BinaryHeap.cs

class BinaryHeap<T> 
{
    public T[] Heap { get; }
    public int Count { get; private set; }
    public IComparer<T> Comparer { get; }
    
    public BinaryHeap(int size, IComparer<T> comparer = null)
    {
        Heap = new T[size];
        Count = 0;
        Comparer = comparer ?? Comparer<T>.Default;
    }

    public T Peek()
    {
        if (Count == 0)
            throw new Exception("Empty");

        return Heap[0];
    }

    public void Push(T value)
    {
        if (Count == Heap.Length)
            throw new Exception("Heap overflow");
        
        var i = Count++;
        Heap[i] = value;
        while (i > 0)
        {
            var parent = (i + 1) / 2 - 1;
            if (IsGreater(Heap[i], Heap[parent]))
                break;

            Swap(i, parent);
            i = parent;
        }
    }

    public T Pop()
    {
        if (Count == 0)
            throw new Exception("Empty");

        var v = Heap[0];
        var size = --Count;
        Swap(0, size);
        var i = 0;
        while (i < size - 1)
        {
            var left = i * 2 + 1;
            var right = i * 2 + 2;
            int child;
            if (right < size && IsGreater(Heap[left], Heap[right]))
                child = right;
            else if (left < size)
                child = left;
            else
                break;

            if (IsGreater(Heap[child], Heap[i]))
                break;

            Swap(i, child);
            i = child;
        }

        return v;
    }

    private bool IsGreater(T a, T b)
    {
        return Comparer.Compare(a, b) > 0;
    }

    private void Swap(int i1, int i2)
    {
        var v = Heap[i1];
        Heap[i1] = Heap[i2];
        Heap[i2] = v;
    }
    
}