Problem 15

/**
 *
 * @author Mat
 */
package problem.pkg11;

public class Problem15 {

    public static void main(String[] args) {
        final int MAXNUM = 21;
        long[][] array = new long[MAXNUM][MAXNUM];


        // set numbers to 1 around "at pos
        for (int i = 0; i < MAXNUM; i++) {
            for (int j = 0; j < MAXNUM; j++) {
                array[0][j] = 1;

            }
            array[i][0] = 1;
        }

        //Work out Pascal's triangle.
        for (int i = 1; i < MAXNUM; i++) {
            for (int j = 1; j < MAXNUM; j++) {
                array[i][j] = array[i][j - 1] + array[i - 1][j];

            }
        }


        // print out array for debugging with smaller numbers
        /*
        for(int i = 0; i < MAXNUM;i++){
        for(int j = 0; j < MAXNUM;j++){
        System.out.printf("%d\t", array[i][j]);
        }
        System.out.println();

        }
         */


        System.out.println("The number of routes on a 20x20 board is "
                + array[MAXNUM - 1][MAXNUM - 1]);

    }
}
/* Output
 * The number of routes on a 20x20 board is 137846528820
 */