1. Recursion Problems

2. Recursion as Repetition
public static void hello (int N)
{ for (int k = 0; k < N; k++)
System.out.println (“Hello World!”); }

3. Recursion as Repetition
public static void hello (int N) {
if ( N == 0)
return;
else
System.out.println (“Hello World!”);
hello (N – 1); }

4. Recursion as Repetition
Write a recursive method pow() that returns xn, where x and n are both integers greater than or equal to zero.

5. Recursion as Repetition
public static long pow (int x, int n)
{ if ( x == 0) return 0;
if ( n == 0) return 1;
long result = x * pow ( x, n – 1);
return result; }

6. Recursive String Methods
Write a recursive method that will print the characters in a string recursively, one character at a time.

7. Recursive String Methods
public static void printString (String s)
{ if ( s.length() == 0)
return;
else
{ System.out.println ( s.charAt(0) );
printString ( s.substring (1) ); }

8. Recursive String Methods
Write a recursive method that will print a String in reverse order one character at a time.

9. Recursive String Methods
public static void printReverse ( String s )
{ if ( s.length() > 0 )
{ printReverse ( s.substring ( 1 ) );
System.out.println ( s.charAt ( 0 ) ); }
Many recursive solutions involve breaking a sequential structure, such as a string or an array, into its head and tail. An operation is performed on the head, and the algorithm recurses on the tail.

10. Recursive String Methods
Write a recursive method that will count the number of occurrences of the character ch in the String s.

11. Recursive String Methods
public static int countChar (String s, char ch)
{ if ( s.length() == 0 )
return 0;
else if ( s.charAt ( 0 ) == ch)
return 1 + countChar ( s.substring (1), ch);
else
return 0 + countChar ( s.substring (1), ch); }

12. Recursive String Methods
Write a recursive method to rotate a String by N characters to the right. For example, rotateR (“hello”, 3) should return “llohe”.

13. Recursive String Methods
public static String rotateR (String s, int n)
{ if ( n == 0 )
return s;
else
{ StringBuffer buf = new StringBuffer ();
buf.append (s.charAt (s.length() - 1));
buf.append (s.substring (0, s.length() - 1));
return rotateR (buf.toString(), n - 1); }

14. Recursive String Methods
Write a recursive method to convert a String representing a binary number to its decimal equivalent. For example, binTodecimal (“101011”) should return the int 43.

15. Recursive String Methods
public static int binTodecimal (String s) {
if ( s.length() == 1)
return Integer.parseInt (s);
else
return Integer.parseInt (s.substring (s.length() - 1)) +
2 * binTodecimal (s.substring (0, s.length() - 1); }

16. Recursive String Methods
A palindrome is a string that is the same as its reverse – “radar” and “able was I ere I saw elba”. Write a recursive boolean method that determines whether its String parameter is a palindrome.

17. Recursive String Methods
public static boolean palindrome ( String s) {
if ( s.length() == 0 || s.length() == 1 )
return true;
else
{ if ( s.charAt(0) != s.charAt (s.length() - 1))
return false;
return palindrome ( s.substring (1, s.length() - 1) ); }

18. Recursive Array Methods
Write a recursive method that will do a sequential search on an array.

19. Recursive Array Methods
public static int rSearch (int[] arr, int head, int key )
{ if ( head == arr.length )
return –1;
else if ( arr[head] == key )
return head;
else
return rSearch ( arr, head + 1, key ); }

20. Recursive Array Methods
Write a recursive method that will do a selection sort on an array.

21. Recursive Array Methods
public static void selectionSort ( int[] arr, int last )
{ if ( last > 0 )
{ int maxLoc = findMaxIdx ( arr, last);
swap ( arr, last, maxLoc );
selectionSort ( arr, last – 1 ); }
public static int findMaxIdx ( arr, last)
{ int maxIdx = 0;
for (int i = 0; i <= last; i++)
if ( arr [i] > arr[maxIdx)
maxIdx = i;