5.19

/* 5.19 Calculating the Value of pi
    Deitel & Deitel C++ How to Program, 10th ed (Indian subcontinent adaptation)
    Visual Studio Community 2019

  Objectives:
  1.) display a table of pi approximations from 1st term in sequence to the 200,000th term
  2.) indicate the number of terms needed to arrive at the first result containing '3.14159'
 */

#include <iostream>
#include <iomanip>

using namespace std;
double const NUM = 4.0;

int main(void) {
    double test{ 4.0 }, denom{ 3.0 };
    int answer;
    int count{ 1 };
    bool isNegative = true;
    int foundIt = 0; // first time '3.14159' pops up foundIt is set to the count

    while (count <= 200000 ) {
        if (isNegative) {
            test -= (NUM / denom);
            isNegative = false;
        }
        else {
            test += (NUM / denom);
            isNegative = true;
        }
        if (foundIt == 0) {
            answer = (int)(test * 100000); // convert to an integer for comparison
            if (answer == 314159) foundIt = count;
        }
        denom += 2;
        cout << count << ": " << setprecision(12) << test << "\n";
        count++;
    }
    cout << "It took " << foundIt << " terms to get the first occurrence of 3.14159\n";
    cout << "Note: This does not take into account the initial term of '4' in the sequence.\n";
    return 0;
}