Entry for the Pi Day Challenge (http://www.fluentcpp.com/2017/03/02/the-pi-day-challenge-for-expressive-code-in-c/)

pi.cpp

/*
 *This program approximates pi using the monte carlo method of counting how
 *many points in a square fall into a circle inscribed in it.
 *
 *The program outputs the deviation from pi for a circle radius from 1 to 10^9
 *and a number of points from 1 to 10^7, where consecutive rows represent an
 *increase in radius by one power of 10 each and consecutive columns represent
 *an increase in number of points by one power of 10, respectively.
 *
 *Author: Ben Steffan
 *Date: 04.03.2017
 */

#include <iostream>
#include <iomanip>
#include <vector>
#include <cmath>
#include <utility>
#include <random>
#include <algorithm>

double calculate_pi_approximation(unsigned radius, unsigned count,
		std::mt19937& rand_engine) {
	using namespace std;

	uniform_real_distribution<double> dist(-(double) (radius), radius);

	vector<pair<double, double>> points(count);
	generate(points.begin(), points.end(), [&] () {
			return make_pair(dist(rand_engine), dist(rand_engine));
			});

	size_t in_circle = count_if(points.cbegin(), points.cend(),
			[&] (auto point) {
				return sqrt(pow(get<0>(point), 2) + pow(get<1>(point), 2))
					<= radius;
			});

	double pi_approximation = (double) (in_circle) / count * 4.0;
	return pi_approximation;
}

int main() {
	const double pi = 3.14159265359;

	std::random_device rnd;
	std::mt19937 engine(rnd());

	for (unsigned radius_power = 0; radius_power <= 9; ++radius_power) {
		for (unsigned count_power = 0; count_power <= 7; ++count_power) {
			double approximation = calculate_pi_approximation(
					std::pow(10, radius_power),
					std::pow(10, count_power), engine);

			double deviation = std::abs(pi - approximation);

			std::cout << std::setw(12) << deviation;
		}
		std::cout << '\n';
	}
}