public static IEnumerable<int?> Find(DirectedWeightedGraph graph, int source)
{
var dist = new int?[graph.NodesCount];
dist[source] = 0;
var closestNodes = new PriorityQueue<int, int>(dist.Select((d, i) => new KeyValuePair<int, int>(i, d.GetValueOrDefault(int.MaxValue))));
var exploredNodes = new HashSet<int>();
while (closestNodes.Count != 0)
{
var node = closestNodes.ExtractHighestPriorityElement();
exploredNodes.Add(node);
foreach (var edge in graph.GetEdges(node).Where(e => !exploredNodes.Contains(e.EndNode)))
{
if (dist[node] != null)
{
var alt = dist[node].Value + edge.Weight;
if (alt < dist[edge.EndNode].GetValueOrDefault(int.MaxValue))
{
dist[edge.EndNode] = alt;
closestNodes.ChangePriority(edge.EndNode, alt);
}
}
}
}
return dist;
}
public static int GetMinimumSpanningTreeLength(DirectedWeightedGraph graph)
{
int length = 0;
var dist = new int[graph.NodesCount];
const int StartNode = 0;
dist[StartNode] = 0;
for (int i = 0; i < dist.Length; i++)
{
if (i != StartNode)
{
dist[i] = int.MaxValue;
}
}
var closestNodes = new PriorityQueue<int, int>(dist.Select((d, i) => new KeyValuePair<int, int>(i, d)));
var exploredNodes = new HashSet<int>();
while (exploredNodes.Count != graph.NodesCount)
{
var node = closestNodes.ExtractHighestPriorityElement();
length += dist[node];
exploredNodes.Add(node);
foreach (var edge in graph.GetEdges(node).Where(e => !exploredNodes.Contains(e.EndNode)))
{
var alt = edge.Weight;
if (alt < dist[edge.EndNode])
{
dist[edge.EndNode] = alt;
closestNodes.ChangePriority(edge.EndNode, alt);
}
}
}
return length;
}
public void ExtractHighestPriorityElementTest()
{
const int N = 100;
var minHeap = new PriorityQueue<int, int>(Enumerable.Range(0, N).Select(x => new KeyValuePair<int, int>(x, x)).Reverse());
for (int i = 0; i < N; i++)
{
minHeap.ExtractHighestPriorityElement().Should().Be(i);
}
}
public static int GetMaxSpacing(DirectedWeightedGraph graph, int clusterCount)
{
int currentClusterCount = graph.NodesCount;
var unionFind = new UnionFind(currentClusterCount);
var edges = new PriorityQueue<WeightedEdge, int>(graph.GetEdges().Select(e => new KeyValuePair<WeightedEdge, int>(e, e.Weight)));
while (currentClusterCount >= clusterCount)
{
var edge = edges.ExtractHighestPriorityElement();
var cluster1 = unionFind.Find(edge.StartNode);
var cluster2 = unionFind.Find(edge.EndNode);
if (cluster1 != cluster2)
{
if (currentClusterCount == clusterCount)
{
return edge.Weight;
}
unionFind.Union(cluster1, cluster2);
currentClusterCount--;
}
}
return 0;
}
