#include <iostream>
#include <iomanip>     //for setprecision
#include <cstdlib>
#include <chrono>      //for chrono::system_clock
#include <random>      //for default_random_engine
#include <functional>  //for bind
using namespace std;

//Approximate the value of pi by a Monte Carlo method.
//Approximately 78% of the random points will fall within the unit circle.
//
//Each time we use r(), it gives us a different random number
//in the range -1.0 to +1.0
//CISC-2000-E01 will explain how we created r.

int main()
{
	unsigned seed = chrono::system_clock::now().time_since_epoch().count();
	default_random_engine engine {seed};
	uniform_real_distribution<double> distribution {-1.0, 1.0};
	auto r {bind(distribution, engine)};

	int n {1000000};   //Will a higher n give us a more accurate answer?
	int count {0};  //How many random points were in the unit circle

	for (int i = 0; i < n; ++i) {
		//Pick a random point (x, y) in the square.
		double x {r()};
		double y {r()};
		//if the point (x, y) is within the unit circle,
		if (sqrt(x*x + y*y) < 1.0) {
			++count;
		}
	}

	double square {4.0}; //area of the square that encloses the unit circle

	cout << count << " out of " << n << " points fell within the circle.\n"
		<< "That's " << 100.0 * count / n << " percent of the points.\n"
		<< fixed << setprecision(5)
		<< "The area of the square is " << square << "\n"
		<< "The area of the circle is " << square * count / n << "\n";

	return EXIT_SUCCESS;
}