WB_Binomial.java

/**
 * 
 */
package wblut.math;

// TODO: Auto-generated Javadoc
/**
 * The Class WB_Binomial.
 *
 * @author Frederik Vanhoutte, W:Blut
 * 
 * Calculates binomial coefficients.
 */
public class WB_Binomial {
	
	/** The binomial. */
	private final long[][]	binomial;

	/**
	 * An instance of WB_Binomial stores a N by K matrix of binomial coefficients.
	 * 
	 * n! / (n-k)! k!
	 * 
	 * This is efficient if the same coefficient are need over and over. The
	 * precalculated coefficient are retrieved with binPreCalc().
	 * If only a few coefficients are needed, the static function bin() can be
	 * more efficient. It can be directly called as WB_Binomial.bin(n,k)
	 * 
	 * @param N n-value
	 * @param K k-value
	 */
	public WB_Binomial(final int N, final int K) {
		binomial = new long[N + 1][K + 1];

		// base cases
		for (int k = 1; k <= K; k++) {
			binomial[0][k] = 0;
		}
		for (int n = 0; n <= N; n++) {
			binomial[n][0] = 1;
		}

		// bottom-up dynamic programming
		for (int n = 1; n <= N; n++) {
			for (int k = 1; k <= K; k++) {
				binomial[n][k] = binomial[n - 1][k - 1] + binomial[n - 1][k];
			}
		}

	}

	/**
	 * Retrieve the precalculated binomial coefficient from an instance
	 * of WB_Binomial.
	 *
	 * @param n n-value, <=N of WB_Binomial instance
	 * @param k k-value, <=K of WB_Binomial instance
	 * @return binomial coefficient as long
	 */
	public long binPrecalc(final int n, final int k) {

		return binomial[n][k];

	}

	/**
	 * Retrieve arbitrary binomial coefficient.
	 *
	 * @param N n-value
	 * @param K k-value
	 * @return binomial coefficient as long
	 */

	public static long bin(final int N, final int K) {
		final long[][] binomial = new long[N + 1][K + 1];
		for (int k = 1; k <= K; k++) {
			binomial[0][k] = 0;
		}
		for (int n = 0; n <= N; n++) {
			binomial[n][0] = 1;
		}

		// bottom-up dynamic programming
		for (int n = 1; n <= N; n++) {
			for (int k = 1; k <= K; k++) {
				binomial[n][k] = binomial[n - 1][k - 1] + binomial[n - 1][k];
			}
		}
		return binomial[N][K];
	}
}