A. Results.ms

``` ini

BenchmarkDotNet=v0.12.1, OS=Windows 10.0.19041.572 (2004/?/20H1)
AMD Ryzen 7 3700X, 1 CPU, 16 logical and 8 physical cores
.NET Core SDK=5.0.100-preview.8.20417.9
  [Host]     : .NET Core 5.0.0 (CoreCLR 5.0.20.40711, CoreFX 5.0.20.40711), X64 RyuJIT
  DefaultJob : .NET Core 5.0.0 (CoreCLR 5.0.20.40711, CoreFX 5.0.20.40711), X64 RyuJIT


```
|        Method |  Size |         Mean |       Error |      StdDev | Ratio | RatioSD |    Gen 0 |    Gen 1 |    Gen 2 | Allocated |
|-------------- |------ |-------------:|------------:|------------:|------:|--------:|---------:|---------:|---------:|----------:|
|      **LinqSort** |    **30** |     **1.078 μs** |   **0.0076 μs** |   **0.0071 μs** |  **1.00** |    **0.00** |   **0.0801** |        **-** |        **-** |     **672 B** |
| PriorityQueue |    30 |     1.048 μs |   0.0042 μs |   0.0039 μs |  0.97 |    0.01 |        - |        - |        - |         - |
|   PrioritySet |    30 |     1.991 μs |   0.0031 μs |   0.0027 μs |  1.85 |    0.01 |        - |        - |        - |         - |
|   PairingHeap |    30 |     2.513 μs |   0.0250 μs |   0.0234 μs |  2.33 |    0.03 |   0.1717 |        - |        - |    1440 B |
|               |       |              |             |             |       |         |          |          |          |           |
|      **LinqSort** |   **300** |    **18.134 μs** |   **0.1345 μs** |   **0.1192 μs** |  **1.00** |    **0.00** |   **0.4578** |        **-** |        **-** |    **3912 B** |
| PriorityQueue |   300 |    22.106 μs |   0.2222 μs |   0.2078 μs |  1.22 |    0.01 |        - |        - |        - |         - |
|   PrioritySet |   300 |    34.303 μs |   0.0602 μs |   0.0533 μs |  1.89 |    0.01 |        - |        - |        - |         - |
|   PairingHeap |   300 |    47.776 μs |   0.5092 μs |   0.4763 μs |  2.64 |    0.03 |   1.7090 |   0.0610 |        - |   14400 B |
|               |       |              |             |             |       |         |          |          |          |           |
|      **LinqSort** |  **3000** |   **306.185 μs** |   **0.7864 μs** |   **0.6972 μs** |  **1.00** |    **0.00** |   **3.9063** |        **-** |        **-** |   **36312 B** |
| PriorityQueue |  3000 |   350.406 μs |   0.8858 μs |   0.7853 μs |  1.14 |    0.00 |        - |        - |        - |         - |
|   PrioritySet |  3000 |   490.053 μs |   2.1830 μs |   2.0420 μs |  1.60 |    0.01 |        - |        - |        - |         - |
|   PairingHeap |  3000 |   635.979 μs |   5.1801 μs |   4.8455 μs |  2.08 |    0.02 |  16.6016 |   3.9063 |        - |  144000 B |
|               |       |              |             |             |       |         |          |          |          |           |
|      **LinqSort** | **30000** | **3,845.923 μs** |   **6.6054 μs** |   **6.1787 μs** |  **1.00** |    **0.00** | **101.5625** | **101.5625** | **101.5625** |  **360973 B** |
| PriorityQueue | 30000 | 4,165.286 μs |  52.2600 μs |  48.8841 μs |  1.08 |    0.01 |        - |        - |        - |         - |
|   PrioritySet | 30000 | 6,432.610 μs |  49.4819 μs |  46.2854 μs |  1.67 |    0.01 |        - |        - |        - |         - |
|   PairingHeap | 30000 | 7,923.529 μs | 107.1215 μs | 100.2015 μs |  2.06 |    0.03 | 171.8750 |  78.1250 |        - | 1440000 B |

BCode.cs

using BenchmarkDotNet.Attributes;
using System;
using System.Linq;
using AlgoKit.Collections.Heaps;
using System.Collections.Generic;

namespace PriorityQueue.Benchmarks
{
    [MemoryDiagnoser]
    public class HeapSortBenchmarks
    {
        [Params(30, 300, 3000, 30_000)]
        public int Size;

        private int[] _priorities;
        private PriorityQueue<int, int> _priorityQueue;
        private PrioritySet<int, int> _prioritySet;
        private PairingHeap<int, int> _pairingHeap;

        [GlobalSetup]
        public void Initialize()
        {
            var random = new Random(42);
            _priorities = new int[Size];
            for (int i = 0; i < Size; i++)
            {
                _priorities[i] = random.Next(20);
            }

            _priorityQueue = new PriorityQueue<int, int>(initialCapacity: Size);
            _prioritySet = new PrioritySet<int, int>(initialCapacity: Size);
            _pairingHeap = new PairingHeap<int, int>(Comparer<int>.Default);
        }

        [Benchmark(Baseline = true)]
        public void LinqSort()
        {
            foreach (int priority in _priorities.OrderBy(x => x))
            {
            }
        }

        [Benchmark]
        public void PriorityQueue()
        {
            var queue = _priorityQueue;
            var priorities = _priorities;

            for (int i = 0; i < Size; i++)
            {
                queue.Enqueue(i, priorities[i]);
            }

            while (queue.Count > 0)
            {
                queue.Dequeue();
            }
        }

        [Benchmark]
        public void PrioritySet()
        {
            var queue = _prioritySet;
            var priorities = _priorities;

            for (int i = 0; i < Size; i++)
            {
                queue.Enqueue(i, priorities[i]);
            }

            while (queue.Count > 0)
            {
                queue.Dequeue();
            }
        }

        [Benchmark]
        public void PairingHeap()
        {
            var queue = _pairingHeap;
            var priorities = _priorities;

            for (int i = 0; i < Size; i++)
            {
                queue.Add(priorities[i], i);
            }

            while (queue.Count > 0)
            {
                queue.Pop();
            }
        }
    }
}