Compute Binomial Coefficients for m and n

BinomialCoefficients.java

package com.hrishikesh.practices.dynamicprogramming;

import static com.hrishikesh.practices.dynamicprogramming.BinomialCoefficients.getBinomialCoefficient;

/**
 * Problem :
 * Compute Binomial Coefficients for m and n
 * (n   k) = n!/((n−k)!k!)
 * Formula :
 * (n k) = (n-1 k-1) + (n-1, k)
 *
 * @author hrishikesh.mishra
 */
public class BinomialCoefficients {

    public static long getBinomialCoefficient(int n, int m) {

        /** Matrix to hold Binomial Coefficients **/
        int[][] bc = new int[n + 1][n + 1];

        /** Filling first column of each row of matrix **/
        for (int i = 0; i <= n; i++) {
            bc[i][0] = 1;
        }

        /** Filling last column of each row of matrix **/
        for (int i = 0; i <= n; i++) {
            bc[i][i] = 1;
        }

        /** Computing rest columns **/
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j < i; j++) {
                bc[i][j] = bc[i - 1][j - 1] + bc[i - 1][j];
            }
        }

        /** Printing Binomial Coefficients **/
        printBinomialCoefficients(bc, n);

        return bc[n][m];
    }

    private static void printBinomialCoefficients(int[][] bc, int n) {

        for (int i = 0; i <= n; i++) {
            for (int j = 0; j <= i; j++) {
                System.out.printf("%5d", bc[i][j]);
            }
            System.out.println();
        }
    }
}

class BinomialCoefficientsTest {
    public static void main(String[] args) {
        int n = 5;
        int m = 2;

        System.out.printf("N :%d, M:%d, Binomial Coefficient: %d\n", n, m, getBinomialCoefficient(n, m));
    }
}