RECURSION - Introduction to Java Programming: Comprehensive Version - page 729

numbers. The current Fibonacci number would then be f0 + f1 . The algorithm
can be described as follows:

f0 = 0 ; // For fib(0)
f1 = 1 ; // For fib(1)

for ( int i = 1 ; i <= n; i++) {
currentFib = f0 + f1;
f0 = f1;
f1 = currentFib;
}
// After the loop, currentFib is fib(n)

Write a test program that prompts the user to enter an index and displays its
Fibonacci number.

*18.3

( Compute greatest common divisor using recursion ) The gcd(m, n) can also
be defined recursively as follows:

If m % n is 0 , gcd(m, n) is n .

■

Otherwise, gcd(m, n) is gcd(n, m % n) . ■

Write a recursive method to find the GCD. Write a test program that prompts the
user to enter two integers and displays their GCD.

18.4

( Sum series ) Write a recursive method to compute the following series:

1
2 +

1
3 + c +

1
i

m ( i ) = 1 +

Write a test program that displays m(i) for i = 1 , 2 , . . ., 10 .

18.5

( Sum series ) Write a recursive method to compute the following series:

1
3

2
5

3
7

4
9

5
11

6
13

i

m ( i ) = + + + + + + c +

2 i + 1

Write a test program that displays m(i) for i = 1 , 2 , . . ., 10 .

*18.6

( Sum series ) Write a recursive method to compute the following series:

1
2

2
3

i

m ( i ) = + + c +

i + 1

1 , 2 , . . ., 10 .
*18.7 ( Fibonacci series ) Modify Listing 18.2, ComputeFibonacci.java, so that the pro-
gram finds the number of times the fib method is called. ( Hint : Use a static
variable and increment it every time the method is called.)
Section 18.4
*18.8

Write a test program that displays m(i) for i =

( Print the digits in an integer reversely ) Write a recursive method that displays
an int value reversely on the console using the following header:

public static void reverseDisplay( int value)

For example, reverseDisplay(12345) displays 54321 . Write a test program
that prompts the user to enter an integer and displays its reversal.

*18.9

( Print the characters in a string reversely ) Write a recursive method that dis-
plays a string reversely on the console using the following header:

public static void reverseDisplay(String value)