The Pi Day Challenge for the Most Descriptive Code in C++

find_pi.cpp

/*Pi Day Challenge: compute an estimate of pi by observing the
 *probability
 *that randomly generated points within a square fall inside of a circle
 *inscribed in the square, given that the square's length is the
 *diameter of the circle.
 *
 *Solution by Jonathan Barisere (jthankgod@ymail.com)
*/

#include <iostream>
#include <iomanip>
#include "pi_day.h++"

int main() {
  
  srand(time(0)); // seed the rand function with a random value
  std::pair<int, int> origin; // (x, y) origin in 2D cartesian plane
  std::pair<float, float> midpoint; /* midpoint of the circle coincides
                                       with that of the square */

  std::cout << "Input x-origin: ";
  std::cin >> origin.first;
  std::cout << "Input y-origin: ";
  std::cin >> origin.second;

  for(int n = 0; n < 10; n++) {
    
    int diameter;
    float radius;
    diameter = pow(10, n);
    radius = diameter / 2;
    int limit_x = diameter + origin.first; // max x-coordinate
    int limit_y = diameter + origin.second; // max y-coordinate
    float x_coord = static_cast<float>(origin.first + limit_x); //x1 + x2
    float y_coord = static_cast<float>(origin.second + limit_y);//y1 + y2
    midpoint = std::make_pair(x_coord / 2,
                              y_coord / 2);
    int m_points = 8;
    int num_points = 0, num_in_circle = 0;

    for(int i = 0; i < m_points; ++i) {
      
      std::pair<int, int> *point = coordinate(origin.first,
                                              origin.second,
                                              diameter);
      
      if(point) {
        
        if(withinCircle(point, &midpoint, radius)) {
          
          ++num_in_circle;
          
        }
        
        ++num_points;
        
        free(point);
        
      }

      std::cout << std::setw(16) << std::fixed << std::setprecision(9)
              << 3.14159265359 - estimatePi(num_points,
                                            num_in_circle
                                            );
    }

    std::cout << std::endl;
    
  }

}

pi_day.cpp

/*Pi Day Challenge: compute an estimate of pi by observing the
 *probability
 *that randomly generated points within a square fall inside of a circle
 *inscribed in the square, given that the square's length is the
 *diameter of the circle.
 *
 *Solution by Jonathan Barisere (jthankgod@ymail.com)
*/

#include "pi_day.h++"

// Allocate memory for a tuple containing a randomly generated
// coordinate, and return a pointer to its location

std::pair<int, int> *coordinate(int floor_x,
                                    int floor_y,
                                    int ceiling) {
  
  int x_val = static_cast<int>(rand()) % ceiling + floor_x;
  int y_val = static_cast<int>(rand()) % ceiling + floor_y;
  std::pair<int, int> *pair_ptr =
      (std::pair<int, int>*)malloc(sizeof(std::pair<int, int>));
  
  if (pair_ptr) {
    
    pair_ptr -> first = x_val;
    pair_ptr -> second = y_val;
    
  } else pair_ptr = 0;
  
  return pair_ptr;
  
}

// determine whether the randomly generated point is within the circle

bool withinCircle(std::pair<int, int> *coordinate,
                  std::pair<float, float> *midpoint,
                  float radius) {
  
  float x = static_cast<float>(coordinate -> first) - midpoint -> first;
  float y = static_cast<float>(coordinate -> second)
      - midpoint -> second;
  x = pow(x, 2);
  y = pow(y, 2);
  
  if((x + y) < pow(radius, 2)) return true;
  else return false;
  
}

// estimate the constant pi

float estimatePi(int num_points, int num_in_circle) {
  
  float ratio = static_cast<float>(num_in_circle)
      / static_cast<float>(num_points);
  return 4 * ratio;
  
}

pi_day.h++

#ifndef PI_DAY_H
#define PI_DAY_H

#include <cmath>
#include <utility>
#include <cstdlib>
#include <ctime>
#include <cmath>
#include <iostream>

std::pair<int, int> *coordinate(int, int, int);
bool withinCircle(std::pair<int, int>*,
                  std::pair<float, float>*,
                  float);
float estimatePi(int, int);
#endif /* PI_DAY_H */