. The Monte Carlo technique is often used to evaluate multi-dimensional integral

Question

. The Monte Carlo technique is often used to evaluate multi-dimensional integrals. As an illustrative example, we can generate random points in the unit square [0, 1]2 in the xy?plane. If we count the points satisfying x^2 + y^2 </ 1 as “hits”, then the hits divided by the total number of points should be an approximation to the area of a quadrant of a disk with unit radius. Since the total area of such a disk is ?, this gives us a (rather inefficient) way of calculating ?.

Write a procedure to estimate the value of ? based on the above Monte Carlo method. Have your program list the deviations from the true value as the number of points increases (for example, give the deviations for every 1000 points).

Use arrays please

Explanation / Answer

Program:

//Include files

#include <iostream>

#include <cmath>

#define LIMIT 200

using namespace std;

//DEfine function

double findPI()

{

//Declare variable

int inter, i;

//Declare variable

double xRand, yRand, distOrigin, pi;

//Declare variable

int ptCircle = 0, ptSquare = 0;

//Loop

for (i = 1; i <= (LIMIT * LIMIT); i++) {

//Create points

//Create x

xRand = double(rand() % (LIMIT + 1)) / LIMIT;

//Create y

yRand = double(rand() % (LIMIT + 1)) / LIMIT;

//Find distance

distOrigin = xRand * xRand + yRand * yRand;

//Check condition

if (distOrigin <= 1)

//Increase circle point count

ptCircle++;

//Increase square point count

ptSquare++;

//Compute pi

pi = double(4 * ptCircle) / ptSquare;

//Check condition

if (i %1000==0)

{

//Print error for every 1000th iteration

cout<<"Error:"<<abs(pi-3.14)<<endl;

}

}

//Return

return pi;

}

//Define function

int main()

{

//Seed

srand(time(NULL));

//Print

cout << " Final Value of PI = " << findPI();

//Return

return 0;

}

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