Recursion

1
Recursion Collections API

• Recursion Revisited
• Programming Assignments using the Collections API

2
Recursion as Repetition

• public static void hello (int N)
• for (int k 0 k lt 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() gt 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
• else
• 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 ( arrhead 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 gt 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 lt last i)
• if ( arr i gt arrmaxIdx)
• maxIdx i

22
Program 1

• Create a class with a method that takes a string
  and returns the number of characters that only
  occur once in the string. It is expected that the
  method will be called repeatedly with the same
  strings. Since the counting operation can be time
  consuming, the method should cache the results so
  that when the method is given a string previously
  encountered, it will simply retrieve the stored
  result. Use collections wherever appropriate.

23
Program 2

• Write a program that reads strings from input and
  outputs them sorted by length, shortest string
  first. If a subset of input strings has the same
  length, your program should output them in
  alphabetical order.