Implement C++ version of Monte Carlo integration (#342)

* Implement C++ version of Monte Carlo integration.
* Update CONTRIBUTORS.md

Author: bsamseth

CONTRIBUTORS.md

@@ -54,4 +54,6 @@ Arun Sahadeo
 <br>
 NIFR91
 <br>
-Michal Hanajik
+Michal Hanajik
+<br>
+Bendik Samseth

contents/monte_carlo_integration/code/c++/monte_carlo.cpp

@@ -0,0 +1,48 @@
+#include <iostream>
+#include <cstdlib>
+#include <random>
+
+constexpr double PI = 3.14159265358979323846264338;
+
+/**
+ * Check if the point (x, y) is within a circle of a given radius.
+ * @param x coordinate one
+ * @param y coordinate two
+ * @param r radius of the circle (optional)
+ * @return true if (x, y) is within the circle.
+ */
+inline bool in_circle(double x, double y, double r = 1) {
+    return x * x + y * y < r * r;
+}
+
+/**
+ * Return an estimate of PI using Monte Carlo integration.
+ * @param samples number of iterations to use
+ * @return estimate of pi
+ */
+double monte_carlo_pi(unsigned samples) {
+    static std::default_random_engine generator;
+    static std::uniform_real_distribution<double> dist(0, 1);
+
+    unsigned count = 0;
+    for (unsigned i = 0; i < samples; ++i) {
+        double x = dist(generator);
+        double y = dist(generator);
+
+        if (in_circle(x, y))
+            ++count;
+    }
+
+    return 4.0 * count / samples;
+}
+
+int main() {
+    unsigned samples;
+
+    std::cout << "Enter samples to use: ";
+    std::cin >> samples;
+
+    double pi_estimate = monte_carlo_pi(samples);
+    std::cout << "Pi = " << pi_estimate << '\n';
+    std::cout << "Percent error is: " << 100 * std::abs(pi_estimate - PI) / PI << " %\n";
+}

contents/monte_carlo_integration/monte_carlo_integration.md

@@ -43,6 +43,8 @@ each point is tested to see whether it's in the circle or not:
 [import:3-10, lang:"clojure"](code/clojure/monte_carlo.clj)
 {% sample lang="c" %}
 [import:7-9, lang:"c_cpp"](code/c/monte_carlo.c)
+{% sample lang="cpp" %}
+[import:7-16, lang:"c_cpp"](code/c++/monte_carlo.cpp)
 {% sample lang="js" %}
 [import:2-6, lang:"javascript"](code/javascript/monte_carlo.js)
 {% sample lang="hs" %}
@@ -100,6 +102,8 @@ Feel free to submit your version via pull request, and thanks for reading!
 [import, lang:"clojure"](code/clojure/monte_carlo.clj)
 {% sample lang="c" %}
 [import, lang:"c_cpp"](code/c/monte_carlo.c)
+{% sample lang="cpp" %}
+[import, lang:"c_cpp"](code/c++/monte_carlo.cpp)
 {% sample lang="js" %}
 [import, lang:"javascript"](code/javascript/monte_carlo.js)
 {% sample lang="hs" %}