Add class for calculating combinations and a unitTest

VocaluxeLib/Utils/Combinatorics/CCombinations.cs

@@ -0,0 +1,157 @@
+using System;
+using System.Collections;
+using System.Collections.Generic;
+using System.Diagnostics;
+
+namespace VocaluxeLib.Utils.Combinatorics
+{
+    /// <summary>
+    ///     Calculates all combinations (without repetition) of a given input sequence <br />
+    ///     Example: {A B C}, select 2 --> {A B}, {A C}, {B C}
+    /// </summary>
+    /// <typeparam name="T">Type of the input elements</typeparam>
+    public class CCombinations<T> : IEnumerable<List<T>>
+    {
+        private readonly List<T> _Values;
+        private readonly int _NumSelected;
+        private readonly int _Count;
+
+        /// <summary>
+        ///     Construct combinations for the input sequence when selecting numSelected elements <br />
+        ///     The values should not contain duplicates as this will result in duplicates in the output
+        /// </summary>
+        /// <param name="values">Input sequence</param>
+        /// <param name="numSelected">Number of elements to select</param>
+        public CCombinations(List<T> values, int numSelected)
+        {
+            _Values = values;
+            _NumSelected = numSelected;
+            // This also acts as a parameter check
+            _Count = Count(_Values.Count, _NumSelected);
+        }
+
+        /// <summary>
+        ///     Calculates how many combinations are possible when k out of n elements are selected
+        /// </summary>
+        /// <param name="n">Number of elements</param>
+        /// <param name="k">Number of selected elements</param>
+        /// <returns></returns>
+        public static int Count(int n, int k)
+        {
+            if (n < 0 || k < 0)
+                throw new ArgumentException("Parameters must not be negative");
+            if (n < k)
+                return 0;
+            // Try to optimize because (n k) = (n n-k)
+            if (n - k < k)
+                k = n - k;
+            if (k == 0) // or k == n but both are the same after the optimization above
+                return 1;
+
+            long result = n;
+            for (long i = 1; i < k; i++)
+            {
+                checked
+                {
+                    result = result * (n - i) / (i + 1);
+                }
+            }
+            return (int)result;
+        }
+
+        /// <summary>
+        ///     Gets the number of combinations that are generated
+        /// </summary>
+        /// <returns></returns>
+        public int Count()
+        {
+            return _Count;
+        }
+
+        /// <summary>
+        ///     Gets all possible combinations as a list
+        /// </summary>
+        /// <returns></returns>
+        public List<List<T>> GetAll()
+        {
+            List<List<T>> result = new List<List<T>>(Count());
+            result.AddRange(this);
+            return result;
+        }
+
+        public IEnumerator<List<T>> GetEnumerator()
+        {
+            return new CEnumerator(this);
+        }
+
+        IEnumerator IEnumerable.GetEnumerator()
+        {
+            return GetEnumerator();
+        }
+
+        private class CEnumerator : IEnumerator<List<T>>
+        {
+            private readonly int _N;
+            private readonly int _K;
+            private readonly CCombinations<T> _Parent;
+            private int[] _CurSet;
+
+            public CEnumerator(CCombinations<T> parent)
+            {
+                _N = parent._Values.Count;
+                _K = parent._NumSelected;
+                _Parent = parent;
+                Debug.Assert(_N >= 0 && _K >= 0);
+            }
+
+            public void Dispose() {}
+
+            public bool MoveNext()
+            {
+                if (_N < _K)
+                    return false;
+
+                if (_CurSet == null)
+                {
+                    _CurSet = new int[_K];
+                    for (int i = 0; i < _K; i++)
+                        _CurSet[i] = i;
+                    return true;
+                }
+
+                // Check if we reached the end
+                if (_K == 0 || _CurSet[0] == _N - _K)
+                    return false;
+                // Search for element to increment
+                int idx = _K - 1;
+                while (idx > 0 && _CurSet[idx] == _N - _K + idx)
+                    idx--;
+                _CurSet[idx]++;
+                // Increment all elements "right" of this to 1+their left neighbour
+                for (int j = idx; j < _K - 1; j++)
+                    _CurSet[j + 1] = _CurSet[j] + 1;
+                return true;
+            }
+
+            public void Reset()
+            {
+                _CurSet = null;
+            }
+
+            public List<T> Current
+            {
+                get
+                {
+                    List<T> result = new List<T>(_K);
+                    for (int i = 0; i < _K; i++)
+                        result.Add(_Parent._Values[_CurSet[i]]);
+                    return result;
+                }
+            }
+            object IEnumerator.Current
+            {
+                get { return Current; }
+            }
+        }
+    }
+}

VocaluxeLib/VocaluxeLib.csproj

@@ -108,6 +108,7 @@
     <Compile Include="Draw\CTextureRef.cs" />
     <Compile Include="Menu\IThemeable.cs" />
     <Compile Include="Menu\SingNotes\CNoteBars.cs" />
+    <Compile Include="Utils\Combinatorics\CCombinations.cs" />
     <Compile Include="XmlStructs.cs" />
     <Compile Include="Xml\CTypeExtensions.cs" />
     <Compile Include="Xml\CXmlDeserializer.cs" />

VocaluxeTests/CTestHelpers.cs

@@ -0,0 +1,21 @@
+using System;
+using Microsoft.VisualStudio.TestTools.UnitTesting;
+
+namespace VocaluxeTests
+{
+    static class CTestHelpers
+    {
+        public static void AssertFail<T>(Action test) where T : Exception
+        {
+            try
+            {
+                test.Invoke();
+                Assert.Fail("Exception " + typeof(T).Name + " not thrown!");
+            }
+            catch (Exception e)
+            {
+                Assert.IsInstanceOfType(e, typeof(T));
+            }
+        }
+    }
+}

