/// <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)); }