Add Binomial and Factorial sequences (#199)

Author: kolosovpetro

Algorithms.Tests/Sequences/BinomialSequenceTests.cs

@@ -0,0 +1,19 @@
+using System.Linq;
+using System.Numerics;
+using Algorithms.Sequences;
+using FluentAssertions;
+using NUnit.Framework;
+
+namespace Algorithms.Tests.Sequences
+{
+    public class BinomialSequenceTests
+    {
+        [Test]
+        public void First4RowsCorrect()
+        {
+            var sequence = new BinomialSequence().Sequence.Take(10);
+            sequence.SequenceEqual(new BigInteger[] {1, 1, 1, 1, 2, 1, 1, 3, 3, 1})
+                .Should().BeTrue();
+        }
+    }
+}

Algorithms.Tests/Sequences/FactorialSequenceTest.cs

@@ -0,0 +1,19 @@
+using System.Linq;
+using System.Numerics;
+using Algorithms.Sequences;
+using FluentAssertions;
+using NUnit.Framework;
+
+namespace Algorithms.Tests.Sequences
+{
+    public class FactorialSequenceTest
+    {
+        [Test]
+        public void First10ItemsCorrect()
+        {
+            var sequence = new FactorialSequence().Sequence.Take(10);
+            sequence.SequenceEqual(new BigInteger[] {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880})
+                .Should().BeTrue();
+        }
+    }
+}

Algorithms.Tests/Sequences/FibonacciSequenceTests.cs

@@ -1,6 +1,7 @@
 using System.Linq;
 using System.Numerics;
 using Algorithms.Sequences;
+using FluentAssertions;
 using NUnit.Framework;
 
 namespace Algorithms.Tests.Sequences
@@ -10,9 +11,9 @@ public class FibonacciSequenceTests
         [Test]
         public void First10ElementsCorrect()
         {
-            var sequence = new FibonacciSequence().Sequence;
-
-            Assert.AreEqual(new BigInteger[] { 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 }, sequence.Take(10));
+            var sequence = new FibonacciSequence().Sequence.Take(10);
+            sequence.SequenceEqual(new BigInteger[] {0, 1, 1, 2, 3, 5, 8, 13, 21, 34})
+                .Should().BeTrue();
         }
     }
 }

Algorithms.Tests/Sequences/NaturalSequenceTests.cs

@@ -1,6 +1,7 @@
 using System.Linq;
 using System.Numerics;
 using Algorithms.Sequences;
+using FluentAssertions;
 using NUnit.Framework;
 
 namespace Algorithms.Tests.Sequences
@@ -10,9 +11,9 @@ public class NaturalSequenceTests
         [Test]
         public void First10ElementsCorrect()
         {
-            var sequence = new NaturalSequence().Sequence;
-
-            Assert.AreEqual(new BigInteger[] { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }, sequence.Take(10));
+            var sequence = new NaturalSequence().Sequence.Take(10);
+            sequence.SequenceEqual(new BigInteger[] {1, 2, 3, 4, 5, 6, 7, 8, 9, 10})
+                .Should().BeTrue();
         }
     }
 }

Algorithms.Tests/Sequences/PrimesSequenceTests.cs

@@ -1,6 +1,7 @@
 using System.Linq;
 using System.Numerics;
 using Algorithms.Sequences;
+using FluentAssertions;
 using NUnit.Framework;
 
 namespace Algorithms.Tests.Sequences
@@ -10,9 +11,9 @@ public class PrimesSequenceTests
         [Test]
         public void First10ElementsCorrect()
         {
-            var sequence = new PrimesSequence().Sequence;
-
-            Assert.AreEqual(new BigInteger[] { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 }, sequence.Take(10));
+            var sequence = new PrimesSequence().Sequence.Take(10);
+            sequence.SequenceEqual(new BigInteger[] {2, 3, 5, 7, 11, 13, 17, 19, 23, 29})
+                .Should().BeTrue();
         }
     }
 }

Algorithms/Sequences/BinomialSequence.cs

@@ -0,0 +1,67 @@
+using System.Collections.Generic;
+using System.Numerics;
+
+namespace Algorithms.Sequences
+{
+    /// <summary>
+    /// <para>
+    ///     Sequence of binomial coefficients.
+    /// </para>
+    /// <para>
+    ///     Wikipedia: https://en.wikipedia.org/wiki/Binomial_coefficient.
+    /// </para>
+    /// <para>
+    ///     OEIS: http://oeis.org/A007318.
+    /// </para>
+    /// </summary>
+    public class BinomialSequence : ISequence
+    {
+        /// <summary>
+        /// Gets sequence of binomial coefficients.
+        /// </summary>
+        public IEnumerable<BigInteger> Sequence
+        {
+            get
+            {
+                var i = 0;
+
+                while (true)
+                {
+                    var row = GenerateRow(i);
+                    foreach (var coefficient in row)
+                    {
+                        yield return coefficient;
+                    }
+
+                    i++;
+                }
+            }
+        }
+
+        private static BigInteger BinomialCoefficient(long n, long k)
+        {
+            if (k == 0 || k == n)
+            {
+                return new BigInteger(1);
+            }
+
+            if (n < 0)
+            {
+                return new BigInteger(0);
+            }
+
+            return BinomialCoefficient(n - 1, k) + BinomialCoefficient(n - 1, k - 1);
+        }
+
+        private static IEnumerable<BigInteger> GenerateRow(long n)
+        {
+            long k = 0;
+
+            while (k <= n)
+            {
+                yield return BinomialCoefficient(n, k);
+                k++;
+            }
+        }
+    }
+}

Algorithms/Sequences/FactorialSequence.cs

@@ -0,0 +1,37 @@
+using System.Collections.Generic;
+using System.Numerics;
+
+namespace Algorithms.Sequences
+{
+    /// <summary>
+    /// <para>
+    ///     Sequence of factorial numbers.
+    /// </para>
+    /// <para>
+    ///     Wikipedia: https://en.wikipedia.org/wiki/Factorial.
+    /// </para>
+    /// <para>
+    ///     OEIS: https://oeis.org/A000142.
+    /// </para>
+    /// </summary>
+    public class FactorialSequence : ISequence
+    {
+        /// <summary>
+        /// Gets sequence of factorial numbers.
+        /// </summary>
+        public IEnumerable<BigInteger> Sequence
+        {
+            get
+            {
+                var n = 0;
+                var factorial = new BigInteger(1);
+                while (true)
+                {
+                    yield return factorial;
+                    n++;
+                    factorial *= n;
+                }
+            }
+        }
+    }
+}