Compute the binomial coefficient

BionomialCoefficient.java

/**
 * Problem: Design an efficient algorithm for computing(n/k) which has the property that it never 
 * overflows if the final result fits in the integer word size
 */
public class BionomialCoefficient {

    /**
     * Bionomial coefficient is nothing but pascal's traingle basic idea is value of cell is sum of
     * value of two cells from previous nodes (n-1) and n
     */
    public int computeBionomialCoefficient(int n, int k){
        if(k == 0 || k == n )
            return 1;

        return computeBionomialCoefficient(n-1,k) + computeBionomialCoefficient(n-1,k-1);
    }
    
    public int computeXChooseY(int x, int y, int[][] xChooseY){
        if( y == 0 || x == y)
            return 1;
        
        if(xChooseY[x][y] == 0){
            int withoutY = computeXChooseY(x-1, y, xChooseY);
            int withY = computeXChooseY(x-1, y-1, xChooseY);
            xChooseY[x][y] = withY + withoutY;
        }
        return xChooseY[x][y];
    }
}