Added PossibleAddends utility.

Author: electricessence

Open.Collections.Numeric.csproj

@@ -16,7 +16,7 @@
 		<PackageProjectUrl>https://github.com/Open-NET-Libraries/Open.Collections.Numeric/</PackageProjectUrl>
 		<RepositoryUrl>https://github.com/Open-NET-Libraries/Open.Collections.Numeric/</RepositoryUrl>
 		<RepositoryType>git</RepositoryType>
-		<Version>1.4.0</Version>
+		<Version>1.5.0</Version>
 		<PackageReleaseNotes></PackageReleaseNotes>
 		<PackageLicenseExpression>MIT</PackageLicenseExpression>
 		<PublishRepositoryUrl>true</PublishRepositoryUrl>
@@ -46,9 +46,10 @@
   </ItemGroup>
 
   <ItemGroup>
-    <PackageReference Include="Open.Collections" Version="2.4.6" />
-    <PackageReference Include="Open.Numeric" Version="1.2.1" />
-    <PackageReference Include="Open.Threading" Version="1.4.2" />
+    <PackageReference Include="Open.Collections" Version="2.10.1" />
+    <PackageReference Include="Open.Numeric" Version="2.3.0" />
+    <PackageReference Include="Open.Threading" Version="1.6.0" />
+    <PackageReference Include="System.Collections.Immutable" Version="5.0.0" />
   </ItemGroup>
 
 </Project>

PossibleAddends.cs

@@ -0,0 +1,62 @@
+using System;
+using System.Collections.Concurrent;
+using System.Collections.Generic;
+using System.Collections.Immutable;
+
+namespace Open.Collections.Numeric
+{
+	public class PossibleAddends : IDisposable
+	{
+		public PossibleAddends()
+		{
+		}
+
+		readonly ConcurrentDictionary<int, ConcurrentDictionary<int, IReadOnlyList<IReadOnlyList<int>>>> Cache = new();
+
+		public IReadOnlyList<IReadOnlyList<int>> UniqueAddendsFor(int sum, int count)
+			=> Cache
+				.GetOrAdd(count, key => new ConcurrentDictionary<int, IReadOnlyList<IReadOnlyList<int>>>())
+				.GetOrAdd(sum, key => GetUniqueAddends(sum, count).Memoize());
+
+		public IEnumerable<IReadOnlyList<int>> GetUniqueAddends(int sum, int count)
+		{
+			if (count > int.MaxValue)
+				throw new ArgumentOutOfRangeException(nameof(count), count, "Cannot be greater than signed 32 bit integer maximum.");
+			if(count<2 || sum < 3)
+				yield break;
+
+
+			if (count==2)
+			{
+				int i = 0;
+			loop2:
+				i++;
+				if (i * 2 >= sum) yield break;
+				yield return ImmutableArray.Create(i, sum - i);
+
+				goto loop2;
+			}
+
+			{
+				int i = 2;
+				var builder = ImmutableArray.CreateBuilder<int>();
+
+				while (++i < sum)
+				{
+					var next = sum - i;
+					var addends = UniqueAddendsFor(i, count - 1);
+					foreach (var a in addends)
+					{
+						builder.Capacity = count;
+						if (a[a.Count - 1] >= next) continue;
+						builder.AddRange(a);
+						builder.Add(next);
+						yield return builder.MoveToImmutable();
+					}
+				}
+			}
+		}
+
+		public void Dispose() => Cache.Clear();
+	}
+}