Refactor timeline factory to generate string ids

The strings are immediately shimmed back to ints for now

MultiversalDiplomacy/Model/Season.cs

@@ -5,16 +5,6 @@ namespace MultiversalDiplomacy.Model;
 /// </summary>
 public class Season
 {
-    /// <summary>
-    /// A shared counter for handing out new timeline numbers.
-    /// </summary>
-    private class TimelineFactory
-    {
-        private int nextTimeline = 0;
-
-        public int NextTimeline() => nextTimeline++;
-    }
-
     /// <summary>
     /// The first turn number.
     /// </summary>
@@ -83,7 +73,7 @@ public class Season
         return new Season(
             past: null,
             turn: FIRST_TURN,
-            timeline: factory.NextTimeline(),
+            timeline: TimelineFactory.StringToInt(factory.NextTimeline()),
             factory: factory);
     }
 
@@ -97,7 +87,7 @@ public class Season
     /// Create a season immediately after this one in a new timeline.
     /// </summary>
     public Season MakeFork()
-        => new Season(this, this.Turn + 1, this.Timelines.NextTimeline(), this.Timelines);
+        => new Season(this, this.Turn + 1, TimelineFactory.StringToInt(Timelines.NextTimeline()), this.Timelines);
 
     /// <summary>
     /// Returns the first season in this season's timeline. The first season is the

MultiversalDiplomacy/Model/TimelineFactory.cs

@@ -0,0 +1,50 @@
+namespace MultiversalDiplomacy.Model;
+
+/// <summary>
+/// A shared counter for handing out new timeline designations.
+/// </summary>
+internal class TimelineFactory
+{
+    private static readonly char[] Letters = [
+        'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j',
+        'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't',
+        'u', 'v', 'w', 'x', 'y', 'z',
+    ];
+
+    /// <summary>
+    /// Convert a string timeline identifier to its serial number.
+    /// </summary>
+    /// <param name="timeline">Timeline identifier.</param>
+    /// <returns>Integer.</returns>
+    public static int StringToInt(string timeline)
+    {
+        int result = Array.IndexOf(Letters, timeline[0]);
+        for (int i = 1; i < timeline.Length; i++) {
+            // The result is incremented by one because timeline designations are not a true base26 system.
+            // The "ones digit" maps a-z 0-25, but the "tens digit" maps a to 1, so "10" (26) is "aa" and not "a0"
+            result = (result + 1) * 26;
+            result += Array.IndexOf(Letters, timeline[i]);
+        }
+        return result;
+    }
+
+    /// <summary>
+    /// Convert a timeline serial number to its string identifier.
+    /// </summary>
+    /// <param name="designation">Integer.</param>
+    /// <returns>Timeline identifier.</returns>
+    public static string IntToString(int designation) {
+        static int downshift(int i ) => (i - (i % 26)) / 26;
+        IEnumerable<char> result = [Letters[designation % 26]];
+        for (int remainder = downshift(designation); remainder > 0; remainder = downshift(remainder) - 1) {
+            // We subtract 1 after downshifting for the same reason we add 1 above after upshifting.
+            // 
+            result = result.Prepend(Letters[(remainder % 26 + 25) % 26]);
+        }
+        return new string(result.ToArray());
+    }
+
+    private int nextTimeline = 0;
+
+    public string NextTimeline() => IntToString(nextTimeline++);
+}

MultiversalDiplomacy/MultiversalDiplomacy.csproj

@@ -7,4 +7,10 @@
     <Nullable>enable</Nullable>
   </PropertyGroup>
 
+  <ItemGroup>
+    <AssemblyAttribute Include="System.Runtime.CompilerServices.InternalsVisibleTo">
+      <_Parameter1>MultiversalDiplomacyTests</_Parameter1>
+    </AssemblyAttribute>
+  </ItemGroup>
+
 </Project>

MultiversalDiplomacyTests/Model/TimelineFactoryTest.cs

@@ -0,0 +1,38 @@
+using MultiversalDiplomacy.Model;
+
+using NUnit.Framework;
+
+namespace MultiversalDiplomacyTests.Model;
+
+public class TimelineFactoryTest
+{
+    [TestCase(0, "a")]
+    [TestCase(1, "b")]
+    [TestCase(25, "z")]
+    [TestCase(26, "aa")]
+    [TestCase(27, "ab")]
+    [TestCase(51, "az")]
+    [TestCase(52, "ba")]
+    [TestCase(53, "bb")]
+    [TestCase(77, "bz")]
+    [TestCase(78, "ca")]
+    public void RoundTripTimelineDesignations(int number, string designation)
+    {
+        Assert.That(TimelineFactory.IntToString(number), Is.EqualTo(designation), "Incorrect string");
+        Assert.That(TimelineFactory.StringToInt(designation), Is.EqualTo(number), "Incorrect number");
+    }
+
+    [Test]
+    public void NoSharedFactoryState()
+    {
+        TimelineFactory one = new();
+        TimelineFactory two = new();
+
+        Assert.That(one.NextTimeline(), Is.EqualTo("a"));
+        Assert.That(one.NextTimeline(), Is.EqualTo("b"));
+        Assert.That(one.NextTimeline(), Is.EqualTo("c"));
+
+        Assert.That(two.NextTimeline(), Is.EqualTo("a"));
+        Assert.That(two.NextTimeline(), Is.EqualTo("b"));
+    }
+}