From 419cee3d721be13c3fbdc5829587b151146a3938 Mon Sep 17 00:00:00 2001
From: Parric007 <liam.huppert@gmx.de>
Date: Thu, 11 Apr 2024 16:14:46 +0200
Subject: [PATCH] init commit

---
 .gitignore     |   3 ++
 CMakeLists.txt |   6 +++
 main.cpp       | 116 +++++++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 125 insertions(+)
 create mode 100644 .gitignore
 create mode 100644 CMakeLists.txt
 create mode 100644 main.cpp

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..1cd7964
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,3 @@
+
+/.idea/
+/cmake-build-debug/
diff --git a/CMakeLists.txt b/CMakeLists.txt
new file mode 100644
index 0000000..8f8435f
--- /dev/null
+++ b/CMakeLists.txt
@@ -0,0 +1,6 @@
+cmake_minimum_required(VERSION 3.28)
+project(MonteCarlo_Cpp)
+
+set(CMAKE_CXX_STANDARD 26)
+
+add_executable(MonteCarlo_Cpp main.cpp)
diff --git a/main.cpp b/main.cpp
new file mode 100644
index 0000000..87bb1b8
--- /dev/null
+++ b/main.cpp
@@ -0,0 +1,116 @@
+#include <iostream>
+#include <random>
+#include <chrono>
+
+double randomFloat()
+{
+    return (double)(rand()) / (double)(RAND_MAX);
+}
+
+class Point {
+private:
+    double x{};
+    double y{};
+
+public:
+    Point(double x, double y): x(x), y(y) {}
+
+    [[nodiscard]] double get_x() const {
+        return this->x;
+    }
+
+    [[nodiscard]] double get_y() const {
+        return this->y;
+    }
+
+    Point() {};
+};
+
+class LinearBounds {
+private:
+    float lower;
+    float higher;
+
+public:
+    LinearBounds(float lower, float higher): lower(lower), higher(higher) {}
+    [[nodiscard]] double length() const {
+        return std::abs(higher - lower);
+    }
+
+    [[nodiscard]] double getRandomValue() const {
+        return this->lower + (randomFloat() * this->length());
+    }
+    [[nodiscard]] float get_lower() const {
+        return lower;
+    }
+    [[nodiscard]] float get_upper() const {
+        return higher;
+    }
+};
+
+
+class Bounds {
+protected:
+    LinearBounds x;
+    LinearBounds y;
+public:
+    Bounds(LinearBounds x, LinearBounds y): x(x), y(y) {}
+    double area() {
+        return x.length() * y.length();
+    }
+    Point getRandomPoint() {
+        return {x.getRandomValue(), y.getRandomValue()};
+    }
+    LinearBounds get_x() {
+        return x;
+    }
+
+};
+
+
+double function(double x) {
+    return pow(x,4)-4*pow(x,3)+18*pow(x,2)-12*x-69;
+}
+double indefiniteIntegral(double x) {
+    return (1.0/5) * pow(x, 5) - pow(x, 4) + 6*pow(x, 3) - 6 * pow(x, 2) -69*x;
+}
+
+bool getIsInside(Point p) {
+    double y_0 = function(p.get_x());
+    return std::abs(y_0) > std::abs(p.get_y()) && y_0* p.get_y() >= 0;
+}
+
+double getRealIntegral(LinearBounds bounds) {
+    return indefiniteIntegral(bounds.get_upper())- indefiniteIntegral(bounds.get_lower());
+}
+
+int main() {
+    auto startTime = std::chrono::high_resolution_clock::now();
+    double pointsInside = 0;
+    double samples = 10000000;
+    Bounds bounds = Bounds(LinearBounds(0, 20), LinearBounds(-100, 150000));
+    Point toTestPoint;
+    for (int i = 0; i< samples; i++) {
+        toTestPoint = bounds.getRandomPoint();
+        if (getIsInside(toTestPoint)) {
+            pointsInside++;
+        }
+    }
+
+    std::cout << std::fixed;
+    std::cout.precision(5);
+    double integral = (pointsInside / samples) * bounds.area();
+    std::cout << "The approximated Integral of the function is: " << integral << "\n";
+
+    double real_value = getRealIntegral(bounds.get_x());
+    std::cout << "The real Integral of the function is: " << real_value << "\n";
+
+    double error = std::abs(real_value-integral);
+    std::cout << "That's an error of " << error <<" or " << (error/real_value)*100 << "%\n";
+    std::chrono::duration<double> duration = std::chrono::duration_cast<std::chrono::duration<double>>(std::chrono::high_resolution_clock::now()-startTime);
+    std::cout << "And the whole thing took " << duration.count() << " Seconds for ";
+    std::cout.precision(0);
+    std::cout << samples << " samples";
+    return 0;
+}
+