approximate_pi.cpp File Reference

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

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

Include dependency graph for approximate_pi.cpp:

Classes
struct	math::Point

Namespaces
namespace	math
	for std::rand

Functions
double	math::approximate_pi (const std::vector< Point > &pts)
static void	test ()
	Self-test implementations. More...
int	main (int argc, char *argv[])
	Main function. More...

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, otherwise 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	(	int	argc,
		char *	argv[]
	)

Main function.

Parameters

argc	commandline argument count (ignored)
argv	commandline array of arguments (ignored)

Returns

0 on exit

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

Here is the call graph for this function:

test()

static void test ( )

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() / (double)RAND_MAX; // 0 <= x <= 1
        p.y = rand() / (double)RAND_MAX; // 0 <= y <= 1
        rands.push_back(p);
    }
    std::cout << math::approximate_pi(rands) << std::endl;          // ~3.14
}

Here is the call graph for this function: