Estimating #1 The value of can be estimated by the infinite series =4(1-1+1-1+1-

Question

Estimating #1 The value of can be estimated by the infinite series =4(1-1+1-1+1-...) The greater the number of terms used in the calculation, the more accurate the estimate. write a function that takes a single integer N and estimates usng the first N terms of this series. Part A: Write a program that prompts the user for N then outputs the estimated value of pi. Part B: Assuming that math.pi is the correct value for pi, prompt the user for the desired accuracy, then find the minimum value of N that delivers that accuracy. ser wants the estimate to be within +/-0.0001, determine the minimum number of term:s required to achieve that level of accuracy. For example,if the u

Explanation / Answer

import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.Scanner;

public class PiEstimation {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        DecimalFormat format = new DecimalFormat("##.#####");
        format.setRoundingMode(RoundingMode.UP);

        System.out.println("1. Estimated Value for Nth Terms 2. Estimate Accuracy");
        int choice = scanner.nextInt();
        PiEstimation obj = new PiEstimation();
        switch (choice) {
            case 1:
                System.out.println("Enter the Nth Term for PI Calculation : ");
                int nthTerm = scanner.nextInt();
                double estimatedValue = obj.calculatePi(nthTerm);
                System.out.println("Estimated PI Value : " + format.format(estimatedValue));
                break;
            case 2:
                System.out.println("Enter Desired Accuracy Level : ");
                int accuracy = scanner.nextInt();
                String precision = "#.#";
                for (int i = 1; i < accuracy; i++) {
                    precision += "#";
                }
                System.out.println("Accuracy Found at : " + obj.getN(precision) + "th Term.");
                break;
                default:
                    System.out.println("Not a valid choice");
        }
    }

    /**
     * Calculate the Nth term value for the given formula
     *
     * @param n
     * @return
     */
    public double calculatePi(int n) {
        boolean signFlipper = false;
        double val = 1.0;
        double estimateValue = 0;
        for (int i = 1; i <= n; i++) {
            double term1 = 1 / val;
            if (i > 1) {
                signFlipper = !signFlipper;
                if (signFlipper) {
                    estimateValue -= term1;
                } else {
                    estimateValue += term1;
                }
            } else
                estimateValue = term1;
            val += 2;
        }
        return (4.0 * estimateValue);
    }

    /**
     * Estimate the Nth term which matches with Math.PI within user specified precision
     *
     * @param accuracyPrecisionFormat
     * @return
     */
    public int getN(String accuracyPrecisionFormat) {
        System.out.println("pattern : "+accuracyPrecisionFormat);
        DecimalFormat format = new DecimalFormat(accuracyPrecisionFormat);
        format.setRoundingMode(RoundingMode.UP);
        double piValue = Math.PI;
        double estimatedValue;
        int i = 1;
        boolean signFlipper = false;
        double val = 1.0;
        double estimateValue = 0;
        while (true){
            double term1 = 1 / val;
            if (i > 1) {
                signFlipper = !signFlipper;
                if (signFlipper) {
                    estimateValue -= term1;
                } else {
                    estimateValue += term1;
                }
            } else
                estimateValue = term1;
            val += 2;
            double tempEstimatedValue=(4.0*estimateValue);
            if (format.format(tempEstimatedValue).equals(format.format(piValue))){
                estimatedValue=tempEstimatedValue;
                break;
            }
            i++;
        }
        System.out.println("Original Value : "+format.format(piValue));
        System.out.println("estimated Value : "+format.format(estimatedValue));
        return i;
    }
}

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