/// <summary>
/// Get shortest distance to target.
/// </summary>
public ShortestPathResult <T, W> FindShortestPath(IGraph <T> graph, T source, T destination)
{
//regular argument checks
if (graph?.GetVertex(source) == null || graph.GetVertex(destination) == null)
{
throw new ArgumentException();
}
if (this.@operator == null)
{
throw new ArgumentException("Provide an operator implementation for generic type W during initialization.");
}
if (!graph.IsWeightedGraph)
{
if ([email protected]() != typeof(int))
{
throw new ArgumentException("Edges of unweighted graphs are assigned an imaginary weight of one (1)." +
"Provide an appropriate IShortestPathOperators<int> operator implementation during initialization.");
}
}
//track progress for distance to each Vertex from source
var progress = new Dictionary <T, W>();
//trace our current path by mapping current vertex to its Parent
var parentMap = new Dictionary <T, T>();
//min heap to pick next closest vertex
var minHeap = new FibonacciHeap <MinHeapWrap <T, W> >();
//keep references of heap Node for decrement key operation
var heapMapping = new Dictionary <T, MinHeapWrap <T, W> >();
//add vertices to min heap and progress map
foreach (var vertex in graph.VerticesAsEnumberable)
{
//init parent
parentMap.Add(vertex.Key, default(T));
//init to max value
progress.Add(vertex.Key, @operator.MaxValue);
if (vertex.Key.Equals(source))
{
continue;
}
}
//start from source vertex as current
var current = new MinHeapWrap <T, W>()
{
Distance = @operator.DefaultValue,
Vertex = source
};
minHeap.Insert(current);
heapMapping.Add(current.Vertex, current);
//until heap is empty
while (minHeap.Count > 0)
{
//next min vertex to visit
current = minHeap.Extract();
heapMapping.Remove(current.Vertex);
//no path exists, so return max value
if (current.Distance.Equals(@operator.MaxValue))
{
return(new ShortestPathResult <T, W>(null, @operator.MaxValue));
}
//visit neighbours of current
foreach (var neighbour in graph.GetVertex(current.Vertex).Edges.Where(x => !x.TargetVertexKey.Equals(source)))
{
//new distance to neighbour
var newDistance = @operator.Sum(current.Distance,
graph.GetVertex(current.Vertex).GetEdge(neighbour.TargetVertex).Weight <W>());
//current distance to neighbour
var existingDistance = progress[neighbour.TargetVertexKey];
//update distance if new is better
if (newDistance.CompareTo(existingDistance) < 0)
{
progress[neighbour.TargetVertexKey] = newDistance;
if (!heapMapping.ContainsKey(neighbour.TargetVertexKey))
{
var wrap = new MinHeapWrap <T, W>()
{
Distance = newDistance, Vertex = neighbour.TargetVertexKey
};
minHeap.Insert(wrap);
heapMapping.Add(neighbour.TargetVertexKey, wrap);
}
else
{
//decrement distance to neighbour in heap
var decremented = new MinHeapWrap <T, W>()
{
Distance = newDistance, Vertex = neighbour.TargetVertexKey
};
minHeap.UpdateKey(heapMapping[neighbour.TargetVertexKey], decremented);
heapMapping[neighbour.TargetVertexKey] = decremented;
}
//trace parent
parentMap[neighbour.TargetVertexKey] = current.Vertex;
}
}
}
return(tracePath(graph, parentMap, source, destination));
}
/// <summary>
/// Get shortest distance to target.
