More Recursion

1
More Recursion

• Intro to Computer Science
• CS1510
• 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

• Recursion
• 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.

11
(No Transcript)
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.

13
(No Transcript)
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
• 112
• 1 1 2
• 123
• 1 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) 3 2 5