Question

Write a Java program that expands a given binomial (x + y)^n, where integer n is user input. To do the work of the binomial expression, first create a method that accepts n as a parameter and then returns an array holding the coefficients needed for the binomial expansion using the Pascal’s Triangle method. Create a 2nd method which takes the array holding the coefficients as a parameter and prints the appropriate binomial expansion. For example, if n = 5 is entered by the user, the method calculating the coefficients should return {1,5,10,10,5,1} and the method that prints the expansion should print the following: (x + y)^5 = x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5 Your main method should use an appropriate loop for repeated inputs and automatically call the methods to calculate the coefficients and print the binomial expansion. There isn’t a need for a menu although you should ask the user if they want to quit or continue

Answer 1

The code is:

import java.util.Scanner;

public class BinomialExpansion {

public static void main(String[] args) {

Scanner input = new Scanner(System.in);

boolean quit = false;

while (!quit) {

System.out.print("Enter a value for n or enter 'q' to quit: ");

String inputStr = input.nextLine();

if (inputStr.equals("q")) {

quit = true;

} else {

try {

int n = Integer.parseInt(inputStr);

int[] coefficients = calculateCoefficients(n);

printBinomialExpansion(n, coefficients);

} catch (NumberFormatException e) {

System.out.println("Invalid input. Please enter an integer or 'q' to quit.");

}

}

}

}

public static int[] calculateCoefficients(int n) {

int[] coefficients = new int[n+1];

coefficients[0] = 1;

for (int i = 1; i <= n; i++) {

coefficients[i] = 1;

for (int j = i-1; j > 0; j--) {

coefficients[j] += coefficients[j-1];

}

}

return coefficients;

}

public static void printBinomialExpansion(int n, int[] coefficients) {

System.out.print("(x + y)^" + n + " = ");

for (int i = 0; i <= n; i++) {

if (i == 0) {

System.out.print("x^" + (n-i) + " + ");

} else if (i == n) {

System.out.print("y^" + i);

} else {

System.out.print(coefficients[i] + "x^" + (n-i) + "y^" + i + " + ");

}

}

System.out.println();

}

}

Here's how the program works:

The main method repeatedly prompts the user to enter a value for n until they enter "q" to quit.

For each input value of n, the calculateCoefficients method is called to generate an array of coefficients using Pascal's Triangle.

The printBinomialExpansion method is called to print the binomial expansion using the coefficients array and the input value of n. The method formats the output string by including x and y variables with appropriate exponents and coefficients.

Again, please note that this is just one example implementation of the problem and may not be the most efficient or optimal solution.