#include <iostream>
using namespace std;

//generate and return a random number
//from a to b: {a, a+1, ..., b-1, b}
int random(int a, int b)
{
	return rand() % (b - a +1) + a;
}


double computePI(int nT, int nH)
{
	return 4 * ((double) nH / nT);
}

//return true if dart hits in circle of
//radius r (centered at origin)
//false otherwise
bool throwOneDart(int r)
{
	//Generate dart location
	int x = random(-1 * r, r);
	int y = random(-1*r, r);

	//Check if location is within circle
	if (sqrt(x * x + y * y) < r)
		return true;
	else
		return false;
}

//Return number of hits
//from throwing n darts at
//radius r board.
int throwDartsCountHits(int r, int n)
{
	int hits = 0;

	//throw n darts, increment hits on hit
	for (int i = 0; i < n; i++)
	{
		if (throwOneDart(r))
			hits++;
	}

	return hits;
}

int main()
{
	//variables
	int radius;
	int numThrows;
	int numHits;
	double PI;

	//Step 1: pick radius of board
	radius = 1000;

	//Step 2: pick number of throws
	numThrows = 800;

	//Step 3: throw the darts at the board, count hits
	numHits = throwDartsCountHits(radius,numThrows);

	//Step 4: compute PI from hits and throws
	PI = computePI(numThrows, numHits);

	//Step 5: report answer to user
	cout << "Our estimate for PI is : " << PI << endl;

	return 0;
}