BinomialCoefficients.java

import java.math.BigInteger;
import java.util.Scanner;

/*
To run, use
`javac *.java && java -ea BinomialCoefficients`
Author: Tim Gianitsos
*/

public class BinomialCoefficients
{
	public static void main(String[] args)
	{
		Scanner scan = new Scanner(System.in);
		System.out.println("Welcome to Binomial Expansion. Enter parameters for an expression of the"
				+ " form (ax + by)^c");
		System.out.println("Enter the value of \"c\", the exponent: ");
		int exponent = scan.nextInt();
		while (exponent < 0)
		{
			System.out.println("You must enter a number greater than or equal to 0. Try again: ");
			exponent = scan.nextInt();
		}
		System.out.println("Enter the value of \"a\", the coefficient of the first term");
		int firstCoef = scan.nextInt();
		System.out.println("Enter the value of \"b\", the coefficient of the second term");
		int secondCoef = scan.nextInt();
		System.out.println("Calculating (" + firstCoef + "x + " + secondCoef + "y)^" + exponent);
		calculatePolynomial(exponent, firstCoef, secondCoef);
		scan.close();
	}

	private static void calculatePolynomial(int exponent, int firstCoef, int secondCoef)
	{
		if (exponent == 0)
		{
			System.out.println("Result: 1");
		}
		else
		{
			BigInteger fc = BigInteger.valueOf(firstCoef);
			BigInteger sc = BigInteger.valueOf(secondCoef);
			System.out.print("Result: " + fc.pow(exponent) + " x^" + exponent);
			for (int i = 1; i < exponent; i++)
			{
				System.out.print(" + " + 
						nCr(exponent, i).multiply(fc.pow(exponent - i)).multiply(sc.pow(i))
						+ " x^" + (exponent - i) + " y^" + i);
			}
			System.out.println(" + " + sc.pow(exponent) + " y^" + exponent);
		}
	}

	private static BigInteger nCr(int n, int r)
	{
		BigInteger result = new BigInteger("1");
		int nMinusr = n - r;
		if (r >= n / 2)
		{
			for (; n > r; n--)
				result = result.multiply(BigInteger.valueOf(n));
			for (; nMinusr > 1; nMinusr--)
				result = result.divide(BigInteger.valueOf(nMinusr));
		}
		else
		{
			for (; n > nMinusr; n--)
				result = result.multiply(BigInteger.valueOf(n));
			for (; r > 1; r--)
				result = result.divide(BigInteger.valueOf(r));
		}
		return result;
	}
}