/// <summary>
/// Traverses graph from start vertex.
/// </summary>
/// <param name="graph">Graph instance.</param>
/// <param name="startVertex">Vertex that search starts from.</param>
/// <param name="action">Action that needs to be executed on each graph vertex.</param>
/// <param name="visited">Hash set with visited vertices.</param>
private void Bfs(IDirectedWeightedGraph <T> graph, Vertex <T> startVertex, Action <Vertex <T> >?action, HashSet <Vertex <T> > visited)
{
var queue = new Queue <Vertex <T> >();
queue.Enqueue(startVertex);
while (queue.Count > 0)
{
var currentVertex = queue.Dequeue();
if (currentVertex == null || visited.Contains(currentVertex))
{
continue;
}
foreach (var vertex in graph.GetNeighbors(currentVertex))
{
queue.Enqueue(vertex !);
}
action?.Invoke(currentVertex);
visited.Add(currentVertex);
}
}
/// <summary>
/// Traverses graph from start vertex.
/// </summary>
/// <param name="graph">Graph instance.</param>
/// <param name="startVertex">Vertex that search starts from.</param>
/// <param name="action">Action that needs to be executed on each graph vertex.</param>
/// <param name="visited">Hash set with visited vertices.</param>
private void Dfs(IDirectedWeightedGraph <T> graph, Vertex <T> startVertex, Action <Vertex <T> >?action, HashSet <Vertex <T> > visited)
{
action?.Invoke(startVertex);
visited.Add(startVertex);
foreach (var vertex in graph.GetNeighbors(startVertex))
{
if (vertex == null || visited.Contains(vertex))
{
continue;
}
Dfs(graph, vertex !, action, visited);
}
}
// X - set of explored vertices of graph G
// V-X - set of unexplored vertices of graph G
//
// Invariant.
// The key of a vertex w belongs to V-X is the min Dijkstra score of an edge with tail v belongs to X
// and head w, or +infinity if no such edge exists.
// key(w) = min len(v) + l(vw)
//
// DijkstraSearch(graph G, vertex s):
// // Initialization
// X = empty set
// H = empty min heap
// key(s) = 0
// for each vertex V in G.vertices do: key(V) = +infinity
// for each vertex V in G.vertices do: H.Insert(V)
// // Main loop
// while H is not empty do:
// w* = H.ExtractMin()
// X.Add(w*)
// len(w*) = key(w*)
// // Update Heap to maintain Invariant
// for every edge(w*, y) do:
// H.Delete(y) // Delete: given a heap H and a pointer to an object y in H, delete y from H.
// key(y) = min {key(y), len(w*) + l(w*y)}
// H.Insert(y)
public static int[] DijkstraMinHeap(IDirectedWeightedGraph <int> weightedGraph, int startVertex)
{
var minHeap = new IndexMinHeap <int>(weightedGraph.VerticesCount);
var exploredVertices = new HashSet <int> {
startVertex
};
var len = new int[weightedGraph.VerticesCount + 1];
for (int i = 1; i <= weightedGraph.VerticesCount; i++)
{
var score = i == startVertex ? 0 : 1000000;
len[i] = score;
minHeap.Insert(i, score);
}
while (!minHeap.IsEmpty())
{
int u = minHeap.GetMin();
len[u] = minHeap.GetItemKey(u);
minHeap.ExtractMin();
exploredVertices.Add(u);
foreach ((int v, int weight) in weightedGraph.GetAdjacentVertices(u))
{
if (!exploredVertices.Contains(v))
{
if (len[v] > len[u] + weight)
{
int vKey = minHeap.GetItemKey(v);
int newScore = Math.Min(len[u] + weight, vKey);
// can use (minHeap.Delete + minHeap.Insert) instead of DecreaseKey
// but this would be less effective
minHeap.DecreaseKey(v, newScore);
len[v] = newScore;
}
}
}
}
return(len);
}
/// <summary>
/// Traverses graph from start vertex.
/// </summary>
/// <param name="graph">Graph instance.</param>
/// <param name="startVertex">Vertex that search starts from.</param>
/// <param name="action">Action that needs to be executed on each graph vertex.</param>
public void VisitAll(IDirectedWeightedGraph <T> graph, Vertex <T> startVertex, Action <Vertex <T> >?action = default)
{
Dfs(graph, startVertex, action, new HashSet <Vertex <T> >());
}
private static (int vertex, int weight) FindMinWeightVertex(IDirectedWeightedGraph <int> weightedGraph, (int tail, int head, int weight) edge)
