chore(CSharp): implemented bitwise sieve of eratosthenes (#506)

algorithms/CSharp/README.md

@@ -7,6 +7,8 @@ For running the `.cs` file please using [.Net Finddle](https://dotnetfiddle.net/
 ## Number Theory
 1. [Big Mod Algorithm](src/Number-Theory/big-mod.cs)
 2. [Sieve of Eratosthenes](src/Number-Theory/sieve-of-eratosthenes.cs)
+3. [Bitwise Sieve of Eratosthenes](src/Number-Theory/bitwise-sieve-of-eratosthenes.cs)
+
 
 ## Sorts
 

algorithms/CSharp/src/Number-Theory/bitwise-sieve-of-eratosthenes.cs

@@ -0,0 +1,58 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+
+namespace Algorithms.NumberTheory
+{
+    public class BitwiseSieveOfEratosthenes
+    {
+        public static bool CheckBit(int number, int position) =>
+            (number & (1 << position)) != 0;
+
+        public static int SetBit(int number, int position) =>
+            number | (1 << position);
+
+        public static List<int> GeneratePrimeNumbers(int max)
+        {
+            int[] status = Enumerable.Repeat(0, max / 32 + 1).ToArray();
+            int squareRoot = (int)Math.Sqrt(max * 1.0);
+
+            for(int i = 3; i <= squareRoot; i += 2)
+            {
+                if(!CheckBit(status[i / 32], i % 32))
+                {
+                    for(int j = 2 * i; j <= max; j += i)
+                    {
+                        status[j / 32] = SetBit(status[j / 32], j % 32);
+                    }
+                }
+            }
+
+            List<int> primeNumbers = new List<int>();
+            primeNumbers.Add(2);
+
+            for(int i = 3; i <= max; i += 2)
+            {
+                if(!CheckBit(status[i / 32], i % 32))
+                {
+                    primeNumbers.Add(i);
+                }
+            }
+
+            return primeNumbers;
+        }
+
+        public static void Main()
+        {
+            List<int> primeNumbers = GeneratePrimeNumbers(100);
+            Console.WriteLine(string.Join(", ", primeNumbers));
+        }
+    }
+}
+
+/*
+ * Bitwise Sieve is an optimized version of the Sieve of Eratosthenes
+ * Instead of keeping the status of a number in a single number, we use a bit
+ * We use 32 bit integers
+ * e.g: 0 has the status of 0-31, 1 has the status of 32-63, etc.
+ */

algorithms/CSharp/test/Number-Theory/bitwise-sieve-of-eratosthenes.cs

@@ -0,0 +1,18 @@
+using NUnit.Framework;
+using System.Collections.Generic;
+
+namespace Algorithms.Tests.Number_Theory
+{
+    [TestFixture]
+    public class BitwiseSieveOfEratosthenes
+    {
+        [TestCase(10, "2, 3, 5, 7")]
+        [TestCase(25, "2, 3, 5, 7, 11, 13, 17, 19, 23")]
+        [TestCase(100, "2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97")]
+        public void BitwiseSieveOfEratosthenes_ShouldReturnExpected(int max, string expected)
+        {
+            List<int> primeNumbers = Algorithms.NumberTheory.BitwiseSieveOfEratosthenes.GeneratePrimeNumbers(max);
+            Assert.AreEqual(expected, string.Join(", ", primeNumbers));
+        }
+    }
+}