public static IReadOnlyDictionary <GraphNode <T>, GraphNode <T> > RunDijkstraFrom(UndirectedGraph <T> graph, T src)
{
if (!graph.Nodes.TryGetValue(new GraphNode <T>(src), out var source))
{
return(null);
}
var predecessors = new Dictionary <GraphNode <T>, GraphNode <T> >();//keeps track of the shortest path predecessor
//using Dijkstra's algorithm
var priorityQ = new MinHeap <GraphNode <T> >(new GraphNode <T>(default(T)));
foreach (var node in graph.Nodes)
{
node.Weight = source.Equals(node) ? 0 : int.MaxValue;
priorityQ.Add(node);
predecessors[source] = null;
}
while (priorityQ.Count != 0)
{
var minNode = priorityQ.GetMin();
minNode.Color = Color.Colored;//indicating that these nodes are done
if (!graph.Neighbors.ContainsKey(minNode))
{
priorityQ.ExtractMin();
continue;
}
foreach (var neighbor in graph.Neighbors[minNode])
{
graph.Nodes.TryGetValue(neighbor, out var neighborNode);
if (neighborNode.Color == Color.Colored)
{
continue;
}
var edge = graph.GetEdge(minNode, neighbor);
//if (!graph.Edges.TryGetValue(new Edge<T>(minNode, neighbor), out var edge))
// throw new InvalidDataException($"failed to find edge to neighbor {minNode.Label}->{neighbor.Label}");
if (neighborNode.Weight > minNode.Weight + edge.Weight)
{
neighborNode.Weight = minNode.Weight + edge.Weight;
predecessors[neighborNode] = minNode;
}
}
priorityQ.ExtractMin();
}
return(predecessors);
}
public void MinHeap_Test()
{
var minHeap = new MinHeap <int>();
minHeap.Insert(5);
minHeap.Insert(3);
minHeap.Insert(1);
minHeap.Insert(4);
minHeap.Insert(2);
var result = minHeap.ExtractMin();
Assert.That(result, Is.EqualTo(1));
var secondResult = minHeap.ExtractMin();
Assert.That(secondResult, Is.EqualTo(2));
}
//for directed Graph
public static IReadOnlyDictionary <GraphNode <T>, GraphNode <T> > RunDijkstraFrom(DirectedGraph <T> graph, T src)
{
if (!graph.Nodes.TryGetValue(new GraphNode <T>(src), out var source))
{
return(null);
}
var predecessors = new Dictionary <GraphNode <T>, GraphNode <T> >();//keeps track of the shortest path predecessor
//using Dijkstra's algorithm
var priorityQ = new MinHeap <GraphNode <T> >(new GraphNode <T>(default(T)));
foreach (var node in graph.Nodes)
{
node.Weight = source.Equals(node) ? 0 : int.MaxValue;
priorityQ.Add(node);
predecessors[source] = null;
}
while (priorityQ.Count != 0)
{
var minNode = priorityQ.GetMin();
if (!graph.Neighbors.ContainsKey(minNode))
{
priorityQ.ExtractMin();
continue;
}
foreach (var neighbor in graph.Neighbors[minNode])
{
graph.Nodes.TryGetValue(neighbor, out var neighborNode);
var edges = graph.GetEdges(minNode, neighbor);
foreach (var edge in edges)
{
if (neighborNode.Weight > minNode.Weight + edge.Weight)
{
neighborNode.Weight = minNode.Weight + edge.Weight;
predecessors[neighborNode] = minNode;
}
}
}
priorityQ.ExtractMin();
}
return(predecessors);
}
/// <summary>
/// Runtime O(n * log(n))
/// </summary>
/// <returns>The kth smallest.</returns>
/// <param name="arr">Arr.</param>
/// <param name="k">K.</param>
public int FindKthSmallest(int[] arr, int k)
{
// push into a heap
var minHeap = new MinHeap <int>();
for (var i = 0; i < arr.Length; i++)
{
minHeap.Insert(arr[i]);
}
// what is insert run time for a heap - log(n)
var min = int.MaxValue;
for (int i = 0; i < k; i++)
{
min = minHeap.ExtractMin();
}
return(min);
}
