# valeriecodes/recursion-review

Intro to recursion with code examples in Python
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 Failed to load latest commit information. README.md countdown-iterative.py countdown.py factorial-iterative.py factorial.py fibonacci-iterative.py fibonacci.py search-iterative.py search.py

# Recursion Review

This repo is a work in progress with resources to learn recursion. Have questions or feedback? Get in touch with me on Twitter, @valeriecodes or via email at valerie.woolard@gmail.com

## What is recursion?

Solving a problem by solving smaller versions of the same problem. A recursive function is one that calls itself.

One mathematical practice that mirrors the structure of a recursive function is an inductive proof. If you've used this, a lot of these concepts may be familiar to you.

In an inductive proof, you can prove that something is true for all natural numbers N by proving that:

• It is true for the first natural number (0 or 1) (this is called the basis or base case)
• It is true for arbitrary natural number n and n + 1 (this is called the inductive step)

By the same token, a recursive function has:

• A base case. This is a defined solution that will not call the function again. (This is where the function stops.)
• A reduction step. This relates the problem to a smaller subproblem of the same function. (Converges to the base case enventually)

###Fun with recursion

Let's think about writing a recursive program that performs a simple countdown.

What is the base case? What is the reduction step?

###Method signature:

``````def countdown(n):
# method body goes here
``````

10 minutes for working. Want to use Python? Try http://www.skulpt.org/

###Desired output

``````>>> countdown(10)
10
9
8
7
6
5
4
3
2
1
BLASTOFF!
``````

Go over the solutions together.

##Pitfalls

• Make sure that you have a base case and that you will always hit it. Otherwise the program will loop infinitely.
• What's wrong here?
``````  def countdown(n):
if n == 0:
print "BLASTOFF!"
else:
print n
countdown(n-1)
``````
• Make sure that your problem is actually getting smaller each time.

##Next problem: Factorial Remember these? https://en.wikipedia.org/wiki/Factorial

3! = 3 * 2 * 1

5! = 5 * 4 * 3 * 2 * 1

And so on...

Let's write it. What is the base case? What is the reduction step?

###Method signature:

``````def factorial(n):
# method body goes here
``````

Let's spend 10 minutes on this. Let's not worry about negative numbers for now. Need that site again? It's http://www.skulpt.org/

###Desired output

``````>>> factorial(5)
120
``````

##Next up: Fibonacci Sequence

Write a function that returns the nth Fibonacci number. Base case? Reduction step?

###Method signature:

``````def fibonacci(n):
# method body goes here
``````

Remember: `fibonacci(0)` is 0 and `fibonacci(1)` is 1

Let's spend 10 minutes on this.

###Desired output

``````>>> fibonacci(6)
8
``````

Other pitfalls

• Redundant calculations
• Stack overflows

##Binary search Given a sorted array and a number, write a recursive function that returns true if the number is in the array and false if not.

Base case? Reduction step?

###Method signature:

``````def search(arr, n):
# method body goes here
``````

15 minutes to work.

###Desired output

``````>>> search([1, 2, 3], 3)
True
>>> search([1, 2, 3], 5)
False
``````

Other things to know:

• Iterative approaches
• Memoization/dynamic programming

Iteration in mathematics may refer to the process of iterating a function i.e. applying a function repeatedly, using the output from one iteration as the input to the next.

Recursive functions are often easier to write with iteration. Simply put, an iteration is a for-loop.

###Countdown program in iterative form

``````def countdown(n):
for i in range(n, 0, -1):
print i
print 'BLASTOFF!'
``````

Exercise if we have time: rewrite previous functions with iteration.

Resources:

http://introcs.cs.princeton.edu/java/23recursion/

https://en.wikipedia.org/wiki/Recursion_(computer_science)