public MinHeapNode BuildHuffmanTree(char[] data, int[] freq, int size)
{
MinHeapNode left, right, top;
MinHeap minHeap = CreateAndBuildMinHeap(data, freq, size);
while (!IsSizeOne(minHeap))
{
// extract two min freq items from min heap
left = ExtractMin(minHeap);
right = ExtractMin(minHeap);
top = NewNode('$', left.Freq + right.Freq);
top.Left = left;
top.Right = right;
InsertMinHeap(minHeap, top);
}
return(ExtractMin(minHeap));
}
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);
}
public void MinHeapify(MinHeap minHeap, int index)
{
int smallest = index;
int left = 2 * index + 1;
int right = 2 * index + 2;
if (left < minHeap.Size && minHeap.Nodes[left].Freq < minHeap.Nodes[smallest].Freq)
{
smallest = left;
}
if (right < minHeap.Size && minHeap.Nodes[right].Freq < minHeap.Nodes[smallest].Freq)
{
smallest = right;
}
if (smallest != index)
{
SwapMinHeapNode(minHeap.Nodes, smallest, index);
MinHeapify(minHeap, smallest);
}
}
public void MinimumSpanningTreePrim(VertexMST <T> root)
{
foreach (var vertex in vertices.OfType <VertexMST <T> >())
{
vertex.Key = int.MaxValue;
vertex.Predecessor = null;
}
root.Key = 0;
var heap = new MinHeap <VertexMST <T> >(vertices.Count, vertices.OfType <VertexMST <T> >().ToArray());
while (!heap.IsEmpty)
{
//had to call heapify before extract min since it's not a min heap anymore due to the change of keys
//instead of decrease key
heap.Heapify(0);
var min = heap.Extract();
foreach (var edge in edges.Where((e) => e.From.Equals(min) || e.To.Equals(min)))
{
if (edge.To.Equals(min))
{
if (heap.Contains(edge.From as VertexMST <T>) &&
edge.Weight < (edge.From as VertexMST <T>).Key)
{
edge.From.Predecessor = min;
(edge.From as VertexMST <T>).Key = edge.Weight;
}
}
else
{
if (heap.Contains(edge.To as VertexMST <T>) &&
edge.Weight < (edge.To as VertexMST <T>).Key)
{
edge.To.Predecessor = min;
(edge.To as VertexMST <T>).Key = edge.Weight;
}
}
}
}
}
//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>);
}
}
}
public bool IsSizeOne(MinHeap minHeap)
{
return(minHeap.Size == 1);
}
