Authors:
Walter Savitch ,kenrick Mock
Chapter:
Recursion
Exercise:
Programming Projects
Question:6 | ISBN:9780132830317 | Edition: 5
Question
The formula for computing the number of ways of choosing r different things from a set of n things is the following:
C(n, r)= n!/(r!*(n – r)!)
The factorial method n! is defined by
n!= n*(n – 1)*(n – 2)*...*1
Discover a recursive version of the formula for C(n , r) and write a recursive method that computes the value of the formula. Place the method in a class that has a main that tests the method.
Answer
import java.util.*;
public class FactorialDemo
{
public static void main(String args[])
{
int n,r;
Scanner input = new Scanner(System.in);
System.out.print("Enter number of elements(n): ");
n= input.nextInt();
System.out.print("Enter size(r): ");
r = input.nextInt();
System.out.println("Total " + computeWays(n, r) + " ways to choose " + r + " different objects.");
}
public static int factorial(int n)
{
if (n == 1)
return 1;
else
return n * factorial(n - 1);
}
public static int computeWays( int x, int y)
{
return (factorial(x)) / (factorial(y) * factorial(x - y));
}
}
OUTPUT:
Enter number of elements(n): 5
Enter size(r): 4
Total 5 ways to choose 4 different objects.