Implement custom comparer for expected carousel sort behaviour

Co-authored-by: Salman Ahmed <frenzibyte@gmail.com>

osu.Game/Utils/OrdinalSortByCaseStringComparer.cs

@@ -0,0 +1,49 @@
+// Copyright (c) ppy Pty Ltd <contact@ppy.sh>. Licensed under the MIT Licence.
+// See the LICENCE file in the repository root for full licence text.
+
+using System;
+using System.Collections.Generic;
+
+namespace osu.Game.Utils
+{
+    /// <summary>
+    /// This string comparer is something of a cross-over between <see cref="StringComparer.Ordinal"/> and <see cref="StringComparer.OrdinalIgnoreCase"/>.
+    /// <see cref="StringComparer.OrdinalIgnoreCase"/> is used first, but <see cref="StringComparer.Ordinal"/> is used as a tie-breaker.
+    /// </summary>
+    /// <remarks>
+    /// This comparer's behaviour somewhat emulates <see cref="StringComparer.InvariantCulture"/>,
+    /// but non-ordinal comparers - both culture-aware and culture-invariant - have huge performance overheads due to i18n factors (up to 5x slower).
+    /// </remarks>
+    /// <example>
+    /// Given the following strings to sort: <c>[A, B, C, D, a, b, c, d, A]</c> and a stable sorting algorithm:
+    /// <list type="bullet">
+    /// <item>
+    /// <see cref="StringComparer.Ordinal"/> would return <c>[A, A, B, C, D, a, b, c, d]</c>.
+    /// This is undesirable as letters are interleaved.
+    /// </item>
+    /// <item>
+    /// <see cref="StringComparer.OrdinalIgnoreCase"/> would return <c>[A, a, A, B, b, C, c, D, d]</c>.
+    /// Different letters are not interleaved, but because case is ignored, the As are left in arbitrary order.
+    /// </item>
+    /// </list>
+    /// <item>
+    /// <see cref="OrdinalSortByCaseStringComparer"/> would return <c>[a, A, A, b, B, c, C, d, D]</c>, which is the expected behaviour.
+    /// </item>
+    /// </example>
+    public class OrdinalSortByCaseStringComparer : IComparer<string>
+    {
+        public static readonly OrdinalSortByCaseStringComparer INSTANCE = new OrdinalSortByCaseStringComparer();
+
+        private OrdinalSortByCaseStringComparer()
+        {
+        }
+
+        public int Compare(string? a, string? b)
+        {
+            int result = StringComparer.OrdinalIgnoreCase.Compare(a, b);
+            if (result == 0)
+                result = -StringComparer.Ordinal.Compare(a, b); // negative to place lowercase letters before uppercase.
+            return result;
+        }
+    }
+}