Recursion

1
Recursion

• B.Ramamurthy

2
Introduction

• Recursion is one of most powerful methods of
  solution available to computer scientists.
• We will study application of recursion for
  solving simple problems.
• Later on we will reexamine recursion in the
  context of tree ADT.

3
Recursive Solutions

• Recursion is an important problem solving
  approach that is an alternative to iteration.
• These are questions to answer when using
  recursive solution
• 1. How can you define the problem in terms of a
  smaller problem of the same type?
• 2. How does each recursive call diminish the size
  of the problem?
• 3. What instance of the problem can serve as the
  base case?
• 4. As the problem size diminishes, will you reach
  this base case?

4
Recursion Methodology

• Initial Case
• Stopping case
• Continue case
• Computation that progresses towards result and
  stopping case

5
Example 1 Factorial of N

• Iterative definition
• Factorial(N) N (N-1) (N-2) 1 for any N gt
  0.
• Factorial(0) 1
• Recursive solution
• 1. Factorial(N) N Factorial(N-1)
• 2. Problem diminishing? yes.
• 3. Base case/stopping case Factorial(0) 1
  base case does not have a recursive call.
• 4. Can reach base case as problem diminishes? yes

6
Java Methods for Factorial
int factorialIterative(int N) tmp 1
while (N gt 1) tmp tmp N N N 1
return tmp int factorial (int
N) if (n 0) return 1 // base case
return (N factorial(N-1))
7
ArrayList
8
ListIterator
An iterator for lists that allows the programmer
to traverse the list in either direction, and
modify the list during iteration.
ListIterator
boolean hasNext() Object next()
Usage See ArrayTest.java discussed earlier