Day 2 – Lesson 9
Iteration: Recursion
Python Mini-Course
University of Oklahoma
Department of Psychology
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Python Mini-Course: Day 3 - Lesson 9
5/02/09
Lesson objectives
1. Define recursion and state why
recursion is useful
2. Use recursive functions
3. Use checkpoints to debug programs
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Python Mini-Course: Day 3 - Lesson 9
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Recursion
 Not only can functions call other
functions (composition), they can
also call themselves
 This is called recursion
 Recursion is a powerful method
that is a key component to
functional programming
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Python Mini-Course: Day 3 - Lesson 9
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Example: Blastoff
def countdown(n):
if n <= 0:
print 'Blastoff!'
else:
print n
countdown(n-1)
countdown(10)
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Python Mini-Course: Day 3 - Lesson 9
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What's happening here?
Base class
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Python Mini-Course: Day 3 - Lesson 9
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Base classes
 All recursive functions must have
a base class
 What happens otherwise?
 Try this:
def recurse():
recurse()
recurse()
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Python Mini-Course: Day 3 - Lesson 9
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Fibonacci sequence
fibonacci(0) = 0
fibonacci(1) = 1
fibonacci(n) =
fibonacci(n−1) + fibonacci(n−2)
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Python Mini-Course: Day 3 - Lesson 9
5/02/09
Fibonacci sequence
def fibonacci(n):
if n == 0:
return 0
elif n == 1:
return 1
else:
return fibonacci(n-1) \
+ fibonacci(n-2)
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Python Mini-Course: Day 3 - Lesson 9
5/02/09
Debugging with checkpoints
 If a function is not working
check:
 Preconditions
 Arguments being passed into the
function
 Postconditions
 Operations in the function itself
 The way the function is being used
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Python Mini-Course: Day 3 - Lesson 9
5/02/09
Testing preconditions
 Add a (temporary) print
statement to the beginning of the
function
 Use type-checking functions
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Python Mini-Course: Day 3 - Lesson 9
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Fibonacci sequence
def fibonacci(n):
print n, type(n)
…
fibonacci(-2)
fibonacci(0.4)
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Python Mini-Course: Day 3 - Lesson 9
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Fibonacci sequence
def fibonacci(n):
if (not type(n) == int) or n < 0:
print "Fibonacci is only \
defined for non-negative \
integers"
return
…
fibonacci(-2)
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Python Mini-Course: Day 3 - Lesson 9
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Testing postconditions
 Use same technique of adding
(temporary) print statements at
critical points in the function
 For large programs or functions,
use the half-splitting technique
 Check beginning, middle, end
 Find the half with a problem
 Recurse
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Python Mini-Course: Day 3 - Lesson 9
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Next session
 More on loops and conditional
execution
 Including the while loop
 Handling strings and text
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Python Mini-Course: Day 3 - Lesson 9
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Suggested exercises
 Exercise 6.5 – The Ackermann
function
 Exercise 6.8 – Euclidean algorithm
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Python Mini-Course: Day 3 - Lesson 9
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