/// <summary>
/// Augment current Path to residual Graph
/// </summary>
/// <param name="graph"></param>
/// <param name="residualGraph"></param>
/// <param name="path"></param>
/// <returns></returns>
private W AugmentResidualGraph(WeightedDiGraph <T, W> graph,
WeightedDiGraph <T, W> residualGraph, List <T> path)
{
var min = operators.MaxWeight;
for (int i = 0; i < path.Count - 1; i++)
{
var vertex_1 = residualGraph.FindVertex(path[i]);
var vertex_2 = residualGraph.FindVertex(path[i + 1]);
var edgeValue = vertex_1.OutEdges[vertex_2];
if (min.CompareTo(edgeValue) > 0)
{
min = edgeValue;
}
}
//augment path
for (int i = 0; i < path.Count - 1; i++)
{
var vertex_1 = residualGraph.FindVertex(path[i]);
var vertex_2 = residualGraph.FindVertex(path[i + 1]);
//substract from forward paths
vertex_1.OutEdges[vertex_2] = operators.SubstractWeights(vertex_1.OutEdges[vertex_2], min);
//add for backward paths
vertex_2.OutEdges[vertex_1] = operators.AddWeights(vertex_2.OutEdges[vertex_1], min);
}
return(min);
}
/// <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 == null || graph.FindVertex(source) == null ||
graph.FindVertex(destination) == null)
{
throw new ArgumentException();
}
var progress = new Dictionary <T, W>();
var parentMap = new Dictionary <T, T>();
foreach (var vertex in graph.Vertices)
{
parentMap.Add(vertex.Key, default(T));
progress.Add(vertex.Key, operators.MaxValue);
}
progress[source] = operators.DefaultValue;
var iterations = graph.Vertices.Count - 1;
var updated = true;
while (iterations > 0 && updated)
{
updated = false;
foreach (var vertex in graph.Vertices)
{
//skip not discovered nodes
if (progress[vertex.Key].Equals(operators.MaxValue))
{
continue;
}
foreach (var edge in vertex.Value.OutEdges)
{
var currentDistance = progress[edge.Key.Value];
var newDistance = operators.Sum(progress[vertex.Key],
vertex.Value.OutEdges[edge.Key]);
if (newDistance.CompareTo(currentDistance) < 0)
{
updated = true;
progress[edge.Key.Value] = newDistance;
parentMap[edge.Key.Value] = vertex.Key;
}
}
}
iterations--;
if (iterations < 0)
{
throw new Exception("Negative cycle exists in this graph.");
}
}
return(tracePath(graph, parentMap, source, destination));
}
/// <summary>
/// Search path to target using the heuristic.
/// </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 FibonacciHeap <AStarWrap <T, W> >();
//keep references of heap Node for decrement key operation
var heapMapping = new Dictionary <T, AStarWrap <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 AStarWrap <T, W>(heuristic, destination)
{
Distance = operators.DefaultValue,
Vertex = source
};
//insert neighbour in heap
minHeap.Insert(current);
heapMapping[source] = 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))
{
//decrement distance to neighbour in heap
var decremented = new AStarWrap <T, W>(heuristic, destination)
{
Distance = newDistance, Vertex = neighbour.Key.Value
};
minHeap.UpdateKey(heapMapping[neighbour.Key.Value], decremented);
heapMapping[neighbour.Key.Value] = decremented;
}
else
{
//insert neighbour in heap
var discovered = new AStarWrap <T, W>(heuristic, destination)
{
Distance = newDistance, Vertex = neighbour.Key.Value
};
minHeap.Insert(discovered);
heapMapping[neighbour.Key.Value] = discovered;
}
//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 == null || 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 FibornacciMinHeap <MinHeapWrap <T, W> >();
//keep references of heap Node for decrement key operation
var heapMapping = new 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 sourceVertex = graph.Vertices[source];
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 ShortestPathResult <T, W> GetShortestPath(WeightedDiGraph <T, W> graph, T source, T destination)
{
if (graph == null || graph.FindVertex(source) == null ||
graph.FindVertex(destination) == null)
{
throw new ArgumentException();
}
var progress = new Dictionary <T, W>();
var parentMap = new Dictionary <T, T>();
var minHeap = new FibornacciMinHeap <MinHeapWrap <T, W> >();
var heapMapping = new Dictionary <T, FibornacciHeapNode <MinHeapWrap <T, W> > >();
foreach (var vertex in graph.Vertices)
{
parentMap.Add(vertex.Key, default(T));
progress.Add(vertex.Key, operators.MaxValue);
if (vertex.Key.Equals(source))
{
continue;
}
var wrap = new MinHeapWrap <T, W>()
{
Distance = operators.MaxValue,
Target = vertex.Key
};
var heapNode = minHeap.Insert(wrap);
heapMapping.Add(vertex.Key, heapNode);
}
var sourceVertex = graph.Vertices[source];
var current = new MinHeapWrap <T, W>()
{
Distance = operators.DefaultValue,
Target = source
};
while (minHeap.Count > 0)
{
if (current.Distance.Equals(operators.MaxValue))
{
return(new ShortestPathResult <T, W>(null, operators.MaxValue));
}
foreach (var neighbour in graph.Vertices[current.Target].OutEdges)
{
var newDistance = operators.Sum(current.Distance,
graph.Vertices[current.Target].OutEdges[neighbour.Key]);
var existingDistance = progress[neighbour.Key.Value];
if (newDistance.CompareTo(existingDistance) < 0)
{
progress[neighbour.Key.Value] = newDistance;
heapMapping[neighbour.Key.Value].Value.Distance = newDistance;
minHeap.DecrementKey(heapMapping[neighbour.Key.Value]);
parentMap[neighbour.Key.Value] = current.Target;
}
}
current = minHeap.ExtractMin();
}
return(tracePath(graph, parentMap, source, destination));
}