/// </summary>
public ShortestPathResult <T, W> FindShortestPath(WeightedDiGraph <T, W> graph, T source, T destination)
{
//regular argument checks
if (graph?.FindVertex(source) == null || graph.FindVertex(destination) == null)
{
throw new ArgumentException();
}
//track progress for distance to each Vertex from source
var progress = new Dictionary <T, W>();
//trace our current path by mapping current vertex to its Parent
var parentMap = new Dictionary <T, T>();
//min heap to pick next closest vertex
var minHeap = new FibornacciHeap <MinHeapWrap <T, W> >();
//keep references of heap Node for decrement key operation
var heapMapping = new Dictionary <T, MinHeapWrap <T, W> >();
//add vertices to min heap and progress map
foreach (var vertex in graph.Vertices)
{
//init parent
parentMap.Add(vertex.Key, default(T));
//init to max value
progress.Add(vertex.Key, operators.MaxValue);
if (vertex.Key.Equals(source))
{
continue;
}
}
//start from source vertex as current
var current = new MinHeapWrap <T, W>()
{
Distance = operators.DefaultValue,
Vertex = source
};
minHeap.Insert(current);
heapMapping.Add(current.Vertex, current);
//until heap is empty
while (minHeap.Count > 0)
{
//next min vertex to visit
current = minHeap.Extract();
heapMapping.Remove(current.Vertex);
//no path exists, so return max value
if (current.Distance.Equals(operators.MaxValue))
{
return(new ShortestPathResult <T, W>(null, operators.MaxValue));
}
//visit neighbours of current
foreach (var neighbour in graph.Vertices[current.Vertex].OutEdges.Where(x => !x.Key.Value.Equals(source)))
{
//new distance to neighbour
var newDistance = operators.Sum(current.Distance,
graph.Vertices[current.Vertex].OutEdges[neighbour.Key]);
//current distance to neighbour
var existingDistance = progress[neighbour.Key.Value];
//update distance if new is better
if (newDistance.CompareTo(existingDistance) < 0)
{
progress[neighbour.Key.Value] = newDistance;
if (!heapMapping.ContainsKey(neighbour.Key.Value))
{
var wrap = new MinHeapWrap <T, W>()
{
Distance = newDistance, Vertex = neighbour.Key.Value
};
minHeap.Insert(wrap);
heapMapping.Add(neighbour.Key.Value, wrap);
}
else
{
//decrement distance to neighbour in heap
var decremented = new MinHeapWrap <T, W>()
{
Distance = newDistance, Vertex = neighbour.Key.Value
};
minHeap.UpdateKey(heapMapping[neighbour.Key.Value], decremented);
heapMapping[neighbour.Key.Value] = decremented;
}
//trace parent
parentMap[neighbour.Key.Value] = current.Vertex;
}
}
}
return(tracePath(graph, parentMap, source, destination));
}
/// <summary>
/// Get shortest distance to target
/// </summary>
/// <param name="graph"></param>
/// <param name="source"></param>
/// <param name="destination"></param>
/// <returns></returns>
public ShortestPathResult <T, W> GetShortestPath(WeightedDiGraph <T, W> graph, T source, T destination)
{
//regular argument checks
if (graph?.FindVertex(source) == null || graph.FindVertex(destination) == null)
{
throw new ArgumentException();
}
//track progress for distance to each Vertex from source
var progress = new System.Collections.Generic.Dictionary <T, W>();
//trace our current path by mapping current vertex to its Parent
var parentMap = new System.Collections.Generic.Dictionary <T, T>();
//min heap to pick next closest vertex
var minHeap = new FibornacciMinHeap <MinHeapWrap <T, W> >();
//keep references of heap Node for decrement key operation
var heapMapping = new System.Collections.Generic.Dictionary <T, FibornacciHeapNode <MinHeapWrap <T, W> > >();
//add vertices to min heap and progress map
foreach (var vertex in graph.Vertices)
{
//init parent
parentMap.Add(vertex.Key, default(T));
//init to max value
progress.Add(vertex.Key, operators.MaxValue);
if (vertex.Key.Equals(source))
{
continue;
}
//construct heap for all vertices with Max Distance as default
var wrap = new MinHeapWrap <T, W>()
{
Distance = operators.MaxValue,
Target = vertex.Key
};
var heapNode = minHeap.Insert(wrap);
heapMapping.Add(vertex.Key, heapNode);
}
//start from source vertex as current
var current = new MinHeapWrap <T, W>()
{
Distance = operators.DefaultValue,
Target = source
};
//until heap is empty
while (minHeap.Count > 0)
{
//no path exists, so return max value
if (current.Distance.Equals(operators.MaxValue))
{
return(new ShortestPathResult <T, W>(null, operators.MaxValue));
}
//visit neighbours of current
foreach (var neighbour in graph.Vertices[current.Target].OutEdges)
{
//new distance to neighbour
var newDistance = operators.Sum(current.Distance,
graph.Vertices[current.Target].OutEdges[neighbour.Key]);
//current distance to neighbour
var existingDistance = progress[neighbour.Key.Value];
//update distance if new is better
if (newDistance.CompareTo(existingDistance) < 0)
{
progress[neighbour.Key.Value] = newDistance;
heapMapping[neighbour.Key.Value].Value.Distance = newDistance;
//decrement distance to neighbour in heap
minHeap.DecrementKey(heapMapping[neighbour.Key.Value]);
//trace parent
parentMap[neighbour.Key.Value] = current.Target;
}
}
//next min vertex to visit
current = minHeap.ExtractMin();
}
return(tracePath(graph, parentMap, source, destination));
}
public int CompareTo(MinHeapWrap <T, W> other)
{
return(Distance.CompareTo(other.Distance));
}