Recursion: Making Big Problems Smaller

Recursion is a key concept in programming, and can be used to simplify code and create elegant solutions. It's also has a reputation of being a little hard to learn. I will show you that it is not as difficult as you think, and that you can take a formulaic approach to writing recursive functions. Doing so will allow you to solve big problems, by dividing them up into smaller, easier ones.

Transcript

1. Recursion
   Making Big Problems Smaller
   By Jeremy Lindblom
   @jeremeamia
   

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2. – some sarcastic jerkface
   “
   “
   To understand recursion,
   you must understand recursion.
   

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3. Why Should You Care?
   1.  You’re Here! – You’re already here, so
   I’m guessing you are interested.
   2.  Academics – Recursion is a key
   concept in computer science and
   mathematics.
   3.  Career – Technical interviews often
   contain questions where recursive
   solutions are a good answer.
   

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4. Why Should You Care?
   4.  Open Source – A survey of 14 major
   PHP projects yielded more than 300
   examples of recursive functions.
   5.  Other Languages – Some languages in
   the functional programming paradigm
   rely solely on recursion for loops.
   6.  Parallelization – Recursive functions
   are stateless and can be parallelized
   easier.
   

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5. Takeaways
   ① Using recursion (when appropriate)
   can result in shorter, simpler code.
   ② Recursion allows you to solve the
   whole problem, by only solving part of
   the problem.
   Recursion: Making Big Problems Smaller
   

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6. Hello! I'm @jeremeamia
   PHP Software Engineer at
   Co-author of the AWS SDK for PHP
   Co-organizer of the Seattle PHP User Group
   Zend Education Advisory Board for 5.5 exam
   

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7. What exactly is recursion?
   

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9. O RLY? K, THX!
   

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10. O RLY? K, THX!
    And yes, I do see what you did there.
    

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11. Recursion is easier
    to visualize, IMO.
    

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16. Fractals
    Images
    created with
    math and
    recursion
    Mandelbrot
    

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17. Sierpinski’s Triangle
    

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18. Sierpinski’s Triangle
    

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22. “I eat recursion for breakfast!”
    

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23. PHP Hypertext Preprocessor
    

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24. PHP Hypertext Preprocessor
    PHP Hypertext Preprocessor Hypertext Preprocessor
    

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25. PHP Hypertext Preprocessor
    PHP Hypertext Preprocessor Hypertext Preprocessor
    PHP Hypertext Preprocessor Hypertext Preprocessor Hypertext Preprocessor
    

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26. So… how about some code!
    (well, a little math first, actually)
    

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27. Factorial — n!  
    20!  =  20  ×  19  ×  18  …  ×  2  ×  1  
    6!  =  720  
    5!  =  120  
    4!  =    24  
    3!  =      6  
    

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28. Factorial — n!  
    20!  =  20  ×  19  ×  18  …  ×  2  ×  1  
    

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29. Factorial — n!  
    20!  =  20  ×  19!  
    

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30. Factorial — n!  
    20!  =  20  ×  19!  
    Hey look! Recursion!
    

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31. Factorial — n!  
    n!  =  n  ×  (n-­‐1)!  
    

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32. Factorial — n!
    n  ×      (n-­‐1)!  
    

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35. Recursive Function Anatomy
    •  Base Case(s)
    •  Recursive Call(s)
    •  Problem Size
    Reduction
    

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36. Anatomy: Base Case
    

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37. Anatomy: Recursive Call
    

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38. Anatomy: Reduce Problem Size
    

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39. OK, but can’t you do that
    without recursion?
    

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40. Anything you can do with
    recursion, you can also do
    without recursion.
    FYI
    

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41. Iterative Factorial
    

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42. Iterative solutions typically
    are faster and require
    less memory than recursive
    solutions.
    FYI
    

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43. Iteration vs. Recursion
    Iterative Factorial
    Benchmark:
    ~4.25  µs  
    Result w/ large input:
    INF  
    

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44. Iteration vs. Recursion
    Iterative Factorial
    Benchmark:
    ~4.25  µs  
    Result w/ large input:
    INF  
    Recursive Factorial
    Benchmark:
    ~10.50  µs  
    Result w/ large input:
    Seg  fault:  11  
    

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45. Iteration vs. Recursion
    Iterative Factorial
    Benchmark:
    ~4.25  µs  
    Result w/ large input:
    INF  
    Recursive Factorial
    Benchmark:
    ~10.50  µs  
    Result w/ large input:
    Seg  fault:  11  
    Yep, that's a stack overflow
    

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46. Not Impressed with Recursion?
    

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47. How about another
    example?
    

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48. Tree Traversal
    ABCDEFGH
    

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49. Tree Traversal
    

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50. Traversal: Base Case
    

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51. Traversal: Recursive Call
    

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52. Traversal: Reduce Size
    

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53. OK, but can’t you do that
    without recursion?
    

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54. Iterative Tree Traversal
    

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55. Iteration vs. Recursion
    Iterative Traversal
    Benchmark:
    ~54  µs  
    Recursive Traversal
    Benchmark:
    ~39  µs  
    w00t!  FTW!  
    

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56. Making Big Problems Smaller
    ① Using recursion (when appropriate)
    can result in shorter, simpler code.
    (that is sometimes faster, too)
    vs.
    Iterative (20 LOC) Recursive (9 LOC)
    

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57. Making Big Problems Smaller
    ② Recursion allows you to solve the
    whole problem, by only solving part of
    the problem.
    This logic only prints 1 node!
    

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58. Making Big Problems Smaller
    ② Recursion allows you to solve the
    whole problem, by only solving part of
    the problem.
    =
    

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59. Recursion is…
    The Adjustable
    Crescent Wrench.
    No matter what the
    problem (nut/bolt)
    size is, you perform
    the same action.
    

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60. Alright, I'm impressed now.
    Recursion is pretty cool,
    but…
    

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61. Alright, I'm impressed now.
    Recursion is pretty cool,
    but…
    Do you have any
    practical examples?
    

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62. General Examples
    •  Mathematical and geometric Series
    •  Tree/graph traversal
    – DOM/XML/array traversing/building
    – Directory structure traversing (-r)
    – Parsing computer languages
    – Resolving dependency graphs (DIC)
    •  “Divide-and-conquer” algorithms
    

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63. Let's Use "Recursed"
    

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64. Recursive Methods in Your
    Phavorite Projects
    •  ZF2: 50+
    •  Symfony: 75+
    •  Laravel 4: 8+
    •  Guzzle 3: 8+
    •  Wordpress: 100+
    •  Drupal 8: 25+
    •  Joomla: 50+
    •  Monolog: 2
    •  Twig: 10+
    •  SwiftMailer: 7+
    •  PHPParser: 10+
    •  AWS PHP SDK: 1+
    •  Doctrine: 7+
    •  CodeIgniter: 35+
    

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65. Example 1 – WordPress
    

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66. Example 2 – ZF2 Mail
    

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67. Example 3 – Laravel Container
    

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68. Takeaways
    ① Using recursion (when appropriate)
    can result in shorter, simpler code.
    ② Recursion allows you to solve the
    whole problem, by only solving part of
    the problem.
    Recursion: Making Big Problems Smaller
    

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69. Recursion
    Making Big Problems Smaller
    By Jeremy Lindblom
    @jeremeamia
    https://joind.in/10803
    

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