//
// Example 7.7. Program to estimate the area under a curve
// using the dartboard method
//

#include <iostream>
#include <cmath>
#include "randDef.h"

using namespace std;

const int NUMDARTS = 1000;     // number of darts to throw
const float SMALLEST_X = 0.0;  // smallest x value
const float LARGEST_X = 2.0;   // largest x value
const float MAX_Y = 1.5;       // upper bound of y values

int main()
{
   int countHitsBelow();

   int   numHitsBelow;         // number of darts below curve
   float areaOfRectangle;      // area of rectangular dartboard
   float estimatedArea;        // estimated area under curve

   seedRand();

   numHitsBelow    = countHitsBelow();
   areaOfRectangle = (LARGEST_X - SMALLEST_X) * MAX_Y;
   estimatedArea   = areaOfRectangle * numHitsBelow / NUMDARTS;

   cout << "Estimated area under curve from " << SMALLEST_X
        << " to " << LARGEST_X << " is " << estimatedArea << endl;

   return 0;
}

//
// Function to throw darts and return number of hits below curve
// Pre:  none
// Post: The number of darts hitting below curve was returned.
//

int countHitsBelow()
{
   float f(float x);

   int   numHitsBelow = 0; // number of darts below curve
   float randomX; 	   // random x between SMALLEST_X & LARGEST_X
   float randomY; 	   // random y between 0 & MAX_Y
   float fOfX; 	           // f(x)

   for (int i = 0; i < NUMDARTS; ++i)
   {
	     randomX = randomDoubleRange(SMALLEST_X, LARGEST_X);
	     randomY = randomDoubleRange(0, MAX_Y);
	     fOfX = f(randomX);
	     if (randomY < fOfX)
	        ++numHitsBelow;
   }

   return numHitsBelow;
}

//
// A mathematical function
// Pre:  	x is a floating point number.
// Post: The square root of ((cos(x))^2 + 1) was returned.
//

float f(float x)
{
   return (sqrt(cos(x) * cos(x) + 1));
}