Question

USE C++ Problem 3: Prompt the user to enter a whole number of points to be used in the approximation and robustly confirm that the number of points is positive (remember always ask user to re-enter before any calculations are performed). Then calculate and output the approximation for pi. Run your program at least twice with the entered number of points varying by at least a thousand. Examine your results and add a comment to the end of your source code file stating the effect of using more points on the approximation of pi. The maximum random number in C++ is stored into a predefined constant called RAND_MAX.

Answer 1

C++ CODE

#include<iostream> #include<ctime> #include<cstdlib> #define seed 35791246 using namespace std; double estimatePi(long numIter); double Xpoint; double Ypoint; double Zpoint = 0; int points = 0; int main() { long numIter; double estimatedPi; cout<<"Input the number of points: "; cin>>numIter; if(numIter < 0) { cout<< "Number of points must be a positive integer."<<endl; return -1; } srand(seed); // seeding random number generator // calling estimatePi function estimatedPi = estimatePi(numIter); cout<<"Estimated pi ~= "<< estimatedPi<<endl;    } double estimatePi(long numIter) { int i = 0; double estimatedPi; while(i < numIter ) { Xpoint = (double)rand()/RAND_MAX; Ypoint = (double)rand()/RAND_MAX;    Zpoint = (Xpoint * Xpoint) + (Ypoint * Ypoint) ; if (Zpoint <= 1) { points++; } i++; } estimatedPi = (double)points / numIter * 4 ; return estimatedPi; }

OUTPUT

E:\Program Files\Cplusplus workspace\Estimate_pi.exe Input the number of points 1000 stimated pi 3.196 rocess exited after 4.658 seconds with return value ress any key to continue - - - EProgram Files\ Cplusplus workspace\ Estimate_pi.exe Input the number of points 2000 Estinated pi -3.19 rocess exited after 2.845 seconds with return value 0 ress any key to continue - .. _