VocaluxeTests/CombinatoricsTest.cs

@@ -0,0 +1,75 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using Microsoft.VisualStudio.TestTools.UnitTesting;
+using VocaluxeLib.Utils.Combinatorics;
+
+namespace VocaluxeTests
+{
+    [TestClass]
+    public class CCombinatoricsTest
+    {
+        [TestMethod]
+        public void TestCounts()
+        {
+            Assert.AreEqual(4, CCombinations<int>.Count(4, 3));
+            Assert.AreEqual(6, CCombinations<int>.Count(4, 2));
+            Assert.AreEqual(66, CCombinations<int>.Count(12, 2));
+            // Corner cases
+            for (int i = 1; i < 12; i++)
+            {
+                Assert.AreEqual(1, CCombinations<int>.Count(i, 0));
+                Assert.AreEqual(1, CCombinations<int>.Count(i, i));
+                Assert.AreEqual(0, CCombinations<int>.Count(i, i + 1));
+            }
+            // Check identity (n k) = (n n-k)
+            for (int i = 0; i <= 12; i++)
+                Assert.AreEqual(CCombinations<int>.Count(12, i), CCombinations<int>.Count(12, 12 - i));
+            CTestHelpers.AssertFail<ArgumentException>(() => CCombinations<int>.Count(-1, -1));
+            CTestHelpers.AssertFail<ArgumentException>(() => CCombinations<int>.Count(-1, 1));
+            CTestHelpers.AssertFail<ArgumentException>(() => CCombinations<int>.Count(1, -1));
+        }
+
+        // ReSharper disable UnusedParameter.Local
+        private static void _CheckResults<T>(CCombinations<T> combs, List<T> input)
+            // ReSharper restore UnusedParameter.Local
+        {
+            List<List<T>> results = new List<List<T>>();
+            foreach (List<T> comb in combs)
+            {
+                foreach (List<T> other in results)
+                    Assert.IsFalse(other.SequenceEqual(comb), "Result must be unique");
+                for (int i = 0; i < comb.Count - 1; i++)
+                {
+                    Assert.IsTrue(comb.IndexOf(comb[i], i + 1) < 0, "Repetition not allowed");
+                    Assert.IsTrue(input.Contains(comb[i]), "Output must be in input sequence");
+                }
+                results.Add(comb);
+            }
+            Assert.AreEqual(combs.Count(), results.Count);
+            List<List<T>> results2 = combs.GetAll();
+            Assert.AreEqual(results.Count, results2.Count);
+            for (int i = 0; i < results2.Count; i++)
+                Assert.IsTrue(results[i].SequenceEqual(results2[i]));
+        }
+
+        [TestMethod]
+        public void TestResults()
+        {
+            Random rand = new Random();
+            for (int n = 0; n < 8; n++)
+            {
+                for (int k = 0; k <= n; k++)
+                {
+                    List<int> collection = new List<int>(n);
+                    int r = rand.Next(1000);
+                    for (int i = 0; i < n; i++)
+                        collection.Add(i + r);
+                    CCombinations<int> combs = new CCombinations<int>(collection, k);
+                    Assert.AreEqual(CCombinations<int>.Count(n, k), combs.Count());
+                    _CheckResults(combs, collection);
+                }
+            }
+        }
+    }
+}

VocaluxeTests/VocaluxeTests.csproj

@@ -70,7 +70,9 @@
     </Otherwise>
   </Choose>
   <ItemGroup>
+    <Compile Include="CTestHelpers.cs" />
     <Compile Include="Properties\AssemblyInfo.cs" />
+    <Compile Include="CombinatoricsTest.cs" />
     <Compile Include="XmlSerializerTest.cs" />
   </ItemGroup>
   <ItemGroup>

VocaluxeTests/XmlSerializerTest.cs

@@ -91,8 +91,7 @@ namespace VocaluxeTests
 
         private struct SDefaultSub
         {
-            [DefaultValue(111)]
-            public int I;            
+            [DefaultValue(111)] public int I;
         }
 
         private struct SDefault
@@ -107,23 +106,10 @@ namespace VocaluxeTests
 #pragma warning restore 169
 #pragma warning restore 649
 
-        private static void _AssertFail<T>(Action test) where T : Exception
-        {
-            try
-            {
-                test.Invoke();
-                Assert.Fail("Exception " + typeof(T).Name + " not thrown!");
-            }
-            catch (Exception e)
-            {
-                Assert.IsInstanceOfType(e, typeof(T));
-            }
-        }
-
         private static void _AssertFail<T, T2>(String xmlString) where T2 : Exception where T : new()
         {
             var deserializer = new CXmlDeserializer();
-            _AssertFail<T2>(() => deserializer.DeserializeString<T>(xmlString));
+            CTestHelpers.AssertFail<T2>(() => deserializer.DeserializeString<T>(xmlString));
         }
 
         private static T _AssertSerDeserMatch<T>(string xmlString) where T : new()
@@ -454,7 +440,7 @@ namespace VocaluxeTests
             Assert.AreEqual(foo.D, 666);
             Assert.AreEqual(foo.Sub.I, 111);
             string newXml = new CXmlSerializer().Serialize(foo);
-            Assert.AreEqual(_Head +@"<root>
+            Assert.AreEqual(_Head + @"<root>
   <Sub />
 </root>", newXml);
         }