Question

om me insert e Search - Assignment - Word Design Layout References Mailings Review Lucida Sans Typ 11 - A A A A - BIU XX A.D.A. View ру mat Painter rd CIT 111 Help! 21 - - 19. ABCD AaBbcDc AaB 1 Normal TNo Spac... Head Paragraph PROGRAMS SPRING 2020 8.3 points Write a method that determines if a positive integer is an abundant number. A number is abundanti the sum of its proper divisors (a divisor that isn't equal to the number) is greater than the number itself. 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4, and 6: these numbers add up to 16. The first 10 abundant numbers are 12, 18, 20, 24, 30, 36, 42, 48, and 54. The method header will look like this: public static boolean isAbundant int number ) A call to isAbundant would look like this: if (isAbundant (nb ) System.out.println("The number " + nbr + " is abundant"): else System.out.println("The number " + nbr + is not abundant"): 9. 3 points Advanced - we won't cover this in class. Research on your own. Write a recursive method that given a positive integer value, returns the ith Fibonacci number. Hint: the tests must be in the order listed. The call would look like: answer = fib(4): The method header would look like: public static int fib(int n) The recursive definition for the Fibonacci sequence is: • Fibonacci(0) 0 • Fibonacci(1) - 1 • Fibonacci(n) Fibonacci(n-1) + Fibonacci(n-2) Added Challenge: Run your method fib for large numbers, say 1,000 or more. What happens? Try a smaller number like 100. What happens? Try a one digit number. What happens? Our solutions before were iterative. Implement an iterative solution for returning the ith Fibonacci number. Modify fib to choose between the iterative and recursive solutions. This will probably) involve writing three fib methods or modifying your main method when calling the fib methods. Several former students have solved this problem, including a sixteen year old

Answer 1

1. Program for Abundant Number :-

package abundantno; import java.util.*; public class AbundantNo { public static void main(String[] args) { System.out.println("Enter the number: "); Scanner sc = new Scanner(System.in); int nbr = sc.nextInt(); AbundantNo a = new AbundantNo(); if(a.isAbundant(nbr)) System.out.println("The number " + nbr + " is Abundant."); else System.out.println("The number " + nbr + " is not Abundant."); } public static boolean isAbundant(int number) { int sum = 0; for (int i=1; i<=Math.sqrt(number); i++) { if (number%i==0) { if (number/i == i) sum = sum + i; else { sum = sum + i; sum = sum + (number / i); } } } sum = sum - number; if (sum>number) return true; else return false; } } 

2. Program for Fibonacci Series :-

  package fibonaccinumber; import java.util.*; public class FibonacciNumber { public static void main(String[] args) { Scanner sc = new Scanner(System.in); int answer; int n; System.out.println("Enter ith element: "); n = sc.nextInt(); answer = fibonacci(n); System.out.println("The "+n+"th element in Fibonacci series is: "+answer); } public static int fibonacci(int n){ if(n == 0) return 0; else if(n == 1) return 1; else return fibonacci(n-1)+fibonacci(n-2); } } 

Output -