Fastest way to generate binomial coefficients

Question

I need to calculate combinations for a number.

What is the fastest way to calculate nCp where n>>p?

I need a fast way to generate binomial coefficients for a

Answer 1

Time Complexity : O(denominator) Space Complexity : O(1)

public class binomialCoeff {
    static double binomialcoeff(int numerator, int denominator) 
    { 
        double res = 1; 
        //invalid numbers
        if (denominator>numerator || denominator<0 || numerator<0) {
            res = -1;
            return res;}
        //default values
        if(denominator==numerator || denominator==0 || numerator==0)
            return res;


        // Since C(n, k) = C(n, n-k) 
        if ( denominator > (numerator - denominator) ) 
            denominator = numerator - denominator;


        // Calculate value of [n * (n-1) *---* (n-k+1)] / [k * (k-1) *----* 1] 
        while (denominator>=1)
        { 

        res *= numerator;
        res = res / denominator; 

        denominator--;
        numerator--;
        } 

        return res; 
    } 

    /* Driver program to test above function*/
    public static void main(String[] args) 
    { 
        int numerator = 120; 
        int denominator = 20; 
        System.out.println("Value of C("+ numerator + ", " + denominator+ ") "
                                + "is" + " "+ binomialcoeff(numerator, denominator)); 
    } 

}