RECURSION - Java Programming: From Problem Analysis to Program Design - page 902

4. Write a recursive function named sumSquares that returns the sum of the
squares of the numbers from 0 to num , where num is a nonnegative int
variable. Do not use global variables, use appropriate parameters. Also write
a program to test your function.
5. Write a recursive method that finds and returns the sum of the elements of
an int array. Also, write a program to test your method.
6. A palindrome is a string that reads the same both forward and backward. For
example, the string '' madam '' is a palindrome. Write a program that uses a
recursive method to check whether a string is a palindrome. Your program
must contain a value-returning recursive method that returns true if the
string is a palindrome and false otherwise. Use appropriate parameters in
your method.
7. Write a program that uses a recursive method to print a string backward.
Your program must contain a recursive method that prints the string back-
ward. Use appropriate parameters in your method.
8. Write a recursive method, reverseDigits , that takes an integer as a
parameter and returns the number with the digits reversed. Also, write a
program to test your method.
9. Write a recursive method, power , that takes as parameters two integers x
and y such that x is nonzero and returns x y . You can use the following
recursive definition to calculate x y . If y 0:

8
< 1 if y ¼ 0

power ð x ; y Þ¼ x if y ¼ 1

:

x power ð x ; y 1 Þ if y > 1

If y < 0:

1
power ð x ; y Þ

power ð x ; y Þ¼

Also, write a program to test your method.
10. Greatest Common Divisor. Given two integers x and y, the following
recursive definition determines the greatest common divisor of x and y,
written gcd(x,y):
gcd ð x ; y Þ¼ x

if y ¼ 0

gcd ð y ; x % y Þ if y 6¼ 0

(Note: In this definition, % is the mod operator.)
(This algorithm to determine the gcd of two integers is called the Eucli-
dean algorithm.) Write a recursive method, gcd , that takes as parameters
two integers and returns the greatest common divisor of the numbers. Also,
write a program to test your method.