Question

using Java

Implement a class called Binomial_Coefficient

o Your class has 2 int attributes, namely K and n
o Create an overloaded constructor to initialize the variables into any positive integers such that n > k > 0o Create a method that calculates the value of binomial coefficient, C(n,k) , using the following rule:

▪ For an array of size (n+1) X (k+1)
▪ Array [n][k] = Array[n-1][ k-1]+ Array[n-1] [k]▪ Array[n][0]= Array[n][n] = 1
▪ Hence, C(n,k) = array [n][k]

o Create a method that prints the content of your array
➢ Write a main method to test your logic with different combinations of n & k.
➢ Make sure in your main function tests the the values of n & k to meet the condition n > k > 0➢ If the user enters wrong combination prompt the user to reenter valid values of n & k

For your information:

• Binomial coefficients are coefficients of the binomial formula:
  (a + b)n = C(n,0)anb0 + . . . + C(n,k)an-kbk + . . . + C(n,n)a0bn

• Binomial Coefficient are calculated as follow:

• C(n,k) = nCk = (nk) = n!/(k! * (n-k)! )

• C(n,k) = C(n-1,k) + C(n-1,k-1) for n > k > 0

• C(n,0)=1, C(n,n)=1 forn0

Answer 1

Screenshot

Program

import java.util.Scanner;

//Create a binomial class
public class Binomial_Coefficient {
   //Instance variables
   private int k;
   private int n;
   //Constructor
   public Binomial_Coefficient(int n,int k){
       Scanner sc=new Scanner(System.in);
       while(!(n>k && k>0)) {
           System.out.println("Enter value of k: ");
           k=sc.nextInt();
           System.out.println("Enter value of n: ");
           n=sc.nextInt();
       }
       this.k=k;
       this.n=n;
   }
   //Coefficient calculation function
   public void calculateCoefficients() {
       int coefficientsArray[][]=new int[n+1][k+1];
       for(int i=0; i<=n; i++) {
           int min = i<k? i:k;
           for(int j = 0; j <= min; j++) {
                 if(j==0 || j == i) {
                   coefficientsArray[i][j] = 1;
                 }
                 else {
                   coefficientsArray[i][j] = coefficientsArray[i-1][j-1] + coefficientsArray[i-1][j];
                 }
           }
        }
       printArray(coefficientsArray,n,k);
   }
   // Create a method that prints the content of your array
   public void printArray(int[][] arr,int n,int k) {
       System.out.println("Coefficients Array: ");
       for(int i=0;i<n;i++) {
           for(int j=0;j<k;j++) {
               System.out.print(arr[i][j]+" ");
           }
           System.out.println();
       }
       System.out.println();
   }
   //Main method
   public static void main(String[] args) {
       //Create test
       Binomial_Coefficient b=new Binomial_Coefficient(7,3);
       b.calculateCoefficients();
   }
}

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Output

Coefficients Array:
1 0 0
1 1 0
1 2 1
1 3 3
1 4 6
1 5 10
1 6 15