= 0)
{
AddEdge(start, adjacentNode, distFromStart, predecessors);
}
newFront.Add(adjacentNode);
visited.Add(adjacentNode);
}
}
front = newFront;
distFromStart++;
}
// Target node was not found because start and target are not connected.
if (target != null)
throw new GraphNotConnectedException();
}
/// <summary>
/// Compounds two ushort node indices into a single uint one, which
/// is independent of the order of the two indices.
/// </summary>
/// <param name="a">The first index.</param>
/// <param name="b">The second index.</param>
/// <returns>The compounded index.</returns>
private static uint GetIndex(GraphNode a, GraphNode b)
{
var aId = a.Id;
var bId = b.Id;
return (uint)(Math.Min(aId, bId) << 16) + Math.Max(aId, bId);
}
/// <summary>
/// Returns whether the given nodes are connected.
/// </summary>
public bool AreConnected(GraphNode a, GraphNode b)
{
try
{
// Null if not connected and _fullyCached
// Exception if not connected and not _fullyCached
return GetShortestPath(a, b) != null;
}
catch (GraphNotConnectedException)
{
return false;
}
}
/// <summary>
/// Retrieves the shortest path from one node to another, or calculates
/// it if it has not yet been found and CalculateFully has not been called.
/// </summary>
/// <param name="a">The first graph node. (not null)</param>
/// <param name="b">The second graph node. (not null)</param>
/// <returns>The shortest path from a to b, not containing either and ordered from a to b or b to a.</returns>
/// <remarks>
/// If CalculateFully has been called and the nodes are not connected, null will be returned.
/// If CalculateFully has been called and the nodes were not both passed to it, a IndexOutOfRangeException will be thrown.
/// If CalculateFully has not been called and the nodes are not connected, a GraphNotConnectedException will be thrown.
/// </remarks>
public ushort[] GetShortestPath(GraphNode a, GraphNode b)
{
if (FullyCached)
{
return _pathsFast[a.DistancesIndex, b.DistancesIndex];
}
var index = GetIndex(a, b);
if (!_distances.ContainsKey(index))
{
Dijkstra(a, b);
}
return _paths[index];
}
