1. New Mexico Computer Science For All
Recursion
Maureen Psaila-Dombrowski

2. Recursion What is Recursion?
It is a concept/method used in computer science and mathematics
Recursive problem: The problem can be described as a reduced or smaller form of the same problem
Sometimes the problem gets so small that the solution of the small problem is trivial  can solved recursively or has a recursive implementation
Recursion occurs in computer science when you use a recursive implementation
….WHAT?

3. Recursion - Example 5! = 5 * 4 * 3 * 2 * 1
Classic example is a factorial: n!
 5!
5! = 5 * 4 * 3 * 2 * 1

4. Recursion - Example 5! = 5 * 4 * 3 * 2 * 1 NON – recursive definition
But ! = 4 * 3 * 2 * 1
5! = 5 * 4!
Recursive definition
SO… The problem can be broken down into a smaller or reduced version of the same problem
   Maybe it can be solved recursively !

5. Recursion - Example TRIVIAL CASE
Look for the smallest MOST TRIVIAL form of the problem:
5! = 5 * 4 * 3 * 2 * 1  5! = 5 * 4!
but 4! = 4 * 3 * 2 * 1 and 4! = 4 * 3!
 since 3! = 3 * 2 * 1
but 3! = 3 * 2 * 1 and 3! = 3 * 2!
 since 2! = 2 * 1
but 2! = 2 * 1!
 since 1! = 1
TRIVIAL CASE

6. 5! = 5 * 4! Can be solved Recursively
Recursion - Example So
5! = 5 * 4 * 3 * 2 * 1 Or
5! = 5 * 4! Can be solved Recursively
Or in general
n! = n * n-1 * n-2 * …* 3 * 2 * 1
n! = n * (n-1)!

7. Recursion in Computer Languages
Implemented by calling a function or procedure in the body of that same function or procedure.
must be prevented from consuming excessive computing resources
Factorial Psuedocode
factorial N
if N <=1
(then factorial = 1)
(else factorial = N * factorial[N-1])
this is done by testing for trivial cases (or other stopping conditions), and avoiding recursive calls in those cases.

8. Recursive Programming
Pros
Recursive description --- simple, elegant, and easy to explain and understand.
Recursive implementation --- straightforward to build and verify.
Cons
Can be difficult to understand at first.
In some programming languages not as efficient as iteratively
Can be difficult to program
circularity  infinite loop  MUST PUT IN A STOP
Once you have a recursive description a recursive iimplementatio…

9. Why use Recursion?
So if can be less efficient and difficult to understand and program, why use recursion?
The problem/program may be easier to understand, solve and program using recursion
When you have a recursive description  recursive solution is the most direct solution path
Usually creating an easy to verify code is more important than creating the most efficient code

10. Recursion in NetLogo
Draw a spiral from the outside in:

11. Recursion in NetLogo Iteratively Specify initial line length
Interative Draw
While (condition?), repeat
Turtle draws a line
Turtle turns right
Reduce line length

12. GO TO MODEL

13. But we forgot something!
Recursion in NetLogo
Recursively
Specify initial line length
Recursive Draw
Turtle draws a line
Turtle turns right
Draw a new line with a reduced length
But we forgot something!
We Forgot The STOP!

14. Recursion in NetLogo Recursively Specify initial line length
Recursive Draw
If (condition?) STOP
Turtle draws a line
Turtle turns right
draw a new live with a reduced length

15. GO to Code

16. Important Note
For every recursive algorithm……
….. There is an equivalent iterative (looping) algorithm!!

17. Summary Recursion: CS method
The solution depends on the solution to smaller instances of the same problem
In most programming languages  a function or procedure calling itself in the code
Pros: shorter, easier to understand, more elegant
Cons: often not as efficient as iterative and can be difficult to program
Why use recursion?
The problem/program is easier to understand using recursion
The problem is easier to solve using recursion