1. Intro to Computer Science CS1510, Section 2 Dr. Sarah Diesburg
More Recursion
Intro to Computer Science
CS1510, Section 2
Dr. Sarah Diesburg

2. Recursion – one way
A class of methods exhibit recursive behavior when they can be defined by two properties:
A simple base case (or cases), and
A set of rules which reduce all other cases toward the base case. (recursive step)

3. Recursion – another way
A recursive function is:
One that calls itself
With “smaller” inputs (a recursive step)
Until those inputs reach a base case

4. A language based example…
The following is a recursive definition of a person's ancestors:
Your parents are your ancestors (base case).
The parents of your ancestors are also your ancestors (recursion step).

5. Recursion Humor
Recursion
See "Recursion".

6. Better Recursion Humor
If you still don't get it, see "Recursion".

7. Recursion Humor

8. Some Examples of things that can be done recursively
Summation of numbers – sum(lower,upper)
Exponents - power(base,exp)
Reverse a string – reverse(string)
Merge Sort – mergeSort(lyst)

9. How Does the Computer Keep Track?

10. The Stack
A Stack is a data structure, like a List or a Dictionary, but with a few different characteristics.
A Stack is a sequence.
A Stack only allows access to one end of its data, the top of the stack.

12. Operations pop: remove top of stack. Stack is one element smaller.
push (val): add val to the stack. Val is now the top. Stack is one element larger.
top: Reveals the top of the stack. No modification to stack.

14. Stack of Function Calls
Python maintains a stack of function calls.
If a function calls another function recursively, the new function is pushed onto the calling stack and the previous function waits.
The top is always the active function.
When a pop occurs, the function below becomes active.

15. Example: Fibonacci Sequence
Start with two numbers in the sequence of
1 1
To get the next number in the sequence, add the previous two numbers together
1+1=2
1 1 2
1+2=3

16. How to make Fibonacci a Recursive Function
Depends on the Fibo results for the two previous values in the sequence.
The base values are Fibo(0) == 1 and Fibo(1) == 1.
fibo (x) = fibo(x-1) + fibo(x-2)

17. Code Listing 16-3
def fibo(n): """Recursive Fibonacci sequence.""" if n == 0 or n == 1: # base case return 1 else: # divide and conquer return fibonacci(n-1) + fibonacci(n-2)

18. Trace fibo(4) = fibo(3) + fibo(2) fibo(3) = fibo(2) + fibo(1)
fibo(2) = fibo(1) + fibo(0) = 2 # base case
fibo(3) = 2 + fibo(1) = 3 # base case
fibo(4) = = 5