1. Recursion
B.Ramamurthy
2/23/2019
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.
2/23/2019
Ramamurthy

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?
2/23/2019
Ramamurthy

4. Recursion Methodology
Initial Case
Stopping case
Continue case
Computation that progresses towards result and stopping case
2/23/2019
Ramamurthy

5. Example 1: Factorial of N
Iterative definition:
Factorial(N) = N * (N-1) * (N-2) *…1 for any N > 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
2/23/2019
Ramamurthy

6. Java Methods for Factorial
int factorialIterative(int N) {
tmp = 1;
while (N > 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)); }
2/23/2019
Ramamurthy

7. ArrayList ArrayList ArrayList(); //constructor boolean add(Object o);
Object remove(int index);
int indexOf(Object o);
boolean isEmpty();
int size();
Object[] toArray();
// it also has a list iterator that it inherits from AbstractList
// this helps in traversal thru’ the list
public ListIterator listIterator()
2/23/2019
Ramamurthy

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
2/23/2019
Ramamurthy