Recursion

1
Recursion

• Overview
• Introduction to recursion and recursive methods
• Simple popular recursive algorithms
• Writing recursive methods
• Preview Parameter passing

2
Recursion

• We have mentioned earlier that a method can call
  itself directly or indirectly using an
  intervening method.
• A recursive method is a method that calls itself.
• A well-defined recursive method has
• A base case
• A recursive step which must always get closer
  to the base case from one invocation to another.
• The code of a recursive method must be structured
  to handle both the base case and the recursive
  case.
• Each call to the method sets up a new execution
  environment, with new parameters and local
  variables.
• As always, when the method completes, control
  returns to the method that invoked it (which may
  be an earlier invocation of itself).

3
Recursion The Factorial Function

• The factocial function is defined as
• n! n(n-1)(n-2)1
• import java.io.IOException
• import TextIO
• class Factorial
• static TextIO inputStream
• new TextIO(System.in)
• public static int factorial(int num)
• if (num 0) return 1
• else return numfactorial(num-1)
• public static void main (String args) throws
  IOException
• int n, answer
• System.out.println("Enter an integer")
• n inputStream.readInt()
• answer factorial(n)

4
Recursion Sample Execution Trace

• Factorial A Sample Trace
• factorial (6)
• (6Factorial(5))
• (6(5Factorial(4)))
• (6(5(4Factorial(3))))
• (6(5(4(3Factorial(2)))))
• (6(5(4(3(2Factorial(1))))))
• (6(5(4(3(21)))))
• (6(5(4(32))))
• (6(5(46)))
• (6(524))
• (6120)
• 720

5
Recursion sumOfSquares

• sumOfSquares Specified as
• sumSquares(m,n)m2(m1)2(m2)3n2
• import java.io.
• import TextIO
• class SumOfSquares
• static TextIO inputStream
• new TextIO(System.in)
• static int sumSquares(int from,
• int to)
• if (from lt to)
• return fromfrom
• sumSquares(from1,to)
• else return fromfrom

6
Recursion sumOfSquares (cont.)

• sumOfSquares (continued)
• public static void main (String args) throws
  IOException
• int from, to, answer
• System.out.println("Enter the smaller
  integer")
• from inputStream.readInt()
  System.out.println("Enter the bigger integer")
• to inputStream.readInt()
• answer sumSquares(from,to)
• System.out.println("Sum of Squares from "
  from " to " to" is " answer)

7
Recursion sumOfSquares Execution Trace

• sumSquares A Sample Trace
• sumSquares (5,10)
• (25sumSquares(6,10))
• (25(36sumSquares(7,10)))
  (25(36(49sumSquares(8,10))))
• (25(36(49(64sumSquares(9,10)))))
• (25(36(49(64(81(sumSquares(10,10)))))))
• (25(36(49(64(81100)))))
• (25(36(49(64181))))
• (25(36(49245)))
• (25(36294))
• (25330)
• 355

8
Recursion The Fibonacci Function

• The famous Fibonacci function is defined as
• fib 0 1
• fib 1 1
• fib n fib(n-1)fib(n-2), ngt2.
• import java.io.
• import TextIO
• class Fibonacci
• static TextIO inputStream new
  TextIO(System.in)
• static int fibonacci (int num)
• if (num 0 num 1)
• return 1
• else return (fibonacci(num-1)
  fibonacci(num-2))

9
Recursion The Fiboacci Function

• Fibonacci
• public static void main (String args) throws
  IOException
• int n, answer
• System.out.println("Enter an integer")
• n inputStream.readInt()
• answer fibonacci(n)
• System.out.println("The "n "th Fibonacci
  number is " answer)

10
Recursion Simple Popular Recursive Algorithms
(cont.)

• Exercises Write complete recursive programs
  for the following algorithms
• 1 power(x,y) that implements xy using repeated
  additions and without using multiplication.
  Assume x to be a floating point value and y to be
  a nonnegative integer.
• 2 gcd(m,n) that implements the Euclids algorithm
  of finding the greatest common divisor of m and
  n. Assume m and n to be positive integers.
• 3. isPlaindrome() which given a string prints an
  informative error message saying whether or not
  the given string is a palindrome (reads the same
  when read from left to right or from right to
  left).