#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.

double pi(int n);

int main()
{
	int a[] {       //how many random points to generate
		     5,
		    10,
		    50,
		   100,
		   500,
		  1000,
		  5000,
		 10000,
		 50000,
		100000,
		500000
	};
	int n {size(a)};   //how many numbers are in the array

	cout << "     n       pi    error\n";   //column headings

	for (int i {0}; i < n; ++i) {
		double p {pi(a[i])}; //the approximate value of pi
		cout << setw(6) << a[i] << "  "
			<< fixed << setprecision(5) << p << "  "
			<< abs(3.14159265358979323846 - p) << "\n"; //absolute
	}

	return EXIT_SUCCESS;
}

//Return an approximation to the value of pi, counting how many of n
//random points lie within the unit circle.

double pi(int n)
{
	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 count {0};  //How many random points were in the unit circle

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

	return 4.0 * count / n;   //4.0 is the area of the enclosing square
}