Priority queue in .Net

You might like IntervalHeap from the C5 Generic Collection Library. To quote the user guide

Class IntervalHeap<T> implements interface IPriorityQueue<T> using an interval heap stored as an array of pairs. The FindMin and FindMax operations, and the indexer’s get-accessor, take time O(1). The DeleteMin, DeleteMax, Add and Update operations, and the indexer’s set-accessor, take time O(log n). In contrast to an ordinary priority queue, an interval heap offers both minimum and maximum operations with the same efficiency.

The API is simple enough

> var heap = new C5.IntervalHeap<int>();
> heap.Add(10);
> heap.Add(5);
> heap.FindMin();
5

Install from Nuget https://www.nuget.org/packages/C5 or GitHub https://github.com/sestoft/C5/

Here's my attempt at a .NET heap

public abstract class Heap<T> : IEnumerable<T>
{
    private const int InitialCapacity = 0;
    private const int GrowFactor = 2;
    private const int MinGrow = 1;

    private int _capacity = InitialCapacity;
    private T[] _heap = new T[InitialCapacity];
    private int _tail = 0;

    public int Count { get { return _tail; } }
    public int Capacity { get { return _capacity; } }

    protected Comparer<T> Comparer { get; private set; }
    protected abstract bool Dominates(T x, T y);

    protected Heap() : this(Comparer<T>.Default)
    {
    }

    protected Heap(Comparer<T> comparer) : this(Enumerable.Empty<T>(), comparer)
    {
    }

    protected Heap(IEnumerable<T> collection)
        : this(collection, Comparer<T>.Default)
    {
    }

    protected Heap(IEnumerable<T> collection, Comparer<T> comparer)
    {
        if (collection == null) throw new ArgumentNullException("collection");
        if (comparer == null) throw new ArgumentNullException("comparer");

        Comparer = comparer;

        foreach (var item in collection)
        {
            if (Count == Capacity)
                Grow();

            _heap[_tail++] = item;
        }

        for (int i = Parent(_tail - 1); i >= 0; i--)
            BubbleDown(i);
    }

    public void Add(T item)
    {
        if (Count == Capacity)
            Grow();

        _heap[_tail++] = item;
        BubbleUp(_tail - 1);
    }

    private void BubbleUp(int i)
    {
        if (i == 0 || Dominates(_heap[Parent(i)], _heap[i])) 
            return; //correct domination (or root)

        Swap(i, Parent(i));
        BubbleUp(Parent(i));
    }

    public T GetMin()
    {
        if (Count == 0) throw new InvalidOperationException("Heap is empty");
        return _heap[0];
    }

    public T ExtractDominating()
    {
        if (Count == 0) throw new InvalidOperationException("Heap is empty");
        T ret = _heap[0];
        _tail--;
        Swap(_tail, 0);
        BubbleDown(0);
        return ret;
    }

    private void BubbleDown(int i)
    {
        int dominatingNode = Dominating(i);
        if (dominatingNode == i) return;
        Swap(i, dominatingNode);
        BubbleDown(dominatingNode);
    }

    private int Dominating(int i)
    {
        int dominatingNode = i;
        dominatingNode = GetDominating(YoungChild(i), dominatingNode);
        dominatingNode = GetDominating(OldChild(i), dominatingNode);

        return dominatingNode;
    }

    private int GetDominating(int newNode, int dominatingNode)
    {
        if (newNode < _tail && !Dominates(_heap[dominatingNode], _heap[newNode]))
            return newNode;
        else
            return dominatingNode;
    }

    private void Swap(int i, int j)
    {
        T tmp = _heap[i];
        _heap[i] = _heap[j];
        _heap[j] = tmp;
    }

    private static int Parent(int i)
    {
        return (i + 1)/2 - 1;
    }

    private static int YoungChild(int i)
    {
        return (i + 1)*2 - 1;
    }

    private static int OldChild(int i)
    {
        return YoungChild(i) + 1;
    }

    private void Grow()
    {
        int newCapacity = _capacity*GrowFactor + MinGrow;
        var newHeap = new T[newCapacity];
        Array.Copy(_heap, newHeap, _capacity);
        _heap = newHeap;
        _capacity = newCapacity;
    }

    public IEnumerator<T> GetEnumerator()
    {
        return _heap.Take(Count).GetEnumerator();
    }

    IEnumerator IEnumerable.GetEnumerator()
    {
        return GetEnumerator();
    }
}

public class MaxHeap<T> : Heap<T>
{
    public MaxHeap()
        : this(Comparer<T>.Default)
    {
    }

    public MaxHeap(Comparer<T> comparer)
        : base(comparer)
    {
    }

    public MaxHeap(IEnumerable<T> collection, Comparer<T> comparer)
        : base(collection, comparer)
    {
    }

    public MaxHeap(IEnumerable<T> collection) : base(collection)
    {
    }

    protected override bool Dominates(T x, T y)
    {
        return Comparer.Compare(x, y) >= 0;
    }
}

public class MinHeap<T> : Heap<T>
{
    public MinHeap()
        : this(Comparer<T>.Default)
    {
    }

    public MinHeap(Comparer<T> comparer)
        : base(comparer)
    {
    }

    public MinHeap(IEnumerable<T> collection) : base(collection)
    {
    }

    public MinHeap(IEnumerable<T> collection, Comparer<T> comparer)
        : base(collection, comparer)
    {
    }

    protected override bool Dominates(T x, T y)
    {
        return Comparer.Compare(x, y) <= 0;
    }
}

Some tests:

[TestClass]
public class HeapTests
{
    [TestMethod]
    public void TestHeapBySorting()
    {
        var minHeap = new MinHeap<int>(new[] {9, 8, 4, 1, 6, 2, 7, 4, 1, 2});
        AssertHeapSort(minHeap, minHeap.OrderBy(i => i).ToArray());

        minHeap = new MinHeap<int> { 7, 5, 1, 6, 3, 2, 4, 1, 2, 1, 3, 4, 7 };
        AssertHeapSort(minHeap, minHeap.OrderBy(i => i).ToArray());

        var maxHeap = new MaxHeap<int>(new[] {1, 5, 3, 2, 7, 56, 3, 1, 23, 5, 2, 1});
        AssertHeapSort(maxHeap, maxHeap.OrderBy(d => -d).ToArray());

        maxHeap = new MaxHeap<int> {2, 6, 1, 3, 56, 1, 4, 7, 8, 23, 4, 5, 7, 34, 1, 4};
        AssertHeapSort(maxHeap, maxHeap.OrderBy(d => -d).ToArray());
    }

    private static void AssertHeapSort(Heap<int> heap, IEnumerable<int> expected)
    {
        var sorted = new List<int>();
        while (heap.Count > 0)
            sorted.Add(heap.ExtractDominating());

        Assert.IsTrue(sorted.SequenceEqual(expected));
    }
}