Add C# implementation for the approximate counting algorithm

Author: stormofice

contents/approximate_counting/approximate_counting.md

@@ -362,6 +362,8 @@ As we do not have any objects to count, we will instead simulate the counting wi
 [import, lang:"julia"](code/julia/approximate_counting.jl)
 {% sample lang="cpp" %}
 [import, lang:"cpp"](code/c++/approximate_counting.cpp)
+{% sample lang="cs" %}
+[import, lang:"csharp"](code/csharp/ApproximateCounting.cs)
 {% endmethod %}
 
 ### Bibliography

contents/approximate_counting/code/csharp/ApproximateCounting.cs

@@ -0,0 +1,71 @@
+using System;
+
+namespace ApproximateCounting
+{
+    class ApproximateCounting
+    {
+        static readonly Random Rng = new();
+
+        // This function takes 
+        //     - v: value in register
+        //     - a: a  scaling value for the logarithm based on Morris's paper
+        // It returns n(v,a), the approximate count
+        static double N(int v, double a)
+        {
+            return a * Math.Pow(1 + 1 / a, v - 1);
+        }
+
+        // This function takes
+        //    - v: value in register
+        //    - a: a scaling value for the logarithm based on Morris's paper
+        // It returns a new value for v
+        static int Increment(int v, double a)
+        {
+            var delta = 1 / (N(v + 1, a) - N(v, a));
+
+            if (Rng.NextDouble() <= delta)
+                return v + 1;
+            else
+                return v;
+        }
+
+        // This simulates counting and takes
+        //     - noItems: number of items to count and loop over
+        //     - a: a scaling value for the logarithm based on Morris's paper
+        // It returns n(v,a), the approximate count
+        static double ApproximateCount(int noItems, double a)
+        {
+            var v = 0;
+            for (var i = 0; i < noItems; i++)
+            {
+                v = Increment(v, a);
+            }
+            return N(v, a);
+        }
+
+        // This function takes
+        //     - noTrials: the number of counting trials
+        //     - noItems: the number of items to count to
+        //     - a: a scaling value for the logarithm based on Morris's paper
+        //     - threshold: the maximum percent error allowed
+        // It returns a "pass" / "fail" test value
+        static string TextApproximateCount(int noTrials, int noItems, double a, double threshold)
+        {
+            var sum = 0.0;
+            for (var i = 0; i < noTrials; i++)
+                sum += ApproximateCount(noItems, a);
+            
+            var avg = sum / noTrials;
+            
+            return Math.Abs((avg - noItems) / noItems) < threshold ? "pass" : "fail";
+        }
+
+        static void Main()
+        {
+            Console.WriteLine("Counting Tests, 100 trials");
+            Console.WriteLine($"Testing 1,000, a = 30, 1% error : {TextApproximateCount(100, 1_000, 30, 0.1)}");
+            Console.WriteLine($"Testing 12,345, a = 10, 1% error : {TextApproximateCount(100, 12_345, 10, 0.1)}");
+            Console.WriteLine($"Testing 222,222, a = 0.5, 10% error : {TextApproximateCount(100, 222_222, 0.5, 0.2)}");
+        }
+    }
+}