1. CSC 205 Programming II
Lecture 8
Recursion

2. Recursive vs. Iterative
Divide and conquer
Decomposition:
Complex systems  subsystems  objects
Procedural
Task  repeat manageable steps a number
of times (iterative)
 small tasks which can be solved in
a similar manor (recursive)

3. An Example
Due to the nature of the task, you should select from the two alternatives which best fit your need
An example: Use a book
Scenario I – read your textbook
Suggested solution: read from the first page to the last which are assigned by the teacher
Scenario II – look up a dictionary for a word
Suggested solution: use the alphabetic order to find it as soon as you can

4. The Factorial of n Definition (the iterative version)
Factorial(n) = n * (n-1) * (n-2) * … * 1, n>0
Factorial(0) = 1
Consider an iterative solution to the problem of computing the factorial of n
A loop is needed
int factorial(int n) {
int f = 1;
for (int i=2; i<=n; i++)
f *= i;
return f; }

5. The Recursive Approach
n! is based on (n-1)!
We can solve a reduced task, (n-1)!, in the same way as we solve n!
The task can reduce to a very manageable size: 1! = 1 or 0! = 1
A recursive approach would look like
Reduce
task size
Solve the
entire task
Solve a base-case directly

6. A Recursive Solution Recursive definition of factorial
0!  1! = 1 * 0! = 1
1!  2! = 2 * 1! = 2
… …
n!  n * (n-1)! Problem solved!
A recursive method
int fact(int n) {
if (n==0)
return 1;
else
return fact(n-1);
} //(A)

7. How Does It Work? The sequence of computation can be depicted as below
Number and order of recursive calls
Parameter(s) passed in each recursive call
Result returned
caller
return 3*fact(2)
3*2
return 2*fact(1)
2*1
return 1*fact(0)
1*1
return 1

8. Four Questions to Ask
How can you define the problem in terms a smaller problem of the same type?
How does each recursive call diminish the size of the problem?
What instance of the problem can serve as the base case?
As the problem diminishes, can you reach the base case?

9. The Trace Box
A trace box is needed for each recursive call to store its local environment, including
The values of parameters passed in
The method’s local variables
A placeholder the value returned from calls made by the current box
The value to be returned
n = 3
A: fact(n-1) = ?
return ?

10. Tracing the Computation – I

11. Tracing the Computation – II

12. Tracing the Computation – III

13. A Recursive void Method
Writing a string backward: CAT  TAC
A recursive strategy
Strip away the first/last letter to reduce problem size
Length of remaining reduced by one per call
The base case: reverse an empty string
An empty string is reachable

14. Strip away the Last Letter
The following recursive method will write a string backward, without changing the string passed in.
void writeBackward(String s, int size) {
if (size > 0) {
System.out.print(s.substring(size-1,size));
writeBackward(s, size-1); }
//base case is implied:
// doing nothing when (size == 0)

15. Strip away the First Letter
The following recursive method will write a string backward, without changing the string passed in.
void writeBackward2(String s) {
if (s.length() > 0) {
System.out.print(s.charAt(0));
writeBackward(s.substring(1)); }
//base case is implied:
// doing nothing when (size == 0)