Add Monte Carlo Integration in C# (#309)

* Add Monte Carlo Integration.

* Rename RunOutput to PiEstimate and adjust variables accordingly.

* Use Math.Pow. Use commas instead of points to make 10,000,000 more readable. Use percent error. Remove user input.

* Calculate the percent error in Main. Use the absolute percent error.

Author: june128

contents/monte_carlo_integration/code/csharp/Circle.cs

@@ -0,0 +1,25 @@
+using System;
+
+namespace MonteCarloIntegration
+{
+    public struct Point
+    {
+        public double X { get; set; }
+        public double Y { get; set; }
+
+        public Point(double x, double y)
+        {
+            this.X = x;
+            this.Y = y;
+        }
+    }
+
+    public class Circle
+    {
+        public double Radius { get; private set; }
+
+        public Circle(double radius) => this.Radius = Math.Abs(radius);
+
+        public bool IsInMe(Point point) => Math.Pow(point.X, 2) + Math.Pow(point.Y, 2) < Math.Pow(Radius, 2);
+    }
+}

contents/monte_carlo_integration/code/csharp/MonteCarlo.cs

@@ -0,0 +1,23 @@
+using System;
+
+namespace MonteCarloIntegration
+{
+    public class MonteCarlo
+    {
+        public double Run(int samples)
+        {
+            var circle = new Circle(1.0);
+            var count = 0;
+            var random = new Random();
+
+            for (int i = 0; i < samples; i++)
+            {
+                var point = new Point(random.NextDouble(), random.NextDouble());
+                if (circle.IsInMe(point))
+                    count++;
+            }
+
+            return 4.0 * count / samples;
+        }
+    }
+}

contents/monte_carlo_integration/code/csharp/Program.cs

@@ -0,0 +1,16 @@
+using System;
+
+namespace MonteCarloIntegration
+{
+    class Program
+    {
+        static void Main(string[] args)
+        {
+            var monteCarlo = new MonteCarlo();
+            System.Console.WriteLine("Running with 10,000,000 samples.");
+            var piEstimate = monteCarlo.Run(10000000);
+            System.Console.WriteLine($"The estimate of pi is: {piEstimate}");
+            System.Console.WriteLine($"The percent error is: {Math.Abs(piEstimate - Math.PI) / Math.PI * 100}%");
+        }
+    }
+}

contents/monte_carlo_integration/monte_carlo_integration.md

@@ -61,6 +61,8 @@ each point is tested to see whether it's in the circle or not:
 [import:15-17, lang:"swift"](code/swift/monte_carlo.swift)
 {% sample lang="py" %}
 [import:5-7, lang:"python"](code/python/monte_carlo.py)
+{% sample lang="cs" %}
+[import:23-23, lang:"csharp"](code/csharp/Circle.cs)
 {% endmethod %}
 
 If it's in the circle, we increase an internal count by one, and in the end,
@@ -116,6 +118,13 @@ Feel free to submit your version via pull request, and thanks for reading!
 [import, lang:"swift"](code/swift/monte_carlo.swift)
 {% sample lang="py" %}
 [import, lang:"python"](code/python/monte_carlo.py)
+{% sample lang="cs" %}
+MonteCarlo.cs
+[import, lang:"csharp"](code/csharp/MonteCarlo.cs)
+Circle.cs
+[import, lang:"csharp"](code/csharp/Circle.cs)
+Program.cs
+[import, lang:"csharp"](code/csharp/Program.cs)
 {% endmethod %}