approximate_pi.cpp File Reference

Implementation to calculate an estimate of the number π (Pi). More...

#include <cassert>
#include <cstdlib>
#include <iostream>
#include <vector>

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Namespaces
namespace	math
	for IO operations

Typedefs
using	math::Point
	structure of points containing two numbers, x and y, such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1.

Functions
double	math::approximate_pi (const std::vector< Point > &pts)
	This function uses the points in a given vector 'pts' (drawn at random) to return an approximation of the number π.
static void	tests ()
	Self-test implementations.
int	main ()
	Main function.

Detailed Description

Implementation to calculate an estimate of the number π (Pi).

We take a random point P with coordinates (x, y) such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. If x² + y² ≤ 1, then the point is inside the quarter disk of radius 1, else the point is outside. We know that the probability of the point being inside the quarter disk is equal to π/4 double approx(vector<Point> &pts) which will use the points pts (drawn at random) to return an estimate of the number π

Note

This implementation is better than naive recursive or iterative approach.

Author

Qannaf AL-SAHMI

Function Documentation

main()

int main

(

void

)

Main function.

Returns

0 on exit

           {
    tests();  // run self-test implementations
    return 0;
}

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tests()

static void tests ( )

static

Self-test implementations.

Returns

void

                    {
    std::vector<math::Point> rands;
    for (std::size_t i = 0; i < 100000; i++) {
        math::Point p;
        p.x = rand() / static_cast<double>(RAND_MAX);  // 0 <= x <= 1
        p.y = rand() / static_cast<double>(RAND_MAX);  // 0 <= y <= 1
        rands.push_back(p);
    }
    assert(math::approximate_pi(rands) > 3.135);
    assert(math::approximate_pi(rands) < 3.145);
 
    std::cout << "All tests have successfully passed!" << std::endl;
}

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