//edges' weights cannot be negative
public void Dijkstra(IVertex <T> source)
{
Initialize(source);
//var set = new List<VertexSSSP<T>>();
var heap = new MinHeap <VertexSSSP <T> >(vertices.Count + edges.Count);
heap.Insert(source as VertexSSSP <T>);
while (!heap.IsEmpty)
{
var vertex = heap.Extract();
if (vertex.Visited)
{
continue;
}
vertex.Visited = true;
//set.Add(node.Key);
foreach (var edge in edges.Where((e) => e.From.Equals(vertex)))
{
Relax(edge.From, edge.To, edge.Weight);
heap.Insert(edge.To as VertexSSSP <T>);
}
}
}
/// <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);